Section 3.1: Diagnostics for Predictor Variables

1. Construct exploratory plots for the predictor in a simple linear regression.

Section 3.2: Residuals

1. State the 6 most important departures from the SLRGN model.
2. Explain why it is necessary to check that the SLRGN model holds before computing inferential statistics under the SLRGN model.

Section 3.3: Diagnostics for Residuals

1. State the five common diagnostic plots involving the sample residuals.
2. Sketch diagnostic plots for the sample residuals when the all of the assumptions of the SLRGN model are met.
3. Given diagnostic plots from sample residuals, identify what departures from the SLRGN model are indicated (or not) by the diagnostic plots.
4. Explain the rationale for each of the five diagnostic plots in terms of the assumptions of the SLRGN model.

Section 3.9: Transformations

1. Explain why a model of the form
   \[Y = \beta_{0} + \beta_{1} f(X) + \epsilon\]
   is still a simple linear regression in the transformed variable \(f(X)\).
2. Identify appropriate transformations of a predictor variable from a plot of the response versus the predictor.

R

1. Access the residuals from an output from lm.
2. Construct residual diagnostic plots “by hand” using functions from ggformula.
3. Construct residual diagnostic plots using plot’s built-in functionality with an output from lm.
4. Fit models of the form
   \[Y = \beta_{0} + \beta_{1} f(X) + \epsilon\]
   using lm where \(f\) is a polynomial or logarithmic function.