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.

Parts B,C,D: Why are we being asked for alpha first, when we need beta1 and beta2 to find alpha? Am I misunderstanding the question?

Parts E,F: Are you refering to the formula in the gray box at the top of page 105?
SE(B) = S-sub-E/sqrt(sum(x-sub-i - x-bar)^2))


EDIT: Nope. It's the forumla in the gray box on page 107. Wish someone had told me a lot sooner.

Why are we using a formula from P.107 for Module 10 when Module 10 covered pages 92-96?