Question 6.68

33. In Exercise 5, you made a scatterplot of city and highway gas mileage for the 12 nonhybrid midsized cars (omitting the Prius) in Table 5.7 (page 196).

  1. The equation of the least-squares regression line for predicting highway mileage from city mileage is

    Redo your scatterplot of highway mileage against city mileage from Exercise 5 (omitting the Prius). Add a graph of the least-squares regression line to the plot. Be sure to show how you were able to plot the line starting with its equation.

    image
  2. Use the “up-and-across” method illustrated in Figure 6.6 (page 251) to show the predicted highway mileage of a midsized car that gets 18 mpg in the city. Approximately what is the predicted highway mileage for this car?
  3. Now use the equation of the least-squares regression line to predict the highway mileage of a car that gets 18 mpg in the city. Compare your result with your graphical estimate in part (b).
  4. Based on the scatterplot and the graph of the least- squares regression line, do you expect your prediction from part (c) to be very accurate? Why or why not?

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Algebra Review Appendix

Graphing a Line in Slope-Intercept Form

33.

(a) One way to graph the least-squares regression line is to mark its , to mark a second point and draw the line.

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(b) Approximately 27 mpg, as shown below

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(c) 26.9 mpg

(d) Sample response: If we look at the two data points associated with 17 City mpg (the closest in City mpg to what we are trying to predict), we see that one car gets 25 City mpg and another gets 28. The corresponding residuals are −1.18 and 1.82, respectively. So, in our prediction, we might expect to be off by as much as 1.82 mpg.

A-15

(a) 11.2, 37.3, and 18.3, respectively

(b) 26.96, 26.49, and 25.87, respectively

(c)

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(d) No; the least-squares line gives the best straight-line fit and these data do not show a straight-line pattern.