Chapter 3.2, Problem 56E

(a)

To determine

To interpret the value of s .

Explanation of Solution

The relationship between the temperature in degrees Fahrenheit and chirps per minute for the striped ground cricket is given in the question. And the regression line is as:

  $\widehat{y}=0.31+0.212x$

And the value of s is, $s=0.97$ . As we know that the standard error of the estimate s represents the average error of predictions thus the average deviation between actual and the predicted values. Thus the predicted chirps per minute for the striped ground cricket using the equation of least square regression line deviated on average by $0.97$ chirps from the actual chirps per minute for the striped ground cricket.

(b)

To determine

To interpret the value of $r^2$ .

Explanation of Solution

The relationship between the temperature in degrees Fahrenheit and chirps per minute for the striped ground cricket is given in the question. And the regression line is as:

  $\widehat{y}=0.31+0.212x$

And the value of $r^2$ is,

  $\begin{array}{l}{r}^2=0.697\\ =69.7\%\end{array}$

As we know that the coefficient of determination measures the proportion of variation in the responses y variable that is explained by the least square regression model using the explanatory x variable. Thus, we can say that $69.7\%$ of the variation in the chirps per minute for the striped ground cricket is explained by the least square regression line using the temperature as explanatory variable.