The regression equation of Y on X is given by the following formula:
[tex]Y-\bar{Y}=b_{yx}(X-\bar{X})[/tex]
Where byx is given by the formula:
[tex]b_{yx}=\frac{N\sum^{}_{}XY-\sum^{}_{}X\sum^{}_{}Y}{N\sum^{}_{}X^2-(\sum^{}_{}X)^2}[/tex]
Where N is the number of values (N=8). We need to find the sum of X values, the sum of Y values, the average of X, the average of Y, the sum of X*Y and the sum of X^2.
The table of values is:
The values we need to know are on the following table:
By replacing the known values in the formula we obtain:
[tex]\begin{gathered} b_{yx}=\frac{8\cdot26125-167\cdot995}{8\cdot4649-(167)^2} \\ b_{yx}=\frac{209000-166165}{37192-27889} \\ b_{yx}=\frac{42835}{9303} \\ b_{yx}=4.6 \end{gathered}[/tex]
Now, the average of X and Y is the sum divided by N, then:
[tex]\begin{gathered} \bar{X}=\frac{167}{8}=20.87 \\ \bar{Y}=\frac{995}{8}=124.37 \end{gathered}[/tex]
Replace these values in the formula and find the regression equation as follows:
[tex]\begin{gathered} Y-124.37=4.6(X-20.87) \\ Y-124.37=4.6X-4.6\cdot20.87 \\ Y=4.6X-96.11+124.37 \\ Y=4.6X+28.26 \end{gathered}[/tex]
The answer is a) y=4.6x+28.26
