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Chapter 12: Q. 66 (page 721)

66. Can a coefficient of determination be negative? Why or why not?

Short Answer

Expert verified

A coefficient of determination cannot be negative.

Step by step solution

01

Given information

A coefficient of determination can be negative or not.

02

Explanation

A Coefficient of finding R2 is the linear equation utilized for prediction. The coefficient of a conclusion is estimated as follows:
R2=1鈭�SSresSStot

SSres=鈭�i=1n鈥�ei2

SStot=鈭�i=1n鈥�yi鈭�y炉2

where SSres,SStotsum of residuals and the total sum of squares, respectively. Since, r nearer to 1 is that the standard is better.
From the earlier, the coefficient of the conclusion can't be negative. It has values between 0 and 1 . And if theR2 is small, the model used for prediction is not appropriate and requires fixing because it received the wrong predicted values.

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Most popular questions from this chapter

60. The following table shows the poverty rates and cell phone usage in the United States. Construct a scatter plot of the data

Year
Poverty Rate
Cellular Usage per Capita
2003
12.7
54.67
2005
12.6
74.19
2007
12
84.86
2009
12
90.82

For a given line of best fit, you computed that r=0.6501 using n=12 data points and the critical value is 0.576. Can the line be used for prediction? Why or why not?

For each of the following situations, state the independent variable and the dependent variable.

a. A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than other drivers. The number of fatalities per100,000 driver is compared to the age of drivers.

b. A study is done to determine if the weekly grocery bill changes based on the number of family members.

c. Insurance companies base life insurance premiums partially on the age of the applicant.

d. Utility bills vary according to power consumption.

e. A study is done to determine if a higher education reduces the crime rate in a population.

Do you think a linear fit is best? Why or why not?

Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges \(25+\)20per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit isy=25+20x. What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.
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