Stat 411/511
# Final Study Guide

The final is cumulative. You can expect questions from all the material we have covered, so look at all the quiz study guides as well.

**Practice Questions: Conceptual Exercises in Sleuth**

Page 198: 1, 3, 4, 5, 6, 7, 8, 9, 10a, 11

Page 235: 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14

State the model for the mean in a simple linear regression? Which variable is the response, and which is the explanatory variable?

In plain English, what is the interpretation of the intercept and slope parameters.

What is the difference between interpolation and extrapolation? Why is extrapolation dangerous?

What is a fitted value? What is a residual?

Use R output from `summary(fit)`

to identify the estimates and their standard errors, and the estimate of the subpopulation standard deviation, σ. What are the degrees of freedom on the standard errors?

Use R output from `summary(fit)`

, to calculate 95% confidence intervals for the slope or intercept (I’d give you the `qt(...)`

value).

Find the estimate of the mean response for a given explanatory value? What does the standard error depend on?

What do we minimize to find the least squares estimate of the slope and intercept?

Is the standard error on a prediction of the response for a given explanatory variable, bigger or smaller than the standard error on the mean response at the same value? Why?

There are three types of interval we might construct in a simple linear regression. Write down the common mathematical form they all take. What are the differences between them?

List the three important properties of the sampling distributions of the least squares estimates for the slope and intercept.

What are the four assumptions of linear regression? Which one is simple linear regression robust to, and under what condition?

Describe the three residual plots used to check assumptions. Which assumption does each check? What patterns in the plot give evidence against the assumption?

What are the two models being compared in the regression ANOVA?

What are the two models being compared in the lack-of-fit F-test?

How could you determine if a log transform of one or both of the variables is appropriate?

What does R-squared measure?

Is simple linear regression resistant to outliers?

Know how to compute a lack-of-fit F-statistic using the results from a regression ANOVA and one-way ANOVA for a dataset with replicated explanatory values.