Long jumps Here are the 40-yard-dash times (in seconds) and long-jump distances (in inches) for a small class of 12 students:

a. Sketch a scatterplot of the data using dash time as the explanatory variable.

b. Use technology to calculate the equation of the least-squares regression line for predicting the long-jump distance based on the dash time. Add the line to the scatterplot from part (a).

c. Explain why the line calculated in part (b) is called the “least-squares” regression line.

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

In the question for the students, the data for the sprint time and the long-jump distance is provided. As a result, the scatterplot for the same is as follows:

On the horizontal axis is the dash time in seconds, while on the vertical axis is the long jump distance in inches.

In the question for the students, the data for the sprint time and the long-jump distance is provided. We must now determine the least-squares regression line's equation. As a result,

$Linreg(a+bx)L1,L2$

Select 1: Edit after pressing STAT for the first time. Then, in list $L1$enter the data, and in list $L2$enter the rest of the information. Next, press $STAT$then pick $CALC$, then $LinReg(a+bx)$After that, we must complete the command by entering the list.

Finally pressing on ENTER ten gives us the following results:

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

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

$\stackrel{⏜}{y}=414.7862-45.7433x$

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

In the question for the students, the data for the sprint time and the long-jump distance is provided. Because it is the straight line that minimizes the sum of the squared residuals, the regression line from component (b) is termed the least-squares regression line. The disparity between the actual and expected y-values is known as a residual.