Stat 552
# Homework 4

##### Due 3pm Dec 5th in class

**Reading**:Faraway Chapter 3 (not 3.3 and not 3.6) & 4

**Due Feb 5th 3pm** Hardcopy in class, .Rmd on canvas. (Use #1 to practice your math typesetting in markdown).

**1.** Your turn from Monday: Consider hypotheses of the form . What are and for exercises 1 and 5 from the F-test exercises handout?

**2.**
Consider the cheddar cheese example and full model fitted,

Examine the output from

Each line corresponds to an F-test. What models are being compared? Verify your answers by fitting the models explicitly and doing three separate `anova`

calls (you might you need to use the `scale`

argument to `anova`

) (Hint: `?anova.lm`

)

**3.** Faraway 3.7 + **(i)** Produce a plot that displays the predicted distances as a function of left leg strength for a range of right leg strengths and average (according to this data) left and right leg flexibilities, using the model you fit in part (a). **(j)** Produce a plot that displays the predicted distances for your preferred model.

**4.** Generate a single fixed design matrix with 30 rows where , and are columns each generated by drawing observations from a Uniform(-1, 1) independently. (We are generating the ’s randomly but once you have done it once, we will treat them as fixed).

Simulate a response according to the model: where

Fit the regression model (using `lm`

) and retain the coefficient estimates .

Repeat 5000 times and produce:

- histograms (or density curves) of the parameter estimates (including ) with curves of their theoretical distributions overlaid.
- a histogram of with a curve of its theoretical distribution overlaid
- a scatter plot of and

This gives us a starting point for examining how violations to our assumption might affect our distributional results.