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{"segments": [{"id": 1, "seek": 2794, "start": 15.58, "end": 27.94, "text": " In general, the regression equation is given by this equation. Y represents the dependent variable for each observation I.", "tokens": [682, 2674, 11, 264, 24590, 5367, 307, 2212, 538, 341, 5367, 13, 398, 8855, 264, 12334, 7006, 337, 1184, 14816, 286, 13], "avg_logprob": -0.20312499870424686, "compression_ratio": 1.2424242424242424, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 15.579999999999998, "end": 16.54, "word": " In", "probability": 0.466064453125}, {"start": 16.54, "end": 17.5, "word": " general,", "probability": 0.904296875}, {"start": 17.66, "end": 17.82, "word": " the", "probability": 0.87109375}, {"start": 17.82, "end": 18.18, "word": " regression", "probability": 0.97998046875}, {"start": 18.18, "end": 18.7, "word": " equation", "probability": 0.958984375}, {"start": 18.7, "end": 18.96, "word": " is", "probability": 0.94775390625}, {"start": 18.96, "end": 19.22, "word": " given", "probability": 0.9033203125}, {"start": 19.22, "end": 19.7, "word": " by", "probability": 0.97119140625}, {"start": 19.7, "end": 21.16, "word": " this", "probability": 0.935546875}, {"start": 21.16, "end": 21.72, "word": " equation.", "probability": 0.978515625}, {"start": 23.06, "end": 23.56, "word": " Y", "probability": 0.681640625}, {"start": 23.56, "end": 25.06, "word": " represents", "probability": 0.8408203125}, {"start": 25.06, "end": 25.58, "word": " the", "probability": 0.9169921875}, {"start": 25.58, "end": 25.96, "word": " dependent", "probability": 0.85009765625}, {"start": 25.96, "end": 26.46, "word": " variable", "probability": 0.92138671875}, {"start": 26.46, "end": 26.88, "word": " for", "probability": 0.92724609375}, {"start": 26.88, "end": 27.1, "word": " each", "probability": 0.95068359375}, {"start": 27.1, "end": 27.56, "word": " observation", "probability": 0.91162109375}, {"start": 27.56, "end": 27.94, "word": " I.", "probability": 0.445068359375}], "temperature": 1.0}, {"id": 2, "seek": 4976, "start": 29.24, "end": 49.76, "text": " Beta 0 is called population Y intercept. Beta 1 is the population stop coefficient. Xi is the independent variable for each observation, I. Epsilon I is the random error theorem. 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So, in order to determine the values of B0 and B1, we have to know first the value of R, the correlation coefficient.", "tokens": [823, 11, 264, 4190, 337, 363, 15, 293, 363, 16, 366, 2212, 538, 613, 11787, 11, 363, 16, 6915, 25855, 56, 6666, 538, 318, 55, 13, 407, 11, 294, 1668, 281, 6997, 264, 4190, 295, 363, 15, 293, 363, 16, 11, 321, 362, 281, 458, 700, 264, 2158, 295, 497, 11, 264, 20009, 17619, 13], "avg_logprob": -0.1637834869325161, "compression_ratio": 1.4475524475524475, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 227.94, "end": 228.56, "word": " Now,", "probability": 0.85986328125}, {"start": 228.64, "end": 228.76, "word": " the", "probability": 0.91943359375}, {"start": 228.76, "end": 229.1, "word": " values", "probability": 0.95361328125}, {"start": 229.1, "end": 229.42, "word": " for", "probability": 0.8984375}, {"start": 229.42, "end": 229.84, "word": " B0", "probability": 0.580078125}, {"start": 229.84, "end": 230.1, "word": " and", "probability": 0.9482421875}, {"start": 230.1, "end": 230.42, "word": " B1", "probability": 0.99609375}, {"start": 230.42, "end": 230.62, "word": " are", "probability": 0.93310546875}, {"start": 230.62, "end": 230.84, "word": " given", "probability": 0.900390625}, {"start": 230.84, "end": 231.12, "word": " by", "probability": 0.97119140625}, {"start": 231.12, "end": 231.4, "word": " these", "probability": 0.76220703125}, {"start": 231.4, "end": 232.0, "word": " equations,", "probability": 0.92578125}, {"start": 232.92, "end": 233.26, "word": " B1", "probability": 0.982666015625}, {"start": 233.26, "end": 233.74, "word": " equals", "probability": 0.85986328125}, {"start": 233.74, "end": 234.6, "word": " RSY", "probability": 0.56597900390625}, {"start": 234.6, "end": 234.8, "word": " divided", "probability": 0.75341796875}, {"start": 234.8, "end": 235.04, "word": " by", "probability": 0.97216796875}, {"start": 235.04, "end": 235.52, "word": " SX.", "probability": 0.851806640625}, {"start": 235.66, "end": 235.84, "word": " So,", "probability": 0.90771484375}, {"start": 235.92, "end": 236.02, "word": " in", "probability": 0.94580078125}, {"start": 236.02, "end": 236.26, "word": " order", "probability": 0.91943359375}, {"start": 236.26, "end": 236.48, "word": " to", "probability": 0.97021484375}, {"start": 236.48, "end": 236.96, "word": " determine", "probability": 0.91357421875}, {"start": 236.96, "end": 238.52, "word": " the", "probability": 0.91552734375}, {"start": 238.52, "end": 239.28, "word": " values", "probability": 0.9609375}, {"start": 239.28, "end": 239.42, "word": " of", "probability": 0.92529296875}, {"start": 239.42, "end": 239.78, "word": " B0", "probability": 0.984130859375}, {"start": 239.78, "end": 239.94, "word": " and", "probability": 0.9482421875}, {"start": 239.94, "end": 240.26, "word": " B1,", "probability": 0.998779296875}, {"start": 240.36, "end": 240.5, "word": " we", "probability": 0.91015625}, {"start": 240.5, "end": 240.7, "word": " have", "probability": 0.94482421875}, {"start": 240.7, "end": 240.88, "word": " to", "probability": 0.96923828125}, {"start": 240.88, "end": 241.04, "word": " know", "probability": 0.87109375}, {"start": 241.04, "end": 241.52, "word": " first", "probability": 0.83740234375}, {"start": 241.52, "end": 242.62, "word": " the", "probability": 0.78564453125}, {"start": 242.62, "end": 242.94, "word": " value", "probability": 0.97314453125}, {"start": 242.94, "end": 243.42, "word": " of", "probability": 0.96923828125}, {"start": 243.42, "end": 244.54, "word": " R,", "probability": 0.9794921875}, {"start": 246.3, "end": 246.76, "word": " the", "probability": 0.8671875}, {"start": 246.76, "end": 247.2, "word": " correlation", "probability": 0.95458984375}, {"start": 247.2, "end": 247.76, "word": " coefficient.", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 12, "seek": 28539, "start": 256.64, "end": 285.4, "text": " Sx and Sy, standard deviations of x and y, as well as the means of x and y. B1 equals R times Sy divided by Sx. B0 is just y bar minus b1 x bar, where Sx and Sy are the standard deviations of x and y.", "tokens": [318, 87, 293, 3902, 11, 3832, 31219, 763, 295, 2031, 293, 288, 11, 382, 731, 382, 264, 1355, 295, 2031, 293, 288, 13, 363, 16, 6915, 497, 1413, 3902, 6666, 538, 318, 87, 13, 363, 15, 307, 445, 288, 2159, 3175, 272, 16, 2031, 2159, 11, 689, 318, 87, 293, 3902, 366, 264, 3832, 31219, 763, 295, 2031, 293, 288, 13], "avg_logprob": -0.16355846702091156, "compression_ratio": 1.558139534883721, "no_speech_prob": 0.0, "words": [{"start": 256.64, "end": 257.36, "word": " Sx", "probability": 0.6368408203125}, {"start": 257.36, "end": 257.88, "word": " and", "probability": 0.9326171875}, {"start": 257.88, "end": 258.4, "word": " Sy,", "probability": 0.92626953125}, {"start": 258.72, "end": 259.16, "word": " standard", "probability": 0.8583984375}, {"start": 259.16, "end": 259.82, "word": " deviations", "probability": 0.931640625}, {"start": 259.82, "end": 261.58, "word": " of", "probability": 0.93310546875}, {"start": 261.58, "end": 262.1, "word": " x", "probability": 0.7919921875}, {"start": 262.1, "end": 262.78, "word": " and", "probability": 0.9482421875}, {"start": 262.78, "end": 263.14, "word": " y,", "probability": 0.99755859375}, {"start": 263.88, "end": 264.78, "word": " as", "probability": 0.947265625}, {"start": 264.78, "end": 264.98, "word": " well", "probability": 0.9296875}, {"start": 264.98, "end": 265.44, "word": " as", "probability": 0.966796875}, {"start": 265.44, "end": 266.54, "word": " the", "probability": 0.88916015625}, {"start": 266.54, "end": 266.9, "word": " means", "probability": 0.810546875}, {"start": 266.9, "end": 269.18, "word": " of", "probability": 0.935546875}, {"start": 269.18, "end": 269.42, "word": " x", "probability": 0.9873046875}, {"start": 269.42, "end": 269.58, "word": " and", "probability": 0.94677734375}, {"start": 269.58, "end": 269.88, "word": " y.", "probability": 0.99853515625}, {"start": 272.92, "end": 273.64, "word": " B1", "probability": 0.813232421875}, {"start": 273.64, "end": 274.08, "word": " equals", "probability": 0.796875}, {"start": 274.08, "end": 274.56, "word": " R", "probability": 0.67919921875}, {"start": 274.56, "end": 275.14, "word": " times", "probability": 0.9052734375}, {"start": 275.14, "end": 275.54, "word": " Sy", "probability": 0.85302734375}, {"start": 275.54, "end": 275.8, "word": " divided", "probability": 0.80908203125}, {"start": 275.8, "end": 276.0, "word": " by", "probability": 0.97216796875}, {"start": 276.0, "end": 276.5, "word": " Sx.", "probability": 0.9892578125}, {"start": 278.14, "end": 278.86, "word": " B0", "probability": 0.90869140625}, {"start": 278.86, "end": 279.06, "word": " is", "probability": 0.6806640625}, {"start": 279.06, "end": 279.26, "word": " just", "probability": 0.90625}, {"start": 279.26, "end": 279.5, "word": " y", "probability": 0.7138671875}, {"start": 279.5, "end": 279.7, "word": " bar", "probability": 0.732421875}, {"start": 279.7, "end": 280.0, "word": " minus", "probability": 0.98046875}, {"start": 280.0, "end": 280.32, "word": " b1", "probability": 0.791259765625}, {"start": 280.32, "end": 280.5, "word": " x", "probability": 0.79736328125}, {"start": 280.5, "end": 280.82, "word": " bar,", "probability": 0.9306640625}, {"start": 280.94, "end": 