- 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:
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
