The following estimated regression equation has been proposed to predict sales at a fast food outlet. ý = 16 - 4x₁ + 8x₂ + 14x3 where x₁ = the number of competitors within 1 mile. x₂ = the population within 1 mile (in 1,000s) X3 = 1 if drive-up windows are present; 0 otherwise ŷ = estimated sales (in $1,000s) (a) What is the interpretation of 14 (the coefficient of x3) in the regression equation? (Give the answer in dollars.) Sales in dollars at outlets with drive-up windows are on average $ 14 X higher than those without (b) Predict sales for an outlet with 3 competitors within one mile, a population of 14,000 within one mile, and one drive-up window (give the answer in dollars). $130 X Need Help? drive-up windows. (c) Predict sales for an outlet with 3 competitors within one mile, a population of 14,000 within one mile, and no drive-up window (give the answer in dollars). $112004 X Read It

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

Does Table 2 represent a linear function? If so, finda linear equation that models the data.

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?