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.

**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: houses <- read.table("/usr/users/presnell/sta6208/houses.dat", header=T) # 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

Thu Apr 18 15:52:37 EDT 1996