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.

Not sure what anybody else is getting for the answers, but I am not getting it, so I will share what I have done, and hopefully I somebody can help guide me on the correct path.

A) Correlation=R=Root(RegSS/TSS)=Root(33.409/82.5)=.6363...

B)A=Ybar-b1x1bar-B2X2bar=4.4893

c/D) the formulas on page 88 for B1 and B2 for answers of .879833 and -.97417 respectively

E) for Se i am getting 5.069936 which is Root(RSS/n-k-1)=root(179.9298/10-2-1),

r is .63

then I plug this into SE(B1)=Se/ROOT{(1-.63^2)*82.5} where 82.5 is sum(xij-Xbarj)^2=.71875

[NEAS: The values for r, B1, and B2 are correct. the standard error is not correct.]