(1) Consider the linear regression model with Y
 
0
 
1
X
 
.
Now, assume you have the following data:
X
3
4
6
7
5
Y
2.2
2.8
3.7
4.5
3.5
8 4.3 a) For this sample, compute the OLS estimator for the slope. b) For this sample, compute the OLS estimator for the intercept. c) One of your data points is ( Y = 4.3, X = 8 ). Compute the residual associated with this data point.

(2) Last week in lecture, we estimated a height/weight equation on a new data set of 20 male customers given by
Y i
 
X i where Y i
= the weight in pounds of person i and X i
= height in inches above five feet of person i . Suppose that a friend suggests adding F i
= the percent body fat of person i to the equation. a) What is the reasoning behind adding F i
to the equation? How does the meaning of the coefficient of
X change when you add F ? b) Assume you now collect data on the percent body fat of the 20 males and estimate:
Y i
 
X i

0.28
F i
Do you prefer the former or the latter equation? Why? c) Suppose that you learn that the mean of F for your sample is 12.0—which equation do you prefer now? Why?