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A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city
and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg
was 35 with a standard deviation of 8.6. The correlation coefﬁcient between city mpg and highway mpg is
-Determine the correct value of the slope for the linear model that predicts highway mpg from city mpg and interpret it in context.
A)The slope is 0.888.For every one mpg increase in city mpg, the highway mpg is predicted to increase by 0.888.
B)The slope is 0.888.For every one mpg increase in highway mpg, the city mpg is predicted to increase by 0.888.
C)The slope is 1.016.For every one mpg increase in city mpg, the highway mpg is predicted to increase by 1.016.
D)The slope is 1.016.For every one mpg increase in highway mpg, the city mpg is predicted to increase by 1.016.

Question

Quizplus · Accepted Answer

The slope of the linear model that predicts highway mpg from city mpg can be calculated using the formula for the slope in linear regression, which is $ \frac{r \cdot \sigma_y}{\sigma_x} $, where $ r $ is the correlation coefficient, $ \sigma_y $ is the standard deviation of the dependent variable (in this case, highway mpg), and $ \sigma_x $ is the standard deviation of the independent variable (in this case, city mpg). Although the correlation coefficient $ r $ is not provided in the question, the correct interpretation of the slope is that for every one unit increase in the independent variable (city mpg), the dependent variable (highway mpg) is predicted to increase by the slope value. Choice A correctly identifies the relationship direction (from city mpg to highway mpg) and provides a plausible slope value with the correct interpretation.

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