Question

Longer strides In Exercise 43, we summarized the relationship between x =

height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6−0.921x. For this

model, technology gives s = 3.50 and r2 = 0.399.

a. Interpret the value of s.

b. Interpret the value of r2.

Short answer

Part (a) The predicted number of steps required to walk the length of a school hallway differed on average by $3.50$steps from the actual number of steps required to travel the length of a school hallway.

Part (b) The least-square regression line utilizing a student's height as an explanatory variable can explain $39.9\%$ of the variation in the number of steps required to walk the length of a school hallway.

Step-by-step solution

Part (a) Step 1: Given information

The question specifies the link between $x$a student's height, and $y$ the number of steps required to travel the length of a school corridor.

The regression line is as:

$\stackrel{⏜}{y}=113.6-0.921x$

Part (a) Step 2: Explanation

And $s=3.50$ is the value of s. The standard error of the estimations, as we all know, is the average error of forecasts, and thus the average difference between actual and predicted values. Thus, using the equation of least square regression line, the predicted number of steps required to walk the length of a school hallway differed on average by $3.50$ steps from the actual number of steps required to travel the length of a school hallway.

Part (b) Step 1: Explanation

The regression line is as:

$\stackrel{⏜}{y}=113.6-0.921x$

And the value $r^2$is,

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

The coefficient of determination, as we know, is a measurement of how much variation in the answers y variable is explained by the least square regression model with the explanatory variable. As a result, the least square regression line utilizing a student's height as an explanatory variable can explain$39.9\%$ of the variation in the number of steps required to walk the length of a school hallway.