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Chapter 3: Q 39. (page 203)
Residual wins Refer to Exercise 37. The Chicago Cubs won the World
Page Number: 203 Series in 2016. They had 103 wins and spent $182 million on the payroll. Calculate and interpret the residual for the Cubs.
Residual is
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Each year, students in an elementary school take a standardized math test at the end of the school year. For a class of fourth-graders, the average score was 55.1 with a standard deviation of 12.3. In the third grade, these same students had an average score of 61.7 with a standard deviation of 14.0. The correlation between the two sets of scores is r = 0.95. Calculate the equation of the least-squares regression line for predicting a fourth-grade score from a third-grade score.
a. y^=3.58+0.835x
b. y^=15.69+0.835x
c. y^=2.19+1.08x
d. y^=鈭�11.54+1.08x
IQ and grades Exercise 3 (page 158) included the plot shown below of school grade point average (GPA) against IQ test score for seventh-grade students. (GPA was recorded on a -point scale with .) Calculation shows that the mean and standard deviation of the IQ scores areand For the GPAs, these values are . The correlation between IQ and GPA is
(a) Find the equation of the least-squares line for predicting GPA from IQ. Show your work.
(b) What percent of the observed variation in these students鈥� GPAs can be explained by the linear relationship between GPA and IQ?
(c) One student has an IQ of but a very low GPA of . Find and interpret the residual for this student
Using data from the LPGA tour, a regression analysis was performed using x = average driving distance and y = scoring average. Using the output from the regression analysis shown below, determine the equation of the least-squares regression line.
a. y^=87.974+2.391x
b. y^=87.974+1.01216x
c. y^=87.974鈭�0.060934x
d. y^=鈭�0.060934+1.01216x
e. y^=鈭�0.060934+87.947x
Penguins diving A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater.41 For all but the shallowest dives, there is an association between x = depth (in meters) and y = dive duration (in minutes) that is different for each penguin. The study gives a scatterplot for one penguin titled 鈥淭he Relation of Dive Duration (y) to Depth (x).鈥� The scatterplot shows an association that is positive, linear, and strong.
a. Explain the meaning of the term positive association in this context.
b. Explain the meaning of the term linear association in this context.
c. Explain the meaning of the term strong association in this context.
d. Suppose the researchers reversed the variables, using x = dive duration and y = depth.
Less gas? Refer to Exercise 38.
a. Interpret the slope of the regression line.
b. Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.
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