2. Deriving the OLS b
Statistics for International Business
Curso 4 de 6 en SpecializationInternational Business Essentials
This course introduces core areas of statistics that will be useful in business and for several MBA modules. It covers a variety of ways to present data, probability, and statistical estimation. You can test your understanding as you progress, while more advanced content is available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit www.londoninternational.ac.uk/mba This course is endorsed by CMI
Statistical Estimation
For statistical analysis to work properly, it’s essential to have a proper sample, drawn from a population of items of interest that have measured characteristics. This week, we will cover statistical estimation, sampling distribution of the mean, point estimation, interval estimation, hypothesis testing, the Null hypothesis and look at some real life examples of their use.
1. Further on the Linear Regression Model3:15
2. Deriving the OLS b2:32
3.The Statistical Properties of the OLS b4:47
4. Gauss-Marcov Theorem Proof3:47
George Kapetanios
Professor of Finance and Econometrics
The parameter we are interested in,
is the slope coefficient which minimize the sum of the squared errors.
Let, B0 be an arbitrary k x 1 vector.
We want to find the B0 that minimizes the residual sum of squares.
y = XB + e
Therefore e =
y- XB Being
a square of vectors we need to find the transpose.
And then, we have e'e
= y- x B0 prime, y- x B0.
The last term on the right
hand side can be written as
y'y- B'0X' y- y'XB0
+ B'0 X' XB0 = 2.
y' y- 2 B'0 X'
y + B'0 X' X B0.
The first order condition for minimum,
is that the first derivative is that equals to 0.
Thus, we calculate the first derivative,
we respect to B0 which is equals to -2X' y+2X' X B0.
Let the OLS estimator be,
beta value of B0 for which the derivative
of the residual sum of squares
squares with respect to B'0 = 0,
that is 2X' y -2X' Xb = 0,