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Chapter 3: Q. 5.1 (page 181)

For the least-squares regression of fat gain on NEA,r2=0.606. Which of the following gives a correct interpretation of this value in context?

(a) 60.6%of the points lie on the least-squares regression line.

(b) 60.6%of the fat gain, values are accounted for by the least-squares line.

(c) 60.6%of the variation in fat gain is accounted for by the least-squares line.

(d) 77.8%of the variation in fat gain is accounted for by the least-squares line.

Short Answer

Expert verified

The correct option is (c) 60.6%of the variation in fat gain is accounted for by the least-squares line.

Step by step solution

01

Given Information

The coefficient of determination r2for the regression equation fat gain on NEA is 0.606.

02

Explanation

This is a measure of how much variation on a response variable can be explained by the predictor variable.

The NEA explains 60.6%of the variation in fat gain, as indicated by the coefficient of determination.

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Most popular questions from this chapter

The scatterplots below show four sets of real data:

(a) repeats the manatee plot in Figures

(b) shows the number of named tropical storms and the number predicted before the start of hurricane season each year between 1984and 2007by William Gray of Colorado State University;

(c) plots the healing rate in micrometers (millionths of a meter) per hour for the two front limbs of several newts in an experiment; and

(d) shows stock market performance in consecutive years over a 56-year period.

For each graph, estimate the correlation r. Then interpret the value of r in context.

(a)

(b)

(c)

(d)

A government report looked at the amount borrowed for college by students who graduated in 2000and had taken out student loans.12 The mean amount was x=\(17,776and the standard deviation was sx=\)12,034. The median was\(15,532and the quartiles were Q1=\)9900and Q3=\(22,500.

(a) Compare the mean and the median. Also compare the distances of Q1 and Q3 from the median. Explain why both comparisons suggest that the distribution is right-skewed.

(b) The right-skew pulls the standard deviation up. So a Normal distribution with the same mean and standard deviation would have a third quartile larger than the actual Q3.Find the third quartile of the Normal distribution withμ=\)17,776and σ=\(12,034and compare it withQ3=\)22,500.

55. Bird colonies Refer to Exercise 53.
(a) Use your calculator to make a residual plot. Describe what this graph tells you about how well the line fits the data.
(b) Which point has the largest residual? Explain what this residual means in context.

57. Bird colonies Refer to Exercises53 and 55 . For the regression you performed earlier, r2=0.56 and s=3.67. Explain what each of these values means in this setting.

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. "The evidence suggests that the association between the number of extracurricular activities a kid participates in and his or her grade point average is close to zero," the guidance counsellor explains.” A correct interpretation of this statement would be that

(a) active students tend to be students with poor grades, and vice versa.

(b) students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa.

(c) students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities.

(d) there is no linear relationship between a number of activities and grade point average for students at this school.

(e) involvement in many extracurricular activities and good grades go hand in hand.
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