1. ## Estimated Regression Equation

Hi,

I like to get some help with the part c of the question below:

 X1 X2 Y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211

For this question I had to the do the following:

a.) Develop an estimated regression equation relating y to x1.

I understand this part and got equation: yˆ = 45.06 + 1.94x1

b.) Develop an estimated regression equation relating y to x2.

I also understand this part and got the equation: yˆ = 85.22 + 4.32x2

c.) Develop an estimated regression equation relating y to x1 and x2.

I can't seem to figure out this part, As per the solution the equation is: = -18.37 + 2.01x1 + 4.74x2

I fail to understand how solution arrives at -18.37, 2.01 and 4.74

Thanks

2. ## Re: Estimated Regression Equation

Originally Posted by scorpio2017
Hi,

I like to get some help with the part c of the question below:

 X1 X2 Y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211

For this question I had to the do the following:

a.) Develop an estimated regression equation relating y to x1.

I understand this part and got equation: yˆ = 45.06 + 1.94x1

b.) Develop an estimated regression equation relating y to x2.

I also understand this part and got the equation: yˆ = 85.22 + 4.32x2

c.) Develop an estimated regression equation relating y to x1 and x2.

I can't seem to figure out this part, As per the solution the equation is: = -18.37 + 2.01x1 + 4.74x2

I fail to understand how solution arrives at -18.37, 2.01 and 4.74

Thanks
My favorite method for two independent variables is to solve for two unknowns in two equations using covariances.

$$Cov(Y,X_1) = b_1 Cov(X_1,X_1) + b_2 Cov(X_2,X_1)$$
$$Cov(Y,X_2) = b_1 Cov(X_1,X_2) + b_2 Cov(X_2,X_2)$$

Remember that you can compute covariance using $\displaystyle Cov(A,B)=E[AB]-E[A]E[B]$.

Also note that $\displaystyle Cov(A,A)=V(A)$, and make sure to use the population variance (varp in Excel).

After computing $\displaystyle b_1$ and $\displaystyle b_2$, you can solve for $\displaystyle b_0$ using the regression line equation:
$$(Y-\bar{Y}) = b_1(X_1-\bar{X_1}) + b_2(X_2-\bar{X_2})$$

By hand, this is is rather cumbersome, but it works! Good luck!
-Andy