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Assignment 4

Due Wednesday, February 21.

Turn in problems # 2 and 3.

Problem 1:
In the case of simple linear regression, show that

where

From this, show that , , and are pairwise orthogonal to each other. (See page 96 of Rawlings.)

Problem 2:
The data in the file fl-crime.dat are described in the file fl-crime.txt. Create a data-frame using the command:
`fl.crime <- read.table("/usr/users/presnell/sta6208/fl-crime.dat")`
(a)
Fit the linear regression of cr on urb, inc, hs, fem, and un. Give the fitted regression equation. Interpret the value of . Comment on anything else that seems interesting.
(b)
After accounting for urb, is there any evidence that cr depends on the socio-economic variables inc, hs, fem, and un? Perform an appropriate F-test to address this question.

We will return to this data in another assignment.
Problem 3:
The data in the file houses.dat are described in the file houses.txt. Use the following sequence of commands to create a data-frame omitting the data for the new houses:
```# Read the data:
# Extract just the old houses for now, and eliminate the variable "New":
old <- houses\$New==0
old.houses <- houses[old,-5]```
(a)
For the old houses, regress Price on Area, Bdrm, and Bath. Comment on the results of the various (partial) t-tests. Would you eliminate any of the predictors from the regression equation? Why or why not?
(b)
Choose a model, and give a 95% prediction interval for the selling price of my (old) Northwest Gainesville home, which has 2300 square feet of floor space, 3 bedrooms, and 2 baths.

Rawlings:
# 3.11, 3.13, 4.1 (Note that the X'X matrix here is block diagonal. To invert it, Replace the blocks by their inverses.), 4.5, 4.7, 4.12

Brett Presnell
Thu Apr 18 15:52:37 EDT 1996