Module 10: Advanced multiple regression

(The attached PDF file has better formatting.)

Homework assignment: Two correlated independent variables

Do this homework assignment after module 12, which gives the equations for the standard errors of the least squares estimators.

We regress the Y values on the X₁ and X₂ values in the table below.

X1	X2	Y	X1	X2	Y
1	1	1.016	6	8	-1.076
2	6	-3.429	7	4	3.461
3	2	0.049	8	9	-2.525
4	7	-3.099	9	5	4.195
5	3	0.359	10	10	-0.746

What is the correlation of X₁ and X₂?

What is the least squares estimator of

á?

What is the least squares estimator of

â₁, the coefficient of X₁?

What is the least squares estimator of

â₂, the coefficient of X₂?

What is the standard error of the least squares estimator of

â₁, the coefficient of X₁?

What is the standard error of the least squares estimator of

â₂, the coefficient of X₂?

Show the formulas and the computations. You can check your work with Excel or other statistical software.

I'm sorry, I lied, we have the same A. our approach was different (i prefer your way, though I can't match your RegSS; I used the formula on the bottom of page 88 to get my A.), but we got the same correlation of .6363.

As far as the SE(Bj), we're differing on the SE. My RSS is 7.709233, which yields an SE of 1.049437 (RSS / n-k-1), and that gives me my 0.1498 SE(Bj) result.

RSS = sum of Ei^2, where Ei = yi - yihat. And yihat = alpha + B1*xi1 + B2*xi2 (see bottom of page 86).

I hope that helps, amigo.