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

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

Short Answer

Expert verified

The equation for the line of best fit isy=2.23+1.98x

Step by step solution

01

Step-1 Given Information

Given in the question that, a random sample of ten professional athletes produced the following data where xis the number of endorsements the player has and yis the amount of money made.

02

Explanation 

To find the regression line in Excel, follow these steps:

Fill in the blanks in Excel as indicated below:


AB
1
x

y
202
338
427
513
6513
7512
849
939
1003
11410

Click on data →Data Analysis→Regression.

Enter the input and output as shown below:

Click on OK. The output is:

03

Final Answer 

Therefore, the linear regression equation is:y=2.23+1.98xy=2.23+1.98x

Amount of money made =2.23+1.98×number of endorsements

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Most popular questions from this chapter

61. Does the higher cost of tuition translate into higher-paying jobs? The table lists the top ten colleges based on mid-career salary and the associated yearly tuition costs. Construct a scatter plot of the data.

School
Mid-Career Salary( in thousands)
Yearly Tuition
Princeton
137
28,540
Harvey Mudd
135
40,133
CalTech
127
39,900
US Naval Academy
122
0
West Point
120
0
MIT
118
42,050
Lehigh University
118
43,220
NYU-Poly
117
39,565
Babson College
117
40,400
Stanford
114
54,506

For a given line of best fit, you compute that r = 0 using n = 100 data points. Can the line be used for prediction? Why or why not?

Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y=12,000x.

How many pounds of soil does the shoreline lose in a year?

Using the data to determine the linear-regression line equation with the outliers removed. Is there a linear correlation for the data set with outliers removed? Justify your answer.

75. The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days:

Swim Time
Heart Rate
34.12
144
35.72
152
34.72
124
34.05
140
34.13
152
35.73
146
36.17
128
35.57
136
35.37
144
35.57
148

a. Enter the data into your calculator and make a scatter plot.
b. Use your calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a.
c. Explain in words what the slope and y-intercept of the regression line tell us.
d. How well does the regression line fit the data? Explain your response.
e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.

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