In a random sample of automobiles the highway mileage (in mpg) and the engine si

Question

In a random sample of automobiles the highway mileage (in mpg) and the engine size (in liters) are measured, and the following computer output for regression is obtained: mpg: Mean = 28.5882 and SD = 5.88493 Mean liter = 2.52353 and SD = 0.898978 Dependent variable is: mpg R-sq = 49.8% R-sq(adj) = 46.5% Variable Coef s.e. t p Constant 40.2462 3.197 12.6 0.0001 liter -4.61969 1.198 -3.86 0.0015 s = 4.306 Assume all conditions for regression inference are met. (a) One of the points on the regression line corresponds to an auto with an engine size of 1.5 liters and highway mileage of 35 miles per gallon. What is die residual of this point? Suppose another auto with an engine size of 5.0 liters and highway mileage of 17 mpg is added to the data set. (b) Explain whether the new slope will be greater than, less than, or about the same as the slope given by the output above. (c) Explain whether the new correlation will be greater than, less than, or about the same in absolute value as the correlation given by the output above.

Explanation / Answer

The regression equation is

highway mileage = 40.2462 - 4.61969*engine size

when engine size=1.5 liters,

predicted highway mileage = 40.2462 - (4.61969*1.5) =33.3167

residual=observed - predicted = 35-33.3167=1.68330

b) when engine size=5 liters,

predicted highway mileage = 40.2462 - (4.61969*5) = 17.1478

observed highway mileage = 17

since there is no significant difference between observed and predicted highway mileage, so the new slope will be almost same as the slope given by the output above.

c) since the slope will not change significantly, so the new correlation will be the same in the absolute value as the correlation given by the output above.

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