Chapter 3.2, Problem 52E

(a)

To determine

To sketch the scatterplot of the data using dash time as the explanatory variable.

Explanation of Solution

The data is given for the dash time and the long-jump distance in the question for the students. Thus, the scatterplot for the same is as:

  

The dash time in seconds is on the horizontal axis and the long jump distance in inches is on the vertical axis.

(b)

To determine

To use the technology to calculate the equation of the least square regression line for predicting the long-jump distance based on the dash time and add the line to the scatterplot of part (a).

Answer to Problem 52E

  $\widehat{y}=414.7862-45.7433x$ .

Explanation of Solution

The data is given for the dash time and the long-jump distance in the question for the students. Now, we have to find the equation of the least squares regression line. Thus, we have,

First press on STAT and then select $1$ : Edit. Then enter the data in the list $L_1$ and enter the other data in the list $L_2$ . Next, press on STAT select CALC and then select LinReg $(a+bx)$ . Next we need to finish the command by entering the list.

  $\text{Linreg}(a+bx)L_1,L_2$

Finally pressing on ENTER ten gives us the following results:

  $\begin{array}{l}y=a+bx\\ a=414.7862\\ b=-45.7433\\ r^2=0.7023\\ r=-0.8380\end{array}$

Thus the equation of the least square regression line will be as:

  $\widehat{y}=414.7862-45.7433x$

And the line added to the scatterplot in part (a) will be as:

  

(c)

To determine

To explain why the line calculated in part (b) is called the least-squares regression line.

Explanation of Solution

The data is given for the dash time and the long-jump distance in the question for the students. Thus, the regression line from part (b) is called the least-squares regression line because this is the straight line that minimizes the sum of the squared residuals. A residual is the difference between the actual y -vale and the predicted y -values.