281.24, "word": " where", "probability": 0.93017578125}, {"start": 281.24, "end": 281.96, "word": " Sx", "probability": 0.9873046875}, {"start": 281.96, "end": 282.2, "word": " and", "probability": 0.9306640625}, {"start": 282.2, "end": 282.6, "word": " Sy", "probability": 0.9267578125}, {"start": 282.6, "end": 283.38, "word": " are", "probability": 0.9384765625}, {"start": 283.38, "end": 283.6, "word": " the", "probability": 0.87841796875}, {"start": 283.6, "end": 283.84, "word": " standard", "probability": 0.9482421875}, {"start": 283.84, "end": 284.32, "word": " deviations", "probability": 0.94091796875}, {"start": 284.32, "end": 284.5, "word": " of", "probability": 0.96240234375}, {"start": 284.5, "end": 284.72, "word": " x", "probability": 0.9697265625}, {"start": 284.72, "end": 285.08, "word": " and", "probability": 0.94384765625}, {"start": 285.08, "end": 285.4, "word": " y.", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 13, "seek": 31091, "start": 286.73, "end": 310.91, "text": " So this, how can we compute the values of B0 and B1? Now the question is, what's our interpretation about B0 and B1? And B0, as we mentioned before, is the Y or the estimated mean value of Y when the value X is 0.", "tokens": [407, 341, 11, 577, 393, 321, 14722, 264, 4190, 295, 363, 15, 293, 363, 16, 30, 823, 264, 1168, 307, 11, 437, 311, 527, 14174, 466, 363, 15, 293, 363, 16, 30, 400, 363, 15, 11, 382, 321, 2835, 949, 11, 307, 264, 398, 420, 264, 14109, 914, 2158, 295, 398, 562, 264, 2158, 1783, 307, 1958, 13], "avg_logprob": -0.21477754085750903, "compression_ratio": 1.445945945945946, "no_speech_prob": 0.0, "words": [{"start": 286.73, "end": 287.41, "word": " So", "probability": 0.54833984375}, {"start": 287.41, "end": 287.79, "word": " this,", "probability": 0.5185546875}, {"start": 287.97, "end": 288.09, "word": " how", "probability": 0.93701171875}, {"start": 288.09, "end": 288.35, "word": " can", "probability": 0.93994140625}, {"start": 288.35, "end": 288.75, "word": " we", "probability": 0.95068359375}, {"start": 288.75, "end": 289.83, "word": " compute", "probability": 0.90869140625}, {"start": 289.83, "end": 290.83, "word": " the", "probability": 0.86279296875}, {"start": 290.83, "end": 291.17, "word": " values", "probability": 0.95458984375}, {"start": 291.17, "end": 291.33, "word": " of", "probability": 0.955078125}, {"start": 291.33, "end": 291.67, "word": " B0", "probability": 0.688232421875}, {"start": 291.67, "end": 291.79, "word": " and", "probability": 0.9453125}, {"start": 291.79, "end": 292.11, "word": " B1?", "probability": 0.9951171875}, {"start": 292.71, "end": 292.99, "word": " Now", "probability": 0.93994140625}, {"start": 292.99, "end": 293.19, "word": " the", "probability": 0.56884765625}, {"start": 293.19, "end": 293.85, "word": " question", "probability": 0.83447265625}, {"start": 293.85, "end": 294.21, "word": " is,", "probability": 0.94775390625}, {"start": 295.15, "end": 295.49, "word": " what's", "probability": 0.950927734375}, {"start": 295.49, "end": 295.73, "word": " our", "probability": 0.89697265625}, {"start": 295.73, "end": 296.41, "word": " interpretation", "probability": 0.8447265625}, {"start": 296.41, "end": 297.37, "word": " about", "probability": 0.86376953125}, {"start": 297.37, "end": 299.35, "word": " B0", "probability": 0.94873046875}, {"start": 299.35, "end": 299.87, "word": " and", "probability": 0.94091796875}, {"start": 299.87, "end": 300.27, "word": " B1?", "probability": 0.99658203125}, {"start": 301.89, "end": 302.13, "word": " And", "probability": 0.83984375}, {"start": 302.13, "end": 302.53, "word": " B0,", "probability": 0.94482421875}, {"start": 302.63, "end": 302.71, "word": " as", "probability": 0.96240234375}, {"start": 302.71, "end": 302.85, "word": " we", "probability": 0.83251953125}, {"start": 302.85, "end": 303.11, "word": " mentioned", "probability": 0.84423828125}, {"start": 303.11, "end": 303.63, "word": " before,", "probability": 0.85546875}, {"start": 303.85, "end": 304.19, "word": " is", "probability": 0.9189453125}, {"start": 304.19, "end": 304.55, "word": " the", "probability": 0.8857421875}, {"start": 304.55, "end": 305.03, "word": " Y", "probability": 0.63037109375}, {"start": 305.03, "end": 305.79, "word": " or", "probability": 0.230224609375}, {"start": 305.79, "end": 306.09, "word": " the", "probability": 0.77734375}, {"start": 306.09, "end": 306.69, "word": " estimated", "probability": 0.477294921875}, {"start": 306.69, "end": 308.89, "word": " mean", "probability": 0.7734375}, {"start": 308.89, "end": 309.29, "word": " value", "probability": 0.96533203125}, {"start": 309.29, "end": 309.49, "word": " of", "probability": 0.95458984375}, {"start": 309.49, "end": 309.77, "word": " Y", "probability": 0.9833984375}, {"start": 309.77, "end": 310.03, "word": " when", "probability": 0.734375}, {"start": 310.03, "end": 310.13, "word": " the", "probability": 0.8994140625}, {"start": 310.13, "end": 310.33, "word": " value", "probability": 0.91552734375}, {"start": 310.33, "end": 310.51, "word": " X", "probability": 0.4345703125}, {"start": 310.51, "end": 310.63, "word": " is", "probability": 0.93359375}, {"start": 310.63, "end": 310.91, "word": " 0.", "probability": 0.5029296875}], "temperature": 1.0}, {"id": 14, "seek": 34236, "start": 317.42, "end": 342.36, "text": " So if X is 0, then Y hat equals B0. That means B0 is the estimated mean value of Y when the value of X equals 0. B1, which is called the estimated change in the mean value of Y as a result of one unit change in X. That means the sign of B1,", "tokens": [407, 498, 1783, 307, 1958, 11, 550, 398, 2385, 6915, 363, 15, 13, 663, 1355, 363, 15, 307, 264, 14109, 914, 2158, 295, 398, 562, 264, 2158, 295, 1783, 6915, 1958, 13, 363, 16, 11, 597, 307, 1219, 264, 14109, 1319, 294, 264, 914, 2158, 295, 398, 382, 257, 1874, 295, 472, 4985, 1319, 294, 1783, 13, 663, 1355, 264, 1465, 295, 363, 16, 11], "avg_logprob": -0.2201704579320821, "compression_ratio": 1.7214285714285715, "no_speech_prob": 0.0, "words": [{"start": 317.42, "end": 317.6, "word": " So", "probability": 0.87255859375}, {"start": 317.6, "end": 317.86, "word": " if", "probability": 0.7744140625}, {"start": 317.86, "end": 318.08, "word": " X", "probability": 0.339599609375}, {"start": 318.08, "end": 318.24, "word": " is", "probability": 0.8427734375}, {"start": 318.24, "end": 318.54, "word": " 0,", "probability": 0.62646484375}, {"start": 318.72, "end": 318.96, "word": " then", "probability": 0.85498046875}, {"start": 318.96, "end": 319.32, 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So the sine of B1 tells us the exact direction. 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So that's the meaning of B0 and B1. Now first thing we have to do in order to determine if there exists linear relationship between X and Y, we have to draw scatter plot, Y versus X. 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So house price versus size of the house. Now by looking carefully at this scatter plot, even if it's a small sample size, but you can see that there exists positive relationship between house price and size of the house. 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But you can tell the exact strength of the relationship by using the value of R. But here we can tell that there exists positive relationship and that relation could be strong. 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R, if you remember last time, R was 0.762. It's moderate relationship between X and Y. Sy and Sx, 60 divided by 4 is 117. That will give 0.109. 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B1 is computed in the previous step, so plug that value here. In addition, we know the values of X bar and Y bar. Simple calculation will give the value of B0, which is about 98.25. 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Hat in this equation means the estimated or the predicted value of the house price. Equals b0 which is 98 plus b1 which is 0.10977 times square feet. 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Since the sign is positive, it means there exists positive associations or relationship between these two variables, number one. Number two, we can interpret carefully the meaning of the intercept. 