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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:

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

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

$\stackrel{铃�}{y}=414.7862鈭�45.7433x$

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.