Chapter 8, Problem 23E

(a)

To determine

To explain what is wrong with each interpretation.

Explanation of Solution

It is given that a biology student who created regression model to use a bird’s height when perched for predicting its wingspan made the statements. Thus, the interpretation he made was that “ my $R^2\text{ of 93\%}$ shows that this linear model is appropriate”. Thus, this interpretation is wrong because $R^2$ does not tell whether the model is appropriate but measures the strength of the linear relationship. And also high $R^2$ could also be due to an outlier.

(b)

To determine

To explain what is wrong with each interpretation.

Explanation of Solution

It is given that a biology student who created regression model to use a bird’s height when perched for predicting its wingspan made the statements. Thus, the interpretation he made was that “A bird ten inches tall have a wingspan of $17$ inches”. Thus, this interpretation is wrong because predictions based on regression line are estimates of average value of y of x . the actual wingspan will vary around the prediction.