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So that means extra one square feet for the size of the house, it cost you around $100 or $110.", "tokens": [1848, 3279, 24, 13, 17512, 13, 407, 300, 1355, 2857, 472, 3732, 3521, 337, 264, 2744, 295, 264, 1782, 11, 309, 2063, 291, 926, 1848, 6879, 420, 1848, 43435, 13], "avg_logprob": -0.2696572676781685, "compression_ratio": 1.09375, "no_speech_prob": 0.0, "words": [{"start": 611.04, "end": 612.6, "word": " $109", "probability": 0.6735432942708334}, {"start": 612.6, "end": 613.34, "word": ".77.", "probability": 0.96337890625}, {"start": 613.92, "end": 614.42, "word": " So", "probability": 0.87060546875}, {"start": 614.42, "end": 614.66, "word": " that", "probability": 0.8564453125}, {"start": 614.66, "end": 615.04, "word": " means", "probability": 0.9375}, {"start": 615.04, "end": 616.74, "word": " extra", "probability": 0.73388671875}, {"start": 616.74, "end": 617.94, "word": " one", "probability": 0.74072265625}, {"start": 617.94, "end": 618.56, "word": " square", "probability": 0.91845703125}, {"start": 618.56, "end": 619.02, "word": " feet", "probability": 0.90234375}, {"start": 619.02, "end": 620.3, "word": " for", "probability": 0.72509765625}, {"start": 620.3, "end": 620.52, "word": " the", "probability": 0.91796875}, {"start": 620.52, "end": 620.76, "word": " size", "probability": 0.85595703125}, {"start": 620.76, "end": 620.88, "word": " of", "probability": 0.96728515625}, {"start": 620.88, "end": 621.0, "word": " the", "probability": 0.916015625}, {"start": 621.0, "end": 621.4, "word": " house,", "probability": 0.8701171875}, {"start": 621.76, "end": 622.66, "word": " it", "probability": 0.9169921875}, {"start": 622.66, "end": 623.06, "word": " cost", "probability": 0.454833984375}, {"start": 623.06, "end": 623.42, "word": " you", "probability": 0.9599609375}, {"start": 623.42, "end": 624.04, "word": " around", "probability": 0.9228515625}, {"start": 624.04, "end": 625.14, "word": " $100", "probability": 0.794921875}, {"start": 625.14, "end": 626.02, "word": " or", "probability": 0.869140625}, {"start": 626.02, "end": 626.62, "word": " $110.", "probability": 0.79345703125}], "temperature": 1.0}, {"id": 26, "seek": 65696, "start": 628.54, "end": 656.96, "text": " So that's the meaning of B1 and the sign actually of the slope. In addition to that, we can make some predictions about house price for any given value of the size of the house. That means if you know that the house size equals 2,000 square feet. So just plug this value here and simple calculation will give the predicted value of the ceiling price of a house.", "tokens": [407, 300, 311, 264, 3620, 295, 363, 16, 293, 264, 1465, 767, 295, 264, 13525, 13, 682, 4500, 281, 300, 11, 321, 393, 652, 512, 21264, 466, 1782, 3218, 337, 604, 2212, 2158, 295, 264, 2744, 295, 264, 1782, 13, 663, 1355, 498, 291, 458, 300, 264, 1782, 2744, 6915, 568, 11, 1360, 3732, 3521, 13, 407, 445, 5452, 341, 2158, 510, 293, 2199, 17108, 486, 976, 264, 19147, 2158, 295, 264, 13655, 3218, 295, 257, 1782, 13], "avg_logprob": -0.16307357519487792, "compression_ratio": 1.6682027649769586, "no_speech_prob": 0.0, "words": [{"start": 628.54, "end": 628.8, "word": " So", "probability": 0.8994140625}, {"start": 628.8, "end": 629.04, "word": " that's", "probability": 0.8740234375}, {"start": 629.04, "end": 629.16, "word": " the", "probability": 0.919921875}, {"start": 629.16, "end": 629.42, "word": " meaning", "probability": 0.86474609375}, {"start": 629.42, "end": 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In other words, we have this equation, so the interpretation of B0 again. B0 is the estimated mean value of Y when the value of X is 0. 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That's the meaning of the B0. But again, because a house cannot have a square footage of zero, so B0 has no practical application.", "tokens": [294, 341, 3613, 295, 264, 13095, 1783, 12, 46033, 13, 663, 311, 264, 3620, 295, 264, 363, 15, 13, 583, 797, 11, 570, 257, 1782, 2644, 362, 257, 3732, 9556, 295, 4018, 11, 370, 363, 15, 575, 572, 8496, 3861, 13], "avg_logprob": -0.20535713611614137, "compression_ratio": 1.3255813953488371, "no_speech_prob": 0.0, "words": [{"start": 678.12, "end": 678.38, "word": " in", "probability": 0.2685546875}, {"start": 678.38, "end": 678.62, "word": " this", "probability": 0.92822265625}, {"start": 678.62, "end": 679.08, "word": " range", "probability": 0.8759765625}, {"start": 679.08, "end": 679.94, "word": " of", "probability": 0.87744140625}, {"start": 679.94, "end": 680.06, "word": " the", "probability": 0.71435546875}, {"start": 680.06, "end": 680.46, "word": " observed", "probability": 0.87646484375}, {"start": 680.46, "end": 680.7, "word": " X", "probability": 0.53955078125}, {"start": 680.7, "end": 681.14, "word": "-values.", "probability": 0.6773681640625}, {"start": 681.96, "end": 682.34, "word": " That's", "probability": 0.9033203125}, {"start": 682.34, "end": 682.5, "word": " the", "probability": 0.9248046875}, {"start": 682.5, "end": 682.68, "word": " meaning", "probability": 0.87841796875}, {"start": 682.68, "end": 682.9, "word": " of", "probability": 0.96728515625}, {"start": 682.9, "end": 683.1, "word": " the", "probability": 0.66357421875}, {"start": 683.1, "end": 683.78, "word": " B0.", "probability": 0.834716796875}, {"start": 683.96, "end": 684.18, "word": " But", "probability": 0.92724609375}, {"start": 684.18, "end": 684.54, "word": " again,", "probability": 0.87255859375}, {"start": 684.82, "end": 685.02, "word": " because", "probability": 0.8623046875}, {"start": 685.02, "end": 685.18, "word": " a", "probability": 0.8984375}, {"start": 685.18, "end": 685.5, "word": " house", "probability": 0.88232421875}, {"start": 685.5, "end": 685.82, "word": " cannot", "probability": 0.861328125}, {"start": 685.82, "end": 686.3, "word": " have", "probability": 0.94775390625}, {"start": 686.3, "end": 686.54, "word": " a", "probability": 0.828125}, {"start": 686.54, "end": 686.9, "word": " square", "probability": 0.955078125}, {"start": 686.9, "end": 687.44, "word": " footage", "probability": 0.9404296875}, {"start": 687.44, "end": 687.7, "word": " of", "probability": 0.9716796875}, {"start": 687.7, "end": 688.08, "word": " zero,", "probability": 0.57275390625}, {"start": 688.68, "end": 688.8, "word": " so", "probability": 0.88427734375}, {"start": 688.8, "end": 689.22, "word": " B0", "probability": 0.973876953125}, {"start": 689.22, "end": 689.54, "word": " has", "probability": 0.9462890625}, {"start": 689.54, "end": 689.78, "word": " no", "probability": 0.95263671875}, {"start": 689.78, "end": 690.32, "word": " practical", "probability": 0.93896484375}, {"start": 690.32, "end": 691.68, "word": " application.", "probability": 0.92138671875}], "temperature": 1.0}, {"id": 29, "seek": 71666, "start": 694.74, "end": 716.66, "text": " On the other hand, the interpretation for B1, B1 equals 0.10977, that means B1 again estimates the change in the mean value of Y as a result of one unit increase in X. In other words, since B1 equals 0.10977, that tells us that the mean value of a house", "tokens": [1282, 264, 661, 1011, 11, 264, 14174, 337, 363, 16, 11, 363, 16, 6915, 1958, 13, 3279, 24, 17512, 11, 300, 1355, 363, 16, 797, 20561, 264, 1319, 294, 264, 914, 2158, 295, 398, 382, 257, 1874, 295, 472, 4985, 3488, 294, 1783, 13, 682, 661, 2283, 11, 1670, 363, 16, 6915, 1958, 13, 3279, 24, 17512, 11, 300, 5112, 505, 300, 264, 914, 2158, 295, 257, 1782], "avg_logprob": -0.1305480124293894, "compression_ratio": 1.6387096774193548, "no_speech_prob": 0.0, "words": [{"start": 694.74, "end": 694.98, "word": " On", "probability": 0.81103515625}, {"start": 694.98, "end": 695.14, "word": " the", "probability": 0.92529296875}, {"start": 695.14, "end": 695.34, "word": " other", "probability": 0.8896484375}, {"start": 695.34, "end": 695.7, "word": " hand,", "probability": 0.91162109375}, {"start": 695.9, "end": 695.92, "word": " the", "probability": 0.7626953125}, {"start": 695.92, "end": 696.34, "word": " interpretation", "probability": 0.90576171875}, {"start": 696.34, "end": 697.08, "word": " for", "probability": 0.931640625}, {"start": 697.08, "end": 697.76, "word": " B1,", "probability": 0.799560546875}, {"start": 698.3, "end": 698.76, "word": " B1", "probability": 0.96337890625}, {"start": 698.76, "end": 698.96, "word": " equals", "probability": 0.252197265625}, {"start": 698.96, "end": 699.22, "word": " 0", "probability": 0.61376953125}, {"start": 699.22, "end": 700.44, "word": ".10977,", "probability": 0.96337890625}, {"start": 700.78, "end": 700.96, "word": " that", "probability": 0.9072265625}, {"start": 700.96, "end": 701.38, "word": " means", "probability": 0.91552734375}, {"start": 701.38, "end": 702.54, "word": " B1", "probability": 0.8828125}, {"start": 702.54, "end": 702.84, "word": " again", "probability": 0.89697265625}, {"start": 702.84, "end": 703.58, "word": " estimates", "probability": 0.87353515625}, {"start": 703.58, "end": 703.92, "word": " the", "probability": 0.86767578125}, {"start": 703.92, "end": 704.34, "word": " change", "probability": 0.896484375}, {"start": 704.34, "end": 704.56, "word": " in", "probability": 0.94384765625}, {"start": 704.56, "end": 704.7, "word": " the", "probability": 0.92041015625}, {"start": 704.7, "end": 704.88, "word": " mean", "probability": 0.96484375}, {"start": 704.88, "end": 705.18, "word": " value", "probability": 0.9736328125}, {"start": 705.18, "end": 705.42, "word": " of", "probability": 0.9599609375}, {"start": 705.42, "end": 705.7, "word": " Y", "probability": 0.82080078125}, {"start": 705.7, "end": 706.02, "word": " as", "probability": 0.93017578125}, {"start": 706.02, "end": 706.16, "word": " a", "probability": 0.98046875}, {"start": 706.16, "end": 706.44, "word": " result", "probability": 0.94677734375}, {"start": 706.44, "end": 706.7, "word": " of", "probability": 0.966796875}, {"start": 706.7, "end": 706.88, "word": " one", "probability": 0.8193359375}, {"start": 706.88, "end": 707.16, "word": " unit", "probability": 0.908203125}, {"start": 707.16, "end": 707.46, "word": " increase", "probability": 0.79638671875}, {"start": 707.46, "end": 707.68, "word": " in", "probability": 0.9326171875}, {"start": 707.68, "end": 707.94, "word": " X.", "probability": 0.9453125}, {"start": 709.2, "end": 709.46, "word": " In", "probability": 0.955078125}, {"start": 709.46, "end": 709.72, "word": " other", "probability": 0.89599609375}, {"start": 709.72, "end": 710.16, "word": " words,", "probability": 0.86328125}, {"start": 710.46, "end": 710.78, "word": " since", "probability": 0.88134765625}, {"start": 710.78, "end": 711.16, "word": " B1", "probability": 0.990234375}, {"start": 711.16, "end": 711.38, "word": " equals", "probability": 0.85546875}, {"start": 711.38, "end": 711.68, "word": " 0", "probability": 0.95654296875}, {"start": 711.68, "end": 712.8, "word": ".10977,", "probability": 0.965087890625}, {"start": 713.16, "end": 713.4, "word": " that", "probability": 0.93603515625}, {"start": 