Question

Which of the following statements is supported by these plots?

(a) There is no striking evidence that the assumptions for regression inference are violated.

(b) The abundance of outliers and influential observations in the plots means that the assumptions for regression are clearly violated.

(c) These plots contain dramatic evidence that the standard deviation of the response about the true regression line is not approximately the same everywhere.

(d) These plots call into question the validity of the assumption that $1991$mean ratings vary Normally about the least-squares line for each value of the $1989$mean ratings.

(e) These plots contain many more points than were used by the researchers to fit the least-squares regression. Obviously, there is a major error present.

Short answer

(a) There is no striking evidence that the assumptions for regression inference are violated.

Step-by-step solution

Part (a) step 1: Given Information

We need to find there is no striking evidence that the assumptions for regression inference are violated.

Part (a) step 2: Explanation

There is no obvious pattern in the residual plot and there appear to be outliers in the scatterplot or the residual plot. Then, (a) is then correct, because the assumptions for regression inference are not violated.

Part (b) step 1: Given Information

We need to find the abundance of outliers and influential observations in the plots mean that the assumptions for regression are clearly violated.

Part (b) step 2: Explanation

By observing the above conclusion the given statement the abundance of outliers and influential observations in the plots mean that the assumptions for regression are clearly violated does not fit according to the question.

Part (c) step 1: Given Information

We need to find the plots that contain dramatic evidence that the standard deviation of the response about the true regression line is not approximately the same everywhere.

Part (c) step 2: Explanation

By observing the above conclusion the given statement these plots contain dramatic evidence that the standard deviation of the response about the true regression line is not approximately the same everywhere does not fit according to the question.

Part (d) step 1: Given Information

We need to find these plots call into question the validity of the assumption that $1991$mean ratings vary Normally about the least-squares line for each value of the $1989$mean ratings.

Part (d) step 2:Explanation

By observing the above conclusion the given statement the validity of the assumption that $1991$mean ratings vary Normally about the least-squares line for each value of the $1989$ mean ratings does not fit according to the question.

Part (e) step 1: Given Information

We need to find these plots contain many more points than were used by the researchers to fit the least-squares regression. Surly, there is a major error present.

Part (e) step 2:Explanation

By observing the above conclusion the given statement these plots contain many more points than were used by the researchers to fit the least-squares regression. Surly, there is a major error present does not fit according to the question.