1. The multicollinearity data from the notes are given below. Recall that x₁=2x₂-10.

x₁ x₂ y

2 6 23

8 9 83

6 8 63

10 10 103

4 7 43

12 11 123

(a) Find a regression model that fits the data perfectly with ₁= 0

(b) Find a regression model that fits the data perfectly with ₁=-10

2. Suppose we run the following regressions on the data below:

Model A: y vs x_1,x₂

Model B: y vs x₁

x₁ x₂ y

2 3.5 -25.4

2 -2.5 5.8

2 -2.5 -0.5

2 1.5 -19.5

-2 1.5 -23.8

-2 -2.5 -4.2

-2 -2.5 -23.2

-2 3.5 -50.2

(a) Compare the slope of x₁ for the two models. Are they equal or different? What feature of the data that makes this happen?

(b) Compare the t-value of x₁ for the two models. Are they equal or different? Can you explain why?