713.4, "end": 713.7, "word": " tells", "probability": 0.8525390625}, {"start": 713.7, "end": 714.0, "word": " us", "probability": 0.9326171875}, {"start": 714.0, "end": 714.34, "word": " that", "probability": 0.93359375}, {"start": 714.34, "end": 715.08, "word": " the", "probability": 0.8994140625}, {"start": 715.08, "end": 715.26, "word": " mean", "probability": 0.970703125}, {"start": 715.26, "end": 715.68, "word": " value", "probability": 0.97509765625}, {"start": 715.68, "end": 716.06, "word": " of", "probability": 0.96630859375}, {"start": 716.06, "end": 716.22, "word": " a", "probability": 0.97509765625}, {"start": 716.22, "end": 716.66, "word": " house", "probability": 0.8916015625}], "temperature": 1.0}, {"id": 30, "seek": 74545, "start": 718.01, "end": 745.45, "text": " Increases by this amount, multiplied by 1,000 on average for each additional one square foot of size. So that's the exact interpretation about P0 and P1. For the prediction, as I mentioned, since we have this equation, and our goal is to predict the price for a house with 2,000 square feet, just plug this value here.", "tokens": [30367, 1957, 538, 341, 2372, 11, 17207, 538, 502, 11, 1360, 322, 4274, 337, 1184, 4497, 472, 3732, 2671, 295, 2744, 13, 407, 300, 311, 264, 1900, 14174, 466, 430, 15, 293, 430, 16, 13, 1171, 264, 17630, 11, 382, 286, 2835, 11, 1670, 321, 362, 341, 5367, 11, 293, 527, 3387, 307, 281, 6069, 264, 3218, 337, 257, 1782, 365, 568, 11, 1360, 3732, 3521, 11, 445, 5452, 341, 2158, 510, 13], "avg_logprob": -0.17694256877576983, "compression_ratio": 1.519047619047619, "no_speech_prob": 0.0, "words": [{"start": 718.01, "end": 718.73, "word": " Increases", "probability": 0.630859375}, {"start": 718.73, "end": 719.13, "word": " by", "probability": 0.9658203125}, {"start": 719.13, "end": 719.47, "word": " this", "probability": 0.9443359375}, {"start": 719.47, "end": 720.07, "word": " amount,", "probability": 0.90673828125}, 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726.33, "word": " of", "probability": 0.837890625}, {"start": 726.33, "end": 726.67, "word": " size.", "probability": 0.8154296875}, {"start": 727.19, "end": 727.41, "word": " So", "probability": 0.95947265625}, {"start": 727.41, "end": 727.77, "word": " that's", "probability": 0.90380859375}, {"start": 727.77, "end": 728.05, "word": " the", "probability": 0.91796875}, {"start": 728.05, "end": 728.49, "word": " exact", "probability": 0.94140625}, {"start": 728.49, "end": 729.69, "word": " interpretation", "probability": 0.8798828125}, {"start": 729.69, "end": 730.11, "word": " about", "probability": 0.8876953125}, {"start": 730.11, "end": 730.61, "word": " P0", "probability": 0.754638671875}, {"start": 730.61, "end": 730.83, "word": " and", "probability": 0.93994140625}, {"start": 730.83, "end": 731.21, "word": " P1.", "probability": 0.972412109375}, {"start": 732.65, "end": 733.19, "word": " For", "probability": 0.96533203125}, {"start": 733.19, "end": 733.35, "word": " the", "probability": 0.91845703125}, {"start": 733.35, "end": 733.73, "word": " prediction,", "probability": 0.91455078125}, {"start": 734.33, "end": 734.49, "word": " as", "probability": 0.96435546875}, {"start": 734.49, "end": 734.63, "word": " I", "probability": 0.984375}, {"start": 734.63, "end": 735.03, "word": " mentioned,", "probability": 0.84716796875}, {"start": 735.33, "end": 735.51, "word": " since", "probability": 0.876953125}, {"start": 735.51, "end": 736.43, "word": " we", "probability": 0.90966796875}, {"start": 736.43, "end": 736.59, "word": " have", "probability": 0.947265625}, {"start": 736.59, "end": 736.83, "word": " this", "probability": 0.94970703125}, {"start": 736.83, "end": 737.33, "word": " equation,", "probability": 0.96923828125}, {"start": 737.97, "end": 738.21, "word": " and", "probability": 0.93408203125}, {"start": 738.21, "end": 738.43, "word": " our", "probability": 0.87890625}, {"start": 738.43, "end": 738.65, "word": " goal", "probability": 0.97216796875}, {"start": 738.65, "end": 738.83, "word": " is", "probability": 0.94482421875}, {"start": 738.83, "end": 738.97, "word": " to", "probability": 0.96875}, {"start": 738.97, "end": 739.37, "word": " predict", "probability": 0.9189453125}, {"start": 739.37, "end": 739.61, "word": " the", "probability": 0.91455078125}, {"start": 739.61, "end": 739.99, "word": " price", "probability": 0.94580078125}, {"start": 739.99, "end": 740.23, "word": " for", "probability": 0.81591796875}, {"start": 740.23, "end": 740.39, "word": " a", "probability": 0.9326171875}, {"start": 740.39, "end": 740.63, "word": " house", "probability": 0.88623046875}, {"start": 740.63, "end": 740.93, "word": " with", "probability": 0.8916015625}, {"start": 740.93, "end": 741.53, "word": " 2", "probability": 0.91650390625}, {"start": 741.53, "end": 742.01, "word": ",000", "probability": 0.995849609375}, {"start": 742.01, "end": 742.93, "word": " square", "probability": 0.904296875}, {"start": 742.93, "end": 743.29, "word": " feet,", "probability": 0.96630859375}, {"start": 743.85, "end": 744.11, "word": " just", "probability": 0.9169921875}, {"start": 744.11, "end": 744.41, "word": " plug", "probability": 0.48779296875}, {"start": 744.41, "end": 744.73, "word": " this", "probability": 0.94580078125}, {"start": 744.73, "end": 745.09, "word": " value", "probability": 0.9697265625}, {"start": 745.09, "end": 745.45, "word": " here.", "probability": 0.845703125}], "temperature": 1.0}, {"id": 31, "seek": 76937, "start": 746.45, "end": 769.37, "text": " Multiply this value by 0.1098, then add the result to 98.25 will give 317.85. This value should be multiplied by 1000, so the predicted price for a house with 2000 square feet is around 317,850 dollars.", "tokens": [31150, 356, 341, 2158, 538, 1958, 13, 3279, 22516, 11, 550, 909, 264, 1874, 281, 20860, 13, 6074, 486, 976, 805, 7773, 13, 19287, 13, 639, 2158, 820, 312, 17207, 538, 9714, 11, 370, 264, 19147, 3218, 337, 257, 1782, 365, 8132, 3732, 3521, 307, 926, 805, 7773, 11, 23, 2803, 3808, 13], "avg_logprob": -0.19444444002928557, "compression_ratio": 1.326797385620915, "no_speech_prob": 0.0, "words": [{"start": 746.45, "end": 747.03, "word": " Multiply", "probability": 0.6953125}, {"start": 747.03, "end": 747.25, "word": " this", "probability": 0.91162109375}, {"start": 747.25, "end": 747.47, "word": " value", "probability": 0.95166015625}, {"start": 747.47, "end": 747.69, "word": " by", "probability": 0.966796875}, {"start": 747.69, "end": 748.11, "word": " 0", "probability": 0.65234375}, {"start": 748.11, "end": 748.89, "word": ".1098,", "probability": 0.9661458333333334}, {"start": 749.53, "end": 749.99, "word": " then", "probability": 0.81591796875}, {"start": 749.99, "end": 750.53, "word": " add", "probability": 0.88916015625}, {"start": 750.53, "end": 750.77, "word": " the", "probability": 0.880859375}, {"start": 750.77, "end": 751.13, "word": " result", "probability": 0.88330078125}, {"start": 751.13, "end": 751.59, "word": " to", "probability": 0.9248046875}, {"start": 751.59, "end": 752.07, "word": " 98", "probability": 0.81591796875}, {"start": 752.07, "end": 753.09, "word": ".25", "probability": 0.984375}, {"start": 753.09, "end": 753.65, "word": " will", "probability": 0.358642578125}, {"start": 753.65, "end": 753.91, "word": " give", "probability": 0.8310546875}, {"start": 753.91, "end": 755.41, "word": " 317", "probability": 0.8095703125}, {"start": 755.41, "end": 756.03, "word": ".85.", "probability": 0.99267578125}, {"start": 756.51, "end": 757.13, "word": " This", "probability": 0.86474609375}, {"start": 757.13, "end": 757.41, "word": " value", "probability": 0.98046875}, {"start": 757.41, "end": 757.59, "word": " should", "probability": 0.9609375}, {"start": 757.59, "end": 757.75, "word": " be", "probability": 0.939453125}, {"start": 757.75, "end": 758.09, "word": " multiplied", "probability": 0.65234375}, {"start": 758.09, "end": 758.37, "word": " by", "probability": 0.9765625}, {"start": 758.37, "end": 758.79, "word": " 1000,", "probability": 0.7080078125}, {"start": 759.83, "end": 760.09, "word": " so", "probability": 0.92724609375}, {"start": 760.09, "end": 760.29, "word": " the", "probability": 0.90771484375}, {"start": 760.29, "end": 760.69, "word": " predicted", "probability": 0.84765625}, {"start": 760.69, "end": 761.19, "word": " price", "probability": 0.91748046875}, {"start": 761.19, "end": 761.43, "word": " for", "probability": 0.931640625}, {"start": 761.43, "end": 761.59, "word": " a", "probability": 0.96435546875}, {"start": 761.59, "end": 761.83, "word": " house", "probability": 0.88720703125}, {"start": 761.83, "end": 762.13, "word": " with", "probability": 0.9072265625}, {"start": 762.13, "end": 762.65, "word": " 2000", "probability": 0.841796875}, {"start": 762.65, "end": 763.09, "word": " square", "probability": 0.64599609375}, {"start": 763.09, "end": 763.51, "word": " feet", "probability": 0.95361328125}, {"start": 763.51, "end": 764.67, "word": " is", "probability": 0.91162109375}, {"start": 764.67, "end": 765.25, "word": " around", "probability": 0.9169921875}, {"start": 765.25, "end": 767.11, "word": " 317", "probability": 0.869384765625}, {"start": 767.11, "end": 769.05, "word": ",850", "probability": 0.8043619791666666}, {"start": 769.05, "end": 769.37, "word": " dollars.", "probability": 0.6689453125}], "temperature": 1.0}, {"id": 32, "seek": 79421, "start": 770.31, "end": 794.21, "text": " That's for making the prediction for selling a price. The last section in chapter 12 talks about coefficient of determination R squared. The definition for the coefficient of determination is the portion", "tokens": [663, 311, 