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 am confused. On the HW it says to show the formulas and the computations. However, you say no need to do work by hand. So can I just give a list of answers to A-F from Excel, or do I need to show the manual work?

[NEAS: Just state the formula or computation that Excel does; you don't have to reproduce the mathematics.]