Answer to Question #262655 in Microeconomics for Zimi

Question

Given the following table, use the matrix method to derive the constant and slope parameters of the sample regression function: Marks = f(Weekly party hours). X (Weekly party hours) 2,4,6,8,10,12,14,16 Y (Marks) 80,77,71,67,66,58,49,36

Answer 1

We first tabulate the values of X and Y and calculate $X^2$ and $XY$

Using matrix;matrix

$X'X=\begin{bmatrix} 8 & 72 \\ 72 & 816 \end{bmatrix}$

$X'Y=$ $\begin{bmatrix} 504 \\ 4048 \end{bmatrix}$

$X'X^{-1}=\begin{bmatrix} 0.607 & -0.0536\\ -0.0536 & 0.00595 \end{bmatrix}$

b=$(X'X^{-1})X'Y$

=$\begin{bmatrix} 0.607 & -0.0536\\ -0.0536 & 0.00595 \end{bmatrix}$$\begin{bmatrix} 504 \\ 4048 \end{bmatrix}$

=$\begin{bmatrix} 88.9552\\ -2.9288 \end{bmatrix}$

constant=88.9552

slope=-2.9288