Consider the soil absorption data in Exercise 12.1.4.

a. Find 95% confidence intervals on the regression coefficients.

b. Find a 95% confidence interval on the mean soil absorption index when \(x_{1}\) = 200 and \(x_{2}\) = 50.

c. Find a 95% prediction interval on the soil absorption index when \(x_{1}\) = 200 and \(x_{2}\) = 50.

Text Transcription:

x_1

x_2

STA 215 Chapter 8 Regression Wisdom Looking at residuals is the easiest way to check for linearity. Residuals reveal subtleties not apparent from the scatterplot. They can also help us focus on the appropriateness of the regression line. Example: Below is a scatter plot of the Dive Heart Rate (beats per minute) and the Duration (minutes) of dives by emperor penguins. This also includes a residual plot. Are the assumptions for linear regression (discussed in Chapter 7) met Discuss. th Intro Stats, 4 Edition, by Richard D. De Veaux, Paul F. Velleman, and David E. Bock, 2014. Example: Nutritionists, concerned about “empty calories” in breakfast cereal, recorded facts about 77 cereals, including their calories per serving and sugar content (in grams). The scatterplot and residual plot are below. Are the assumptions for linear regression met Discuss. Below is a histogram of the residuals for the breakfast cereal data. What features of this histogram may cause concern that the scatterplot and residual plot did not alert us to Intro Stats, 4 Edition, by Richard D. De Veaux, Paul F. Velleman, and David E. Bock, 2014. As it turns out, the high residual cereals are what you would call the “healthy cereals.” Most of these contain both fruit and nuts and