Chapter 23

The regression parameters

1. State the assumptions of the Simple Linear Regression with Normal Noise (SLRNN) model.
2. State the three parameters of the SLRNN model.
3. Relate the components of the SLRNN model (intercept, slope, errors) to their sample analogs (intercept, slope, residuals).
4. Explain in what sense the SLRNN model is “a line plus noise.”
5. State the estimator for the standard deviation of the noise term in the SLRNN model.
6. Identify the estimates for the intercept, slope, and standard deviation of the noise term in an output from summary.

Checking the conditions for inference

1. Use the following four plots to diagnose the validity of the SLRNN model from residuals of a simple linear regression:
   a. A Q-Q plot of the residuals.
   b. A plot of the residuals against the fitted values of the response.
   c. A plot of the squared residuals against fitted values of the response.
   d. A plot of the residuals against the individual index.
2. Identify which SLRNN model assumption is checked using the four residual plots from the previous learning objective.
3. Use mplot and gf_line in mosaic to generate residual diagnostic plots from an output from lm.