Chapter 3.2, Problem 55E

(a)

To determine

To interpret the value of s .

Explanation of Solution

The relationship between the x , the height of a student and y , number of steps required to walk the length of a school hallway is given in the question. The regression line is as:

  $\widehat{y}=113.6-0.921x$

And the value of s is as, $s=3.50$ . 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 number of steps required to walk the length of a school hallway using the equation of least square regression line deviated on average by $3.50$ steps from the actual number of steps required to walk the length of a school hallway.

(b)

To determine

To interpret the value of $r^2$ .

Explanation of Solution

The relationship between the x , the height of a student and y , number of steps required to walk the length of a school hallway is given in the question. The regression line is as:

  $\widehat{y}=113.6-0.921x$

And the value of $r^2$ is,

  $\begin{array}{l}{r}^2=0.399\\ =39.9\%\end{array}$

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 $39.9\%$ of the variation in the number of steps required to walk the length of a school hallway is explained by the least square regression line using the height of a student as explanatory variable.