Q 52. Long jumps Here are the 40-yard-... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 3: Q 52. (page 205)

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 鈥渓east-squares鈥� regression line.

Short Answer

Expert verified

Part (b) $\overset{铃�}{y} = 414.7862 鈭� 45.7433 x$

Part (c) A residual is a difference between the actual $y -$ values and the predicted $y -$ values.

Part (a)

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Concept

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

Part (a) Step 3: Explanation

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.

Part (b) Step 1: Calculation

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,

$L i n r e g (a + b x) L 1, L 2$

Select 1: Edit after pressing STAT for the first time. Then, in list $L 1$ enter the data, and in list $L 2$ enter the rest of the information. Next, press $S T A T$ then pick $C A L C$ , then $L i n R e g (a + b x)$ After that, we must complete the command by entering the list.

Finally pressing on ENTER ten gives us the following results:

$y = a + b x a = 414.7862 b = 鈭� 45.7433 r^{2} = 0.7023 r = 鈭� 0.8380$

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

$\overset{铃�}{y} = 414.7862 鈭� 45.7433 x$

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

Part (c) Step 1: Explanation

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.