# 10.4E: The Regression Equation (Exercise)

• • OpenStax
• OpenStax
$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where $$x$$ is the number of endorsements the player has and $$y$$ is the amount of money made (in millions of dollars).

$$x$$ $$y$$ $$x$$ $$y$$
0 2 5 12
3 8 4 9
2 7 3 9
1 3 0 3
5 13 4 10
##### Exercise 12.4.2

Draw a scatter plot of the data.

##### Exercise 12.4.3

Use regression to find the equation for the line of best fit.

$$\hat{y} = 2.23 + 1.99x$$

##### Exercise 12.4.4

Draw the line of best fit on the scatter plot.

##### Exercise 12.4.5

What is the slope of the line of best fit? What does it represent?

The slope is 1.99 ($$b = 1.99$$). It means that for every endorsement deal a professional player gets, he gets an average of another \$1.99 million in pay each year.

##### Exercise 12.4.6

What is the $$y$$-intercept of the line of best fit? What does it represent?

##### Exercise 12.4.7

What does an $$r$$ value of zero mean?

It means that there is no correlation between the data sets.

##### Exercise 12.4.8

When $$n = 2$$ and $$r = 1$$, are the data significant? Explain.

##### Exercise 12.4.9

When $$n = 100$$ and $$r = -0.89$$, is there a significant correlation? Explain.

This page titled 10.4E: The Regression Equation (Exercise) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.