337, 1455, 264, 17630, 337, 6511, 257, 3218, 13, 440, 1036, 3541, 294, 7187, 2272, 6686, 466, 17619, 295, 18432, 497, 8889, 13, 440, 7123, 337, 264, 17619, 295, 18432, 307, 264, 8044], "avg_logprob": -0.18901909184124735, "compression_ratio": 1.59375, "no_speech_prob": 0.0, "words": [{"start": 770.31, "end": 770.93, "word": " That's", "probability": 0.814453125}, {"start": 770.93, "end": 771.27, "word": " for", "probability": 0.91064453125}, {"start": 771.27, "end": 772.07, "word": " making", "probability": 0.5908203125}, {"start": 772.07, "end": 772.93, "word": " the", "probability": 0.65185546875}, {"start": 772.93, "end": 773.45, "word": " prediction", "probability": 0.91650390625}, {"start": 773.45, "end": 774.91, "word": " for", "probability": 0.9228515625}, {"start": 774.91, "end": 776.57, "word": " selling", "probability": 0.8173828125}, {"start": 776.57, "end": 776.73, "word": " a", "probability": 0.68310546875}, {"start": 776.73, "end": 777.03, "word": " price.", "probability": 0.88232421875}, {"start": 778.29, "end": 778.85, "word": " The", "probability": 0.888671875}, {"start": 778.85, "end": 779.23, "word": " last", "probability": 0.88671875}, {"start": 779.23, "end": 780.43, "word": " section", "probability": 0.86865234375}, {"start": 780.43, "end": 781.17, "word": " in", "probability": 0.88232421875}, {"start": 781.17, "end": 781.47, "word": " chapter", "probability": 0.61181640625}, {"start": 781.47, "end": 782.05, "word": " 12", "probability": 0.80126953125}, {"start": 782.05, "end": 783.31, "word": " talks", "probability": 0.7490234375}, {"start": 783.31, "end": 784.03, "word": " about", "probability": 0.90576171875}, {"start": 784.03, "end": 786.33, "word": " coefficient", "probability": 0.77978515625}, {"start": 786.33, "end": 786.69, "word": " of", "probability": 0.94580078125}, {"start": 786.69, "end": 787.27, "word": " determination", "probability": 0.93505859375}, {"start": 787.27, "end": 787.55, "word": " R", "probability": 0.6572265625}, {"start": 787.55, "end": 787.87, "word": " squared.", "probability": 0.78759765625}, {"start": 789.53, "end": 789.97, "word": " The", "probability": 0.90380859375}, {"start": 789.97, "end": 790.43, "word": " definition", "probability": 0.9384765625}, {"start": 790.43, "end": 790.71, "word": " for", "probability": 0.90673828125}, {"start": 790.71, "end": 790.87, "word": " the", "probability": 0.90234375}, {"start": 790.87, "end": 791.29, "word": " coefficient", "probability": 0.953125}, {"start": 791.29, "end": 791.55, "word": " of", "probability": 0.95166015625}, {"start": 791.55, "end": 792.09, "word": " determination", "probability": 0.9453125}, {"start": 792.09, "end": 793.53, "word": " is", "probability": 0.9091796875}, {"start": 793.53, "end": 793.69, "word": " the", "probability": 0.92431640625}, {"start": 793.69, "end": 794.21, "word": " portion", "probability": 0.89306640625}], "temperature": 1.0}, {"id": 33, "seek": 81819, "start": 795.45, "end": 818.19, "text": " of the total variation in the dependent variable that is explained by the variation in the independent variable. Since we have two variables X and Y. And the question is, what's the portion of the total variation that can be explained by X?", "tokens": [295, 264, 3217, 12990, 294, 264, 12334, 7006, 300, 307, 8825, 538, 264, 12990, 294, 264, 6695, 7006, 13, 4162, 321, 362, 732, 9102, 1783, 293, 398, 13, 400, 264, 1168, 307, 11, 437, 311, 264, 8044, 295, 264, 3217, 12990, 300, 393, 312, 8825, 538, 1783, 30], "avg_logprob": -0.2021683624812535, "compression_ratio": 1.7851851851851852, "no_speech_prob": 0.0, "words": [{"start": 795.45, "end": 795.75, "word": " of", "probability": 0.30419921875}, {"start": 795.75, "end": 795.91, "word": " the", "probability": 0.9072265625}, {"start": 795.91, "end": 796.19, "word": " total", "probability": 0.89404296875}, {"start": 796.19, "end": 796.73, "word": " variation", "probability": 0.90869140625}, {"start": 796.73, "end": 797.07, "word": " in", "probability": 0.8642578125}, {"start": 797.07, "end": 797.19, "word": " the", "probability": 0.81640625}, {"start": 797.19, "end": 797.51, "word": " dependent", "probability": 0.52490234375}, {"start": 797.51, "end": 798.05, "word": " variable", "probability": 0.9306640625}, {"start": 798.05, "end": 799.17, "word": " that", "probability": 0.52880859375}, {"start": 799.17, "end": 799.33, "word": " is", "probability": 0.6611328125}, {"start": 799.33, "end": 799.75, "word": " explained", "probability": 0.75341796875}, {"start": 799.75, "end": 800.17, "word": " by", "probability": 0.95849609375}, {"start": 800.17, "end": 800.35, "word": " the", "probability": 0.888671875}, {"start": 800.35, "end": 800.81, "word": " variation", "probability": 0.90185546875}, {"start": 800.81, "end": 801.21, "word": " in", "probability": 0.9296875}, {"start": 801.21, "end": 801.33, "word": " the", "probability": 0.9169921875}, {"start": 801.33, "end": 801.73, "word": " independent", "probability": 0.8935546875}, {"start": 801.73, "end": 802.19, "word": " variable.", "probability": 0.8994140625}, {"start": 802.89, "end": 803.29, "word": " Since", "probability": 0.7763671875}, {"start": 803.29, "end": 803.47, "word": " we", "probability": 0.9228515625}, {"start": 803.47, "end": 803.67, "word": " have", "probability": 0.9501953125}, {"start": 803.67, "end": 803.89, "word": " two", "probability": 0.8779296875}, {"start": 803.89, "end": 804.33, "word": " variables", "probability": 0.931640625}, {"start": 804.33, "end": 804.61, "word": " X", "probability": 0.357177734375}, {"start": 804.61, "end": 804.81, "word": " and", "probability": 0.9375}, {"start": 804.81, "end": 805.13, "word": " Y.", "probability": 0.994140625}, {"start": 809.51, "end": 809.99, "word": " And", "probability": 0.82568359375}, {"start": 809.99, "end": 810.09, "word": " the", "probability": 0.90380859375}, {"start": 810.09, "end": 810.37, "word": " question", "probability": 0.92919921875}, {"start": 810.37, "end": 810.75, "word": " is,", "probability": 0.9482421875}, {"start": 811.81, "end": 812.23, "word": " what's", "probability": 0.86376953125}, {"start": 812.23, "end": 812.43, "word": " the", "probability": 0.92431640625}, {"start": 812.43, "end": 812.95, "word": " portion", "probability": 0.888671875}, {"start": 812.95, "end": 814.35, "word": " of", "probability": 0.96337890625}, {"start": 814.35, "end": 814.49, "word": " the", "probability": 0.9140625}, {"start": 814.49, "end": 814.75, "word": " total", "probability": 0.8759765625}, {"start": 814.75, "end": 815.15, "word": " variation", "probability": 0.880859375}, {"start": 815.15, "end": 815.69, "word": " that", "probability": 0.93603515625}, {"start": 815.69, "end": 815.95, "word": " can", "probability": 0.939453125}, {"start": 815.95, "end": 816.77, "word": " be", "probability": 0.9560546875}, {"start": 816.77, "end": 817.51, "word": " explained", "probability": 0.78173828125}, {"start": 817.51, "end": 817.83, "word": " by", "probability": 0.96923828125}, {"start": 817.83, "end": 818.19, "word": " X?", "probability": 0.966796875}], "temperature": 1.0}, {"id": 34, "seek": 84343, "start": 819.09, "end": 843.43, "text": " So the question is, what's the portion of the total variation in Y that is explained already by the variation in X? For example, suppose R² is 90%, 0.90. That means 90% in the variation of the selling price is explained by its size.", "tokens": [407, 264, 1168, 307, 11, 437, 311, 264, 8044, 295, 264, 3217, 12990, 294, 398, 300, 307, 8825, 1217, 538, 264, 12990, 294, 1783, 30, 1171, 1365, 11, 7297, 497, 27643, 307, 4289, 8923, 1958, 13, 7771, 13, 663, 1355, 4289, 4, 294, 264, 12990, 295, 264, 6511, 3218, 307, 8825, 538, 1080, 2744, 13], "avg_logprob": -0.19405691751411983, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 819.09, "end": 819.39, "word": " So", "probability": 0.7080078125}, {"start": 819.39, "end": 819.53, "word": " the", "probability": 0.666015625}, {"start": 819.53, "end": 819.83, "word": " question", "probability": 0.9111328125}, {"start": 819.83, "end": 820.15, "word": " is,", "probability": 0.9501953125}, {"start": 820.63, "end": 820.81, "word": " what's", "probability": 0.8095703125}, {"start": 820.81, "end": 821.01, "word": " the", "probability": 0.92626953125}, {"start": 821.01, "end": 821.33, "word": " portion", "probability": 0.8154296875}, {"start": 821.33, "end": 821.65, "word": " of", "probability": 0.96875}, {"start": 821.65, "end": 821.79, "word": " the", "probability": 0.84912109375}, {"start": 821.79, "end": 822.03, "word": " total", "probability": 0.86865234375}, {"start": 822.03, "end": 822.51, "word": " variation", "probability": 0.87353515625}, {"start": 822.51, "end": 822.77, "word": " in", "probability": 0.8310546875}, {"start": 822.77, "end": 823.05, "word": " Y", "probability": 0.7080078125}, {"start": 823.05, "end": 823.93, "word": " that", "probability": 0.81884765625}, {"start": 823.93, "end": 824.15, "word": " is", "probability": 0.88037109375}, {"start": 824.15, "end": 824.53, "word": " explained", "probability": 0.88623046875}, {"start": 824.53, "end": 825.23, "word": " already", "probability": 0.8935546875}, {"start": 825.23, "end": 825.89, "word": " by", "probability": 0.95263671875}, {"start": 825.89, "end": 826.07, "word": " the", "probability": 0.88671875}, {"start": 826.07, "end": 826.45, "word": " variation", "probability": 0.86376953125}, {"start": 826.45, "end": 826.67, "word": " in", "probability": 0.923828125}, {"start": 826.67, "end": 827.01, "word": " X?", "probability": 0.96923828125}, {"start": 828.27, "end": 828.71, "word": " For", "probability": 0.9150390625}, {"start": 828.71, "end": 