Chapter 9, Problem 6E

(a)

To determine

To explain does this mean that a linear model is not appropriate.

Answer to Problem 6E

It is not appropriate.

Explanation of Solution

A student who has created a linear model is disappointed to find that her $R^2$ value is very low that is, $R^2=13\%$ . But, $R^2=13\%$ just means that the particular linear model that the student is utilizing is not appropriate as the proportion of the variance for a dependent variable that's explained by an independent variable or variables in the model is very low. Thus, the linear model is not appropriate.

(b)

To determine

To explain does this model allow the student to make accurate predictions or not.

Answer to Problem 6E

It does not allow to make accurate predictions.

Explanation of Solution

A student who has created a linear model is disappointed to find that her $R^2$ value is very low that is, $R^2=13\%$ . It explains that the proportion of the variance for a dependent variable that's explained by an independent variable or variables in the model is very low. And we know that the linear model the student is using will only accurately predict $13\%$ of the time, which is very inaccurate. Thus, we can say that it does not allow to make accurate predictions.