Chapter 12.1, Problem 4E

To determine

To check whether the conditions are performing inference about the regression model are met.

Answer to Problem 4E

All conditions are met.

Explanation of Solution

In the question researchers examined how well does the number of beers a person drinks predict his or her blood alcohol content. Sixteen volunteers with an initial BAC of zero drank randomly assigned number of cans of beer. Least squared regression line was performed on the data. A residual plot and a histogram of the residual are shown in the question. Thus, as we know that there are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random. Thus, we have,

Linear: Satisfied, because all points in the residual plot are centered about 0.

Independent: Satisfied, because the subjects were randomly assigned.

Normal: Satisfied, because the histogram is roughly bell-shaped.

Equal variance: Satisfied, because the vertical spread of the points in the residual plot is about the same everywhere.

Random: Satisfied, because the subjects were randomly assigned.

Thus all conditions have been satisfied.