829.05, "word": " example,", "probability": 0.96630859375}, {"start": 829.25, "end": 829.87, "word": " suppose", "probability": 0.861328125}, {"start": 829.87, "end": 831.59, "word": " R²", "probability": 0.47613525390625}, {"start": 831.59, "end": 832.75, "word": " is", "probability": 0.8076171875}, {"start": 832.75, "end": 834.03, "word": " 90%,", "probability": 0.6419677734375}, {"start": 834.03, "end": 834.45, "word": " 0", "probability": 0.537109375}, {"start": 834.45, "end": 834.89, "word": ".90.", "probability": 0.98095703125}, {"start": 835.55, "end": 836.31, "word": " That", "probability": 0.90185546875}, {"start": 836.31, "end": 836.71, "word": " means", "probability": 0.9296875}, {"start": 836.71, "end": 837.81, "word": " 90", "probability": 0.8193359375}, {"start": 837.81, "end": 838.13, "word": "%", "probability": 0.97119140625}, {"start": 838.13, "end": 838.91, "word": " in", "probability": 0.87939453125}, {"start": 838.91, "end": 839.05, "word": " the", "probability": 0.916015625}, {"start": 839.05, "end": 839.43, "word": " variation", "probability": 0.91064453125}, {"start": 839.43, "end": 839.63, "word": " of", "probability": 0.94775390625}, {"start": 839.63, "end": 839.77, "word": " the", "probability": 0.8251953125}, {"start": 839.77, "end": 840.01, "word": " selling", "probability": 0.87109375}, {"start": 840.01, "end": 840.61, "word": " price", "probability": 0.919921875}, {"start": 840.61, "end": 841.87, "word": " is", "probability": 0.91162109375}, {"start": 841.87, "end": 842.27, "word": " explained", "probability": 0.8408203125}, {"start": 842.27, "end": 842.73, "word": " by", "probability": 0.96923828125}, {"start": 842.73, "end": 842.99, "word": " its", "probability": 0.83056640625}, {"start": 842.99, "end": 843.43, "word": " size.", "probability": 0.845703125}], "temperature": 1.0}, {"id": 35, "seek": 87110, "start": 844.86, "end": 871.1, "text": " That means the size of the house contributes about 90% to explain the variability of the selling price. So we would like to have R squared to be large enough. Now, R squared for simple regression only is given by this equation, correlation between X and Y squared.", "tokens": [663, 1355, 264, 2744, 295, 264, 1782, 32035, 466, 4289, 4, 281, 2903, 264, 35709, 295, 264, 6511, 3218, 13, 407, 321, 576, 411, 281, 362, 497, 8889, 281, 312, 2416, 1547, 13, 823, 11, 497, 8889, 337, 2199, 24590, 787, 307, 2212, 538, 341, 5367, 11, 20009, 1296, 1783, 293, 398, 8889, 13], "avg_logprob": -0.13572443344376303, "compression_ratio": 1.440217391304348, "no_speech_prob": 0.0, "words": [{"start": 844.86, "end": 845.26, "word": " That", "probability": 0.873046875}, {"start": 845.26, "end": 845.7, "word": " means", "probability": 0.92626953125}, {"start": 845.7, "end": 846.24, "word": " the", "probability": 0.78173828125}, {"start": 846.24, "end": 846.6, "word": " size", "probability": 0.83154296875}, {"start": 846.6, "end": 846.78, "word": " of", "probability": 0.9697265625}, {"start": 846.78, "end": 846.9, "word": " the", "probability": 0.92236328125}, {"start": 846.9, "end": 847.32, "word": " house", "probability": 0.88134765625}, {"start": 847.32, "end": 848.36, "word": " contributes", "probability": 0.93408203125}, {"start": 848.36, "end": 848.9, "word": " about", "probability": 0.904296875}, {"start": 848.9, "end": 849.86, "word": " 90", "probability": 0.95947265625}, {"start": 849.86, "end": 850.52, "word": "%", "probability": 0.912109375}, {"start": 850.52, "end": 852.58, "word": " to", "probability": 0.402587890625}, {"start": 852.58, "end": 853.16, "word": " explain", "probability": 0.92578125}, {"start": 853.16, "end": 853.48, "word": " the", "probability": 0.90869140625}, {"start": 853.48, "end": 853.96, "word": " variability", "probability": 0.9638671875}, {"start": 853.96, "end": 854.5, "word": " of", "probability": 0.96728515625}, {"start": 854.5, "end": 854.7, "word": " the", "probability": 0.91552734375}, {"start": 854.7, "end": 855.16, "word": " selling", "probability": 0.8076171875}, {"start": 855.16, "end": 855.64, "word": " price.", "probability": 0.91650390625}, {"start": 857.22, "end": 857.7, "word": " So", "probability": 0.96728515625}, {"start": 857.7, "end": 857.98, "word": " we", "probability": 0.8212890625}, {"start": 857.98, "end": 858.24, "word": " would", "probability": 0.91357421875}, {"start": 858.24, "end": 858.5, "word": " like", "probability": 0.93603515625}, {"start": 858.5, "end": 858.84, "word": " to", "probability": 0.9658203125}, {"start": 858.84, "end": 859.3, "word": " have", "probability": 0.9404296875}, {"start": 859.3, "end": 859.56, "word": " R", "probability": 0.71044921875}, {"start": 859.56, "end": 859.78, "word": " squared", "probability": 0.75634765625}, {"start": 859.78, "end": 860.02, "word": " to", "probability": 0.9365234375}, {"start": 860.02, "end": 860.14, "word": " be", "probability": 0.95166015625}, {"start": 860.14, "end": 860.46, "word": " large", "probability": 0.96484375}, {"start": 860.46, "end": 860.84, "word": " enough.", "probability": 0.869140625}, {"start": 862.46, "end": 862.76, "word": " Now,", "probability": 0.94140625}, {"start": 863.0, "end": 863.3, "word": " R", "probability": 0.97802734375}, {"start": 863.3, "end": 863.72, "word": " squared", "probability": 0.83740234375}, {"start": 863.72, "end": 864.92, "word": " for", "probability": 0.8076171875}, {"start": 864.92, "end": 865.5, "word": " simple", "probability": 0.89599609375}, {"start": 865.5, "end": 866.02, "word": " regression", "probability": 0.95068359375}, {"start": 866.02, "end": 866.62, "word": " only", "probability": 0.8994140625}, {"start": 866.62, "end": 867.78, "word": " is", "probability": 0.74560546875}, {"start": 867.78, "end": 868.02, "word": " given", "probability": 0.8984375}, {"start": 868.02, "end": 868.24, "word": " by", "probability": 0.96875}, {"start": 868.24, "end": 868.46, "word": " this", "probability": 0.9111328125}, {"start": 868.46, "end": 868.94, "word": " equation,", "probability": 0.962890625}, {"start": 869.1, "end": 869.54, "word": " correlation", "probability": 0.86572265625}, {"start": 869.54, "end": 869.98, "word": " between", "probability": 0.90380859375}, {"start": 869.98, "end": 870.2, "word": " X", "probability": 0.53271484375}, {"start": 870.2, "end": 870.38, "word": " and", "probability": 0.94384765625}, {"start": 870.38, "end": 870.64, "word": " Y", "probability": 0.99462890625}, {"start": 870.64, "end": 871.1, "word": " squared.", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 36, "seek": 90051, "start": 874.09, "end": 900.51, "text": " So if we have the correlation between X and Y and then you just square this value, that will give the correlation or the coefficient of determination. So simply, determination coefficient is just the square of the correlation between X and Y. We know that R ranges between minus 1 and plus 1. 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So again, r squared is used to explain the portion of the total variability in the dependent variable that is already explained by the variability in x. 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R squared is one only happens if R is one or negative one. So if there exists perfect relationship either negative or positive, I mean if R is plus one or negative one, then R squared is one. That means perfect linear relationship between Y and X. 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And that's really never happened in real life. Because R equals 1 or plus 1 or negative 1 cannot be happened in real life. 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But for sure there is an error, and that error may be due to some variables that are not included in the regression model. 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It means as X increases, Y stays the same, constant. So that means there is no relationship or actually there is no linear relationship because it could be there exists non-linear relationship. But here we are.", "tokens": [1436, 510, 11, 382, 1783, 8637, 11, 398, 10834, 6217, 294, 264, 912, 2535, 13, 467, 1355, 382, 1783, 8637, 11, 398, 10834, 264, 912, 11, 5754, 13, 407, 300, 1355, 456, 307, 572, 2480, 420, 767, 456, 307, 572, 8213, 2480, 570, 309, 727, 312, 456, 8198, 2107, 12, 28263, 2480, 13, 583, 510, 321, 366, 13], "avg_logprob": -0.24708685733504215, "compression_ratio": 1.8051948051948052, "no_speech_prob": 0.0, "words": [{"start": 1099.35, "end": 1099.71, "word": " Because", "probability": 0.65771484375}, {"start": 1099.71, "end": 1100.07, "word": " here,", "probability": 0.8017578125}, {"start": 1100.53, "end": 1100.65, "word": " as", "probability": 0.92529296875}, {"start": 1100.65, "end": 1100.87, "word": " X", "probability": 0.54248046875}, {"start": 1100.87, "end": 1101.37, "word": " increases,", "probability": 0.9306640625}, {"start": 1101.93, "end": 1102.27, "word": " Y", "probability": 0.9765625}, {"start": 1102.27, "end": 1103.95, "word": " stays", "probability": 0.6298828125}, {"start": 1103.95, "end": 1104.49, "word": " nearly", "probability": 0.60205078125}, {"start": 1104.49, "end": 1104.71, "word": " in", "probability": 0.89453125}, {"start": 1104.71, "end": 1104.87, "word": " the", "probability": 0.91259765625}, {"start": 1104.87, "end": 1105.21, "word": " same", "probability": 0.90380859375}, {"start": 1105.21, "end": 1106.07, "word": " position.", "probability": 0.9345703125}, {"start": 1106.69, "end": 1106.83, "word": " It", "probability": 0.8779296875}, {"start": 1106.83, "end": 1107.19, "word": " means", "probability": 0.9267578125}, {"start": 1107.19, "end": 1107.59, "word": " as", "probability": 