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Data were recorded for 117 months on a household's gas bill (in dollars) and the average monthly temperatures for its neighborhood. The mean monthly temperature was 48.7° F with a standard deviation of 20.6. The mean gas bill price was $81.20 with a standard deviation of 66.5. The correlation coefﬁcient between monthly temperature and gas bill price is −0.92.
-Determine the correct value of the slope for the linear model that predicts gas bill price from monthly temperature and interpret it in context.
A)The slope is −2.97.For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $2.97.
B)The slope is −2.97.For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by 2.97°.
C)The slope is −0.28.For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $0.28.
D)The slope is −0.28.For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by 0.28°.

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Quizplus · Accepted Answer

The slope of the linear model that predicts gas bill price from monthly temperature can be calculated using the formula for the slope in a regression line, which is $slope = r(\frac{s_y}{s_x})$, where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the dependent variable (in this case, gas bill price), and $s_x$ is the standard deviation of the independent variable (in this case, monthly temperature). Plugging in the given values: $slope = -0.92(\frac{66.5}{20.6}) ≈ -2.97$. This means for every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $2.97, which matches choice A's interpretation.

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