STAT 425
Statistical Modeling I
Spring 2024
Homework No. 4
1
Instructions
Due Date: Mar 4th, 11:59 pm
Homework presentation should be neat and submitted through Canvas.
R codes should be sub-
mitted through Canvas as well. Please use RMardown to prepare your solutions, and submit your
.Rmd file (source code) and your .pdf file, after doing the
knitting
of the .Rmd file. Only two files
should be submitted for your homework: Your .Rmd files and your .pdf file. For more information
about R Markdown you can also check this link.
You must show all your work for full credit.
If you feel it would help, you are encouraged
to work together with your class mates on the Homework, but you have to present assignments
individually using your own words.
The aim of the Homework is to help you learn the material and practice for the exams.
Late
assignments will not be accepted
. Graduate students should attempt
all
problems. Under-
graduate students can skip problems marked as GR (if any).
2
Problems
1.
Problem 1
: For the
salmonella
data set fit a linear model with
colonies
as the response,
and log(
dose
+ 1) as predictor.
(a) Comments on the diagnostic plot results.
(b) Use an appropriate test to determine whether the model fits the data well (Hint: Check
for lack of fit)
2.
Problem 2
: The
gammaray
data set shows the x-ray decay light curve of gamma ray burst.
Note that the measurement errors on the response are provided (
error
).
(a) Plot the data and comment on your results.
(b) Is there any transformation suggested for the response and/or the predictors? Justify
your answer.
(c) Build a model to predict the flux as a function of time using appropriate transformations
of the response and/or predictors and appropriate weights (Hint: consider using weighted
least squares).
3.
Problem 3
: For the
longley
data set, fit a model with
Employed
as the response and the
other variables as predictors.
(a) Compute and comment on the correlation between predictors.
(b) Compute and comment on the Condition number. Is there an indication of collinearity?
(c) Compute and comment on the variance inflation factors.