0.517578125}, {"start": 1107.59, "end": 1107.87, "word": " X", "probability": 0.98291015625}, {"start": 1107.87, "end": 1108.43, "word": " increases,", "probability": 0.9375}, {"start": 1108.85, "end": 1109.01, "word": " Y", "probability": 0.9892578125}, {"start": 1109.01, "end": 1109.31, "word": " stays", "probability": 0.85791015625}, {"start": 1109.31, "end": 1109.47, "word": " the", "probability": 0.3916015625}, {"start": 1109.47, "end": 1109.73, "word": " same,", "probability": 0.8916015625}, {"start": 1109.83, "end": 1110.19, "word": " constant.", "probability": 0.91943359375}, {"start": 1111.01, "end": 1111.25, "word": " So", "probability": 0.91650390625}, {"start": 1111.25, "end": 1111.55, "word": " that", "probability": 0.7568359375}, {"start": 1111.55, "end": 1111.75, "word": " means", "probability": 0.93701171875}, {"start": 1111.75, "end": 1111.93, "word": " there", "probability": 0.84326171875}, {"start": 1111.93, "end": 1112.07, "word": " is", "probability": 0.92626953125}, {"start": 1112.07, "end": 1112.23, "word": " no", "probability": 0.94970703125}, {"start": 1112.23, "end": 1112.79, "word": " relationship", "probability": 0.890625}, {"start": 1112.79, "end": 1113.25, "word": " or", "probability": 0.44873046875}, {"start": 1113.25, "end": 1113.73, "word": " actually", "probability": 0.85107421875}, {"start": 1113.73, "end": 1114.49, "word": " there", "probability": 0.76416015625}, {"start": 1114.49, "end": 1114.67, "word": " is", "probability": 0.9453125}, {"start": 1114.67, "end": 1114.89, "word": " no", "probability": 0.9443359375}, {"start": 1114.89, "end": 1115.41, "word": " linear", "probability": 0.91748046875}, {"start": 1115.41, "end": 1116.07, "word": " relationship", "probability": 0.92138671875}, {"start": 1116.07, "end": 1116.57, "word": " because", "probability": 0.400390625}, {"start": 1116.57, "end": 1116.87, "word": " it", "probability": 0.677734375}, {"start": 1116.87, "end": 1117.01, "word": " could", "probability": 0.90185546875}, {"start": 1117.01, "end": 1117.29, "word": " be", "probability": 0.9248046875}, {"start": 1117.29, "end": 1118.17, "word": " there", "probability": 0.73583984375}, {"start": 1118.17, "end": 1118.63, "word": " exists", "probability": 0.82470703125}, {"start": 1118.63, "end": 1119.23, "word": " non", "probability": 0.953125}, {"start": 1119.23, "end": 1119.57, "word": "-linear", "probability": 0.727294921875}, {"start": 1119.57, "end": 1120.07, "word": " relationship.", "probability": 0.853515625}, {"start": 1120.37, "end": 1120.51, "word": " But", "probability": 0.92919921875}, {"start": 1120.51, "end": 1120.71, "word": " here", "probability": 0.84423828125}, {"start": 1120.71, "end": 1120.85, "word": " we", "probability": 0.86669921875}, {"start": 1120.85, "end": 1121.05, "word": " are.", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 46, "seek": 114474, "start": 1121.88, "end": 1144.74, "text": " Just focusing on linear relationship between X and Y. So if R is zero, that means the value of Y does not depend on the value of X. So as X increases, Y is constant. Now for the previous example, R was 0.7621. To determine the coefficient of determination,", "tokens": [1449, 8416, 322, 8213, 2480, 1296, 1783, 293, 398, 13, 407, 498, 497, 307, 4018, 11, 300, 1355, 264, 2158, 295, 398, 775, 406, 5672, 322, 264, 2158, 295, 1783, 13, 407, 382, 1783, 8637, 11, 398, 307, 5754, 13, 823, 337, 264, 3894, 1365, 11, 497, 390, 1958, 13, 25026, 4436, 13, 1407, 6997, 264, 17619, 295, 18432, 11], "avg_logprob": -0.1704661816847129, "compression_ratio": 1.4120879120879122, "no_speech_prob": 0.0, "words": [{"start": 1121.88, "end": 1122.44, "word": " Just", "probability": 0.428466796875}, {"start": 1122.44, "end": 1123.0, "word": " focusing", "probability": 0.89453125}, {"start": 1123.0, "end": 1123.44, "word": " on", "probability": 0.94677734375}, {"start": 1123.44, "end": 1124.3, "word": " linear", "probability": 0.7041015625}, {"start": 1124.3, "end": 1124.98, "word": " relationship", "probability": 0.90625}, {"start": 1124.98, "end": 1125.32, "word": " between", "probability": 0.91259765625}, {"start": 1125.32, "end": 1125.48, "word": " X", "probability": 0.56396484375}, {"start": 1125.48, "end": 1125.64, "word": " and", "probability": 0.9345703125}, {"start": 1125.64, "end": 1125.86, "word": " Y.", "probability": 0.9892578125}, {"start": 1126.38, "end": 1126.58, "word": " So", "probability": 0.8447265625}, {"start": 1126.58, "end": 1127.78, "word": " if", "probability": 0.60400390625}, {"start": 1127.78, "end": 1128.06, "word": " R", "probability": 0.82080078125}, {"start": 1128.06, "end": 1128.3, "word": " is", "probability": 0.86376953125}, {"start": 1128.3, "end": 1128.56, "word": " zero,", "probability": 0.54443359375}, {"start": 1128.68, "end": 1128.86, "word": " that", "probability": 0.93017578125}, {"start": 1128.86, "end": 1129.28, "word": " means", "probability": 0.93017578125}, {"start": 1129.28, "end": 1130.02, "word": " the", "probability": 0.81591796875}, {"start": 1130.02, "end": 1130.3, "word": " value", "probability": 0.9755859375}, {"start": 1130.3, "end": 1130.44, "word": " of", "probability": 0.9482421875}, {"start": 1130.44, "end": 1130.56, "word": " Y", "probability": 0.966796875}, {"start": 1130.56, "end": 1130.76, "word": " does", "probability": 0.97021484375}, {"start": 1130.76, "end": 1130.94, "word": " not", "probability": 0.9521484375}, {"start": 1130.94, "end": 1131.24, "word": " depend", "probability": 0.91748046875}, {"start": 1131.24, "end": 1131.5, "word": " on", "probability": 0.94775390625}, {"start": 1131.5, "end": 1131.66, "word": " the", "probability": 0.90380859375}, {"start": 1131.66, "end": 1131.9, "word": " value", "probability": 0.97607421875}, {"start": 1131.9, "end": 1132.06, "word": " of", "probability": 0.818359375}, {"start": 1132.06, "end": 1132.18, "word": " X.", "probability": 0.98876953125}, {"start": 1132.26, "end": 1132.4, "word": " So", "probability": 0.94140625}, {"start": 1132.4, "end": 1132.68, "word": " as", "probability": 0.72314453125}, {"start": 1132.68, "end": 1133.02, "word": " X", "probability": 0.98486328125}, {"start": 1133.02, "end": 1133.72, "word": " increases,", "probability": 0.93505859375}, {"start": 1134.36, "end": 1134.66, "word": " Y", "probability": 0.9853515625}, {"start": 1134.66, "end": 1135.48, "word": " is", "probability": 0.345947265625}, {"start": 1135.48, "end": 1136.22, "word": " constant.", "probability": 0.83251953125}, {"start": 1137.5, "end": 1138.06, "word": " Now", "probability": 0.89013671875}, {"start": 1138.06, "end": 1138.22, "word": " for", "probability": 0.6513671875}, {"start": 1138.22, "end": 1138.36, "word": " the", "probability": 0.9208984375}, {"start": 1138.36, "end": 1138.56, "word": " previous", "probability": 0.80615234375}, {"start": 1138.56, "end": 1139.08, "word": " example,", "probability": 0.974609375}, {"start": 1139.8, "end": 1140.08, "word": " R", "probability": 0.97900390625}, {"start": 1140.08, "end": 1140.42, "word": " was", "probability": 0.93798828125}, {"start": 1140.42, "end": 1140.64, "word": " 0", "probability": 0.78369140625}, {"start": 1140.64, "end": 1141.58, "word": ".7621.", "probability": 0.9210611979166666}, {"start": 1142.72, "end": 1142.92, "word": " To", "probability": 0.9462890625}, {"start": 1142.92, "end": 1143.34, "word": " determine", "probability": 0.90771484375}, {"start": 1143.34, "end": 1143.62, "word": " the", "probability": 0.9189453125}, {"start": 1143.62, "end": 1144.04, "word": " coefficient", "probability": 0.89990234375}, {"start": 1144.04, "end": 1144.26, "word": " of", "probability": 0.96923828125}, {"start": 1144.26, "end": 1144.74, "word": " determination,", "probability": 0.89404296875}], "temperature": 1.0}, {"id": 47, "seek": 116998, "start": 1145.84, "end": 1169.98, "text": " One more time, square this value, that's only valid for simple linear regression. Otherwise, you cannot square the value of R in order to determine the coefficient of determination. So again, this is only true for simple linear regression.", "tokens": [1485, 544, 565, 11, 3732, 341, 2158, 11, 300, 311, 787, 7363, 337, 2199, 8213, 24590, 13, 10328, 11, 291, 2644, 3732, 264, 2158, 295, 497, 294, 1668, 281, 6997, 264, 17619, 295, 18432, 13, 407, 797, 11, 341, 307, 787, 2074, 337, 2199, 8213, 24590, 13], "avg_logprob": -0.15429688214013973, "compression_ratio": 1.643835616438356, "no_speech_prob": 0.0, "words": [{"start": 1145.84, "end": 1146.24, "word": " One", "probability": 0.41650390625}, {"start": 1146.24, "end": 1146.42, "word": " more", "probability": 0.93701171875}, {"start": 1146.42, "end": 1146.76, "word": " time,", "probability": 0.88916015625}, {"start": 1147.46, "end": 1147.76, "word": " square", "probability": 0.65625}, {"start": 1147.76, "end": 1148.1, "word": " this", "probability": 0.89697265625}, {"start": 1148.1, "end": 1148.5, "word": " value,", "probability": 0.9677734375}, {"start": 1148.9, "end": 1149.36, "word": " that's", "probability": 0.889892578125}, {"start": 1149.36, "end": 1149.72, "word": " only", "probability": 0.9287109375}, {"start": 1149.72, "end": 1150.22, "word": " valid", "probability": 0.95751953125}, {"start": 1150.22, "end": 1151.2, "word": " for", "probability": 0.92822265625}, {"start": 1151.2, "end": 1151.76, "word": " simple", "probability": 0.86572265625}, {"start": 1151.76, "end": 1152.2, "word": " linear", "probability": 0.92236328125}, {"start": 1152.2, "end": 1152.62, "word": " regression.", "probability": 0.93505859375}, {"start": 1152.94, "end": 1153.34, "word": " Otherwise,", "probability": 0.904296875}, {"start": 1154.02, "end": 1154.2, "word": " you", "probability": 