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Regression

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8. Consumer Debt Credit card debt has risen steadily over the years. The table above gives the average U.S. credit card debt (in dollars) per household. Years are represented as the number of years since 1900. (The table above includes all credit cards and U.S. households with at least one credit card.)*
a. Plot the data. Does the graph show a linear pattern?
b. Find the equation of the least squares line and graph it on the same axes. Does the line appear to be a good fit?
c. Find and interpret the coefficient of correlation.
d. If this linear trend continues, when will household debt reach $10,000?
9. Used Car Sales As cars are becoming more expensive, used car sales have increased at a faster rate since 1984 than new car sales.* Sales in millions from 1984 to 1996 are given in the table below.
Sales
Year Sales Year

84 12.3 91 12.3
85 13.2 92 12.8
86 13.6 93 13.9
87 13.2 94 15.0
88 14.5 95 14.7
89 14.5 96 14.6
90 13.8

9.
a. Find the equation of the least squares line and the coefficient of correlation.
b. Find the equation of the least squares line using only the data for every other year starting with 1985,1987, and so on. Find the coefficient of correlation.
c. Compare your answers for parts a and b. What do you find? Why do you think this happens?

10. Medical School Admissions According to the American Association of Medical Colleges, the number of applica¬tions to medical schools in the United States began to decrease since 1996 as indicated in the following table.* Years are represented as the number of years since 1900 and applications are given in thousands.

Year (x) 94 95 96 97 98 99 00
Applications (y) 45.4 46.6 47.0 43.0 41.0 38.5 37.1
a. Plot the data. Do the data points lie in a linear pattern?
b. Determine the least squares line for this data and graph it on the same coordinate axes. Does the line fit the data reasonably well?
c. Find the coefficient of correlation. Does it agree with your estimate of the fit in part b?

d. Explain why the coefficient of correlation is close to 1, even though some of the data points do not appear to be linear.

11. Bird Eggs The average length and width of various bird eggs are given in the following table.

Bird Name Width (cm) Length (cm)
Canada goose 5.8 8.6
Robin 1.5 1.9
Turtledove 2.3 3.1
Hummingbird 1.0 1.0
Raven 3.3 5.0
a. Plot the points, putting the length on the y-axis and the width on the x-axis. Do the data appear to be linear?
b. Find the least squares line, and plot it on the same graph as the data.
c. Suppose there are birds with eggs even smaller than those of hummingbirds. Would the equation found in part b continue to make sense for all positive widths, no matter how small? Explain.
d. Find the coefficient of correlation.

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