Section 2.4: Interval Estimation for the Mean Response

1. State the mean and variance of the estimate of the mean response under the SLR model.
2. State the sampling distribution of the estimate of the mean response under the SLRGN model.
3. Explain how to studentize the estimate of the mean response under the SLRGN model, and how this is useful for performing hypothesis tests, constructing confidence intervals, etc., related to the mean response.
4. State and compute the confidence interval for the mean response under the SLRGN model.
5. Sketch, roughly, how the confidence interval for the mean response behaves as a function of the predictor variable.
6. Properly interpret what a confidence interval for the mean response indicates provided its confidence level.

Section 2.5: Prediction Intervals for a New Response

1. Define a prediction interval for a new response, and contrast it with the confidence interval for the mean response.
2. State and compute the prediction interval for a new response under the SLRGN model when the population parameters are known.
3. State and compute the prediction interval for a new response under the SLRGN model when the population parameters are unknown.
4. Sketch, roughly, how the prediction interval for a new response behaves as a function of the predictor variable.
5. Sketch, roughly, how the confidence interval for the mean response and the prediction interval for a new response compare in terms of their widths.
6. State the limiting behavior of the width of confidence intervals for the mean response and prediction intervals for a new response under the SLRGN model.

Computing and Plotting SLRGN Intervals in R (Lecture Notes for Lecture 9)

1. Compute confidence intervals for the mean response under the SLRGN model using an output from makeFun.
2. Compute prediction intervals for a new response under the SLRGN model using an output from makeFun.
3. Plot confidence intervals for the mean response and prediction intervals for a new response using gf_lm.