0.9619140625}, {"start": 1154.2, "end": 1154.54, "word": " cannot", "probability": 0.84423828125}, {"start": 1154.54, "end": 1154.98, "word": " square", "probability": 0.92431640625}, {"start": 1154.98, "end": 1155.14, "word": " the", "probability": 0.91357421875}, {"start": 1155.14, "end": 1155.36, "word": " value", "probability": 0.97509765625}, {"start": 1155.36, "end": 1155.56, "word": " of", "probability": 0.9580078125}, {"start": 1155.56, "end": 1155.8, "word": " R", "probability": 0.62109375}, {"start": 1155.8, "end": 1156.06, "word": " in", "probability": 0.82666015625}, {"start": 1156.06, "end": 1156.28, "word": " order", "probability": 0.9326171875}, {"start": 1156.28, "end": 1156.46, "word": " to", "probability": 0.95751953125}, {"start": 1156.46, "end": 1156.88, "word": " determine", "probability": 0.91943359375}, {"start": 1156.88, "end": 1157.58, "word": " the", "probability": 0.90185546875}, {"start": 1157.58, "end": 1158.04, "word": " coefficient", "probability": 0.9072265625}, {"start": 1158.04, "end": 1158.26, "word": " of", "probability": 0.96337890625}, {"start": 1158.26, "end": 1158.76, "word": " determination.", "probability": 0.9287109375}, {"start": 1159.66, "end": 1159.94, "word": " So", "probability": 0.93408203125}, {"start": 1159.94, "end": 1160.24, "word": " again,", "probability": 0.8203125}, {"start": 1160.42, "end": 1160.68, "word": " this", "probability": 0.93115234375}, {"start": 1160.68, "end": 1160.82, "word": " is", "probability": 0.94677734375}, {"start": 1160.82, "end": 1161.2, "word": " only", "probability": 0.92138671875}, {"start": 1161.2, "end": 1161.54, "word": " true", "probability": 0.9677734375}, {"start": 1161.54, "end": 1166.42, "word": " for", "probability": 0.8818359375}, {"start": 1166.42, "end": 1167.54, "word": " simple", "probability": 0.9111328125}, {"start": 1167.54, "end": 1169.62, "word": " linear", "probability": 0.89306640625}, {"start": 1169.62, "end": 1169.98, "word": " regression.", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 48, "seek": 119804, "start": 1175.46, "end": 1198.04, "text": " So R squared is 0.7621 squared will give 0.5808. Now, the meaning of this value, first you have to multiply this by 100. 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But since the size of the house explains 58%, that means it's a significant variable. Now, if we add more variables,", "tokens": [663, 1062, 3345, 264, 1319, 295, 3218, 13, 583, 1670, 264, 2744, 295, 264, 1782, 13948, 21786, 8923, 300, 1355, 309, 311, 257, 4776, 7006, 13, 823, 11, 498, 321, 909, 544, 9102, 11], "avg_logprob": -0.20491071428571428, "compression_ratio": 1.2380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1251.2, "end": 1251.58, "word": " That", "probability": 0.45751953125}, {"start": 1251.58, "end": 1251.92, "word": " might", "probability": 0.89404296875}, {"start": 1251.92, "end": 1252.58, "word": " affect", "probability": 0.8125}, {"start": 1252.58, "end": 1253.02, "word": " the", "probability": 0.89306640625}, {"start": 1253.02, "end": 1253.34, "word": " change", "probability": 0.76611328125}, {"start": 1253.34, "end": 1253.54, "word": " of", "probability": 0.94482421875}, {"start": 1253.54, "end": 1253.82, "word": " price.", "probability": 0.4775390625}, {"start": 1264.84, "end": 1265.22, "word": " But", "probability": 0.6494140625}, {"start": 1265.22, "end": 1266.72, "word": " since", "probability": 0.68505859375}, {"start": 1266.72, "end": 1267.0, "word": " the", "probability": 0.91357421875}, {"start": 1267.0, "end": 1267.3, "word": " size", "probability": 0.84033203125}, {"start": 1267.3, "end": 1267.44, "word": " of", "probability": 0.96826171875}, {"start": 1267.44, "end": 1267.58, "word": " the", "probability": 0.90234375}, {"start": 1267.58, "end": 1267.86, "word": " house", "probability": 0.87744140625}, {"start": 1267.86, "end": 1268.48, "word": " explains", "probability": 0.9296875}, {"start": 1268.48, "end": 1269.62, "word": " 58%,", "probability": 0.7685546875}, {"start": 1269.62, "end": 1271.16, "word": " that", "probability": 0.818359375}, {"start": 1271.16, "end": 1271.54, "word": " means", "probability": 0.93212890625}, {"start": 1271.54, "end": 1272.08, "word": " it's", "probability": 0.891357421875}, {"start": 1272.08, "end": 1272.16, "word": " a", "probability": 0.8486328125}, {"start": 1272.16, "end": 1272.62, "word": " significant", "probability": 0.87841796875}, {"start": 1272.62, "end": 1273.1, "word": " variable.", "probability": 0.91064453125}, {"start": 1274.4, "end": 1275.02, "word": " Now,", "probability": 0.93896484375}, {"start": 1275.1, "end": 1275.22, "word": " if", "probability": 0.95068359375}, {"start": 1275.22, "end": 1275.38, "word": " we", "probability": 0.95556640625}, {"start": 1275.38, "end": 1275.66, "word": " add", "probability": 0.89013671875}, {"start": 1275.66, "end": 1275.96, "word": " more", "probability": 0.94091796875}, {"start": 1275.96, "end": 1276.5, "word": " variables,", "probability": 0.931640625}], "temperature": 1.0}, {"id": 52, "seek": 129395, "start": 1277.69, "end": 1293.95, "text": " to the regression equation for sure this value will be increased. So maybe 60 or 65 or 67 and so on. But 60% or 50 is more enough sometimes. 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So that's for the coefficient of determination. Any question? So we covered simple linear regression model. We know now how can we compute the values of B0 and B1.", "tokens": [663, 1355, 264, 2316, 307, 8559, 281, 6997, 420, 281, 652, 512, 17630, 13, 407, 300, 311, 337, 264, 17619, 295, 18432, 13, 2639, 1168, 30, 407, 321, 5343, 2199, 8213, 24590, 2316, 13, 492, 458, 586, 577, 393, 321, 14722, 264, 4190, 295, 363, 15, 293, 363, 16, 13], "avg_logprob": -0.16681985820040984, "compression_ratio": 1.451219512195122, "no_speech_prob": 0.0, "words": [{"start": 1294.95, "end": 1295.25, "word": " That", "probability": 0.77734375}, {"start": 1295.25, "end": 1295.53, "word": " means", "probability": 0.927734375}, {"start": 1295.53, "end": 1295.91, "word": " the", "probability": 0.87841796875}, {"start": 1295.91, "end": 1296.49, "word": " model", "probability": 0.94482421875}, {"start": 1296.49, "end": 1297.07, "word": " is", "probability": 0.94580078125}, {"start": 1297.07, "end": 1297.75, "word": " accurate", "probability": 0.88623046875}, {"start": 1297.75, "end": 1298.61, "word": " to", "probability": 0.85009765625}, {"start": 1298.61, "end": 1299.07, "word": " determine", "probability": 0.76416015625}, {"start": 1299.07, "end": 1300.39, "word": " or", "probability": 0.59326171875}, {"start": 1300.39, "end": 1300.65, "word": " to", "probability": 0.955078125}, {"start": 1300.65, "end": 1300.89, "word": " make", "probability": 0.94287109375}, {"start": 1300.89, "end": 1301.23, "word": " some", "probability": 0.89697265625}, {"start": 1301.23, "end": 1301.75, "word": " prediction.", "probability": 0.89697265625}, {"start": 1302.69, "end": 1303.01, "word": " So", "probability": 0.9609375}, {"start": 1303.01, "end": 1303.95, "word": " that's", "probability": 0.927734375}, {"start": 1303.95, "end": 1304.41, "word": " for", "probability": 0.93115234375}, {"start": 1304.41, "end": 1304.77, "word": " the", "probability": 0.92431640625}, {"start": 1304.77, "end": 1305.77, "word": " coefficient", "probability": 0.896484375}, {"start": 1305.77, "end": 1306.43, "word": " of", "probability": 0.96875}, {"start": 1306.43, "end": 1307.47, "word": " determination.", "probability": 0.794921875}, {"start": 1308.61, "end": 1309.11, "word": " Any", "probability": 0.919921875}, {"start": 1309.11, "end": 1309.47, "word": " question?", "probability": 0.783203125}, {"start": 1310.97, "end": 1311.33, "word": " So", "probability": 0.9423828125}, {"start": 1311.33, "end": 1312.01, "word": " we", "probability": 0.80615234375}, {"start": 1312.01, "end": 1312.87, "word": " covered", "probability": 0.76318359375}, {"start": 1312.87, "end": 1318.35, "word": " simple", "probability": 0.2291259765625}, {"start": 1318.35, "end": 1318.59, "word": " linear", "probability": 0.7578125}, {"start": 1318.59, "end": 1318.95, "word": " regression", "probability": 0.97265625}, {"start": 1318.95, "end": 1319.31, "word": " model.", "probability": 0.9443359375}, {"start": 1320.41, "end": 1320.77, "word": " We", "probability": 0.96240234375}, {"start": 1320.77, "end": 1320.99, "word": " know", "probability": 0.8818359375}, {"start": 1320.99, "end": 1321.23, "word": " now", "probability": 0.90625}, {"start": 1321.23, "end": 1321.43, "word": " how", "probability": 0.8642578125}, {"start": 1321.43, "end": 1321.63, "word": " can", "probability": 0.869140625}, {"start": 1321.63, "end": 1321.79, "word": " we", "probability": 0.93798828125}, {"start": 1321.79, "end": 1322.19, "word": " compute", "probability": 0.93212890625}, {"start": 1322.19, "end": 1322.41, "word": " the", "probability": 0.91552734375}, {"start": 1322.41, "end": 1322.75, "word": " values", "probability": 0.9521484375}, {"start": 1322.75, "end": 1322.89, "word": " of", "probability": 0.9150390625}, {"start": 1322.89, "end": 1323.21, "word": " B0", "probability": 0.5699462890625}, {"start": 1323.21, "end": 1323.35, "word": " and", "probability": 0.9443359375}, {"start": 1323.35, "end": 1323.71, "word": " B1.", "probability": 0.996337890625}], "temperature": 1.0}, {"id": 54, "seek": 135303, "start": 1324.99, "end": 1353.03, "text": " We can state or write the regression equation, and we can do some interpretation about P0 and P1, making predictions, and make some comments about the coefficient of determination. That's all. 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