Task

Given a set of data vectors in the following format:

   
  
    
      
        y
        =
        {
        
          y
          
            1
          
        
        ,
        
          y
          
            2
          
        
        ,
        .
        .
        .
        ,
        
          y
          
            n
          
        
        }
        
      
    
    {\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
  


   
  
    
      
        
          X
          
            i
          
        
        =
        {
        
          x
          
            i
            1
          
        
        ,
        
          x
          
            i
            2
          
        
        ,
        .
        .
        .
        ,
        
          x
          
            i
            n
          
        
        }
        ,
        i
        ∈
        1..
        k
        
      
    
    {\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
  


Compute the vector 



β
=
{

β

1


,

β

2


,
.
.
.
,

β

k


}


{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}

 using ordinary least squares regression using the following equation:

   
  
    
      
        
          y
          
            j
          
        
        =
        
          Σ
          
            i
          
        
        
          β
          
            i
          
        
        ⋅
        
          x
          
            i
            j
          
        
        ,
        j
        ∈
        1..
        n
      
    
    {\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
  


You can assume  y  is given to you as a vector (a one-dimensional array), and  X  is given to you as a two-dimensional array (i.e. matrix).




package main
 
import (
    "fmt"
 
    "github.com/gonum/matrix/mat64"
)
 
func givens() (x, y *mat64.Dense) {
    height := []float64{1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
        1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83}
    weight := []float64{52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
        61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46}
    degree := 2
    x = Vandermonde(height, degree)
    y = mat64.NewDense(len(weight), 1, weight)
    return
}
 
func Vandermonde(a []float64, degree int) *mat64.Dense {
    x := mat64.NewDense(len(a), degree+1, nil)
    for i := range a {
        for j, p := 0, 1.; j <= degree; j, p = j+1, p*a[i] {
            x.Set(i, j, p)
        }
    }
    return x
}
 
func main() {
    x, y := givens()
    fmt.Printf("%.4f\n", mat64.Formatted(mat64.QR(x).Solve(y)))
}