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Chapter 4: Q. 4.133 (page 189)
The coefficient of determination of a set of data points is and the slope of the regression line is . Determine the linear correlation coefficient of the data.
The linear correlation coefficient
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Fill in the blanks.
a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.
b. In regression analysis, an_______ is a data point where removal causes the regression equation to change considerably:
Rental-Car Costs. During one month, the Avis Rent Car rate for renting a Buick LeSabre in Mobile, Alabama, was per day plus per mile. For a one day rental, let denote the number of miles driven and let denote the total cost, in dollars.. The linear equation is
a. Find the y-intercept and slope of the specified linear equation.
b. Explain what the y-intercept and slope represent in terms of the graph of the equation.
c. Explain what the y-intercept and slope represent in terms relating to the application.
Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years and what influences it is a concern in U.S. colleges and universities.
US News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the per centage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).
a. Draw a scatterplot of the data.
b. Is finding a regression line for the data reasonable? Explain your answer.
c. Determine the regression equation for the data, and draw its graph
on the scatterplot you drew in part (a).
d. Describe the apparent relationship between student-to-faculty
ratio and graduation rate.
e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?
f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.
g. Identify outliers and potential influential observations
Fill in the blank.
The graph of a linear equation with one independent variable is a _____.
Corvette Prices. The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10 randomly selected Corvettes between 1 and 6 years old.
Here, denotes age, in years, and denotes price, in hundreds of dollars. For part (g). predict the prices of a 2 -year-old Corvette and a 3-year-old Corvette.
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