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.

Did you use the same value of Rj in calculating the values of SE(B1) and SE(B2)?
I am getting SE(B1) = SE(B2) = 0.19196 and r=0.636363 which is what I used as Rj

Some one please elaborate on the calculation of Rj part? Will it be the same for calculating for both SE(B1) and SE(B2)?

[NEAS: X₁ and X₂ have the same ten values, though arranged differently, so they have the same standard errors, which are 0.14978. The correlation of the two independent variables is 0.636364, as noted above.]