8 scientists compared the maximum weight (in pounds) and average life expectancy (in years) of 16 dog…

8 scientists compared the maximum weight (in pounds) and average life expectancy (in years) of 16 dog breeds. let x be the average life expectancy of the dog breed and y be the maximum weight of the dog breed. the least - squares regression line $hat{y}=329.4 - 21.6x$ was calculated from the data. suppose all the values for maximum dog weight were converted from pounds to kilograms (1 kilogram = 2.2 pounds). which of the following gives the equation of the least - squares regression line for the updated data with x = average life expectancy and y = maximum weight (in kilograms)? a) $hat{y}=149.73 - 21.6x$ b) $hat{y}=149.73 - 9.82x$ c) $hat{y}=329.4 - 9.82x$ d) $hat{y}=329.4 - 21.6x$ e) not enough information

8 scientists compared the maximum weight (in pounds) and average life expectancy (in years) of 16 dog breeds. let x be the average life expectancy of the dog breed and y be the maximum weight of the dog breed. the least - squares regression line $hat{y}=329.4 - 21.6x$ was calculated from the data. suppose all the values for maximum dog weight were converted from pounds to kilograms (1 kilogram = 2.2 pounds). which of the following gives the equation of the least - squares regression line for the updated data with x = average life expectancy and y = maximum weight (in kilograms)? a) $hat{y}=149.73 - 21.6x$ b) $hat{y}=149.73 - 9.82x$ c) $hat{y}=329.4 - 9.82x$ d) $hat{y}=329.4 - 21.6x$ e) not enough information

Answer

Explanation:

Step1: Analyze the effect on the intercept

The intercept of the regression line is not affected by changing the unit of the response - variable (from pounds to kilograms). The original intercept is $329.4$, and it remains $329.4$ in the new - unit regression line.

Step2: Analyze the effect on the slope

The slope of the regression line changes when the unit of the response - variable changes. If the original relationship is $\hat{y}=329.4 - 21.6x$ where $y$ is in pounds, and we convert $y$ to kilograms ($y_{new}=\frac{y_{old}}{2.2}$). Let the original regression line be $\hat{y}{old}=b_0 + b_1x$. The new regression line $\hat{y}{new}$ in terms of the old variables is $\hat{y}{new}=\frac{\hat{y}{old}}{2.2}=\frac{b_0 + b_1x}{2.2}=\frac{b_0}{2.2}+\frac{b_1}{2.2}x$. The original slope $b_1=- 21.6$ (in pounds per unit of $x$). When we convert $y$ to kilograms, the new slope $b_{1,new}=\frac{-21.6}{2.2}\approx - 9.82$. So the new regression line is $\hat{y}=329.4-9.82x$.

Answer:

C. $\hat{y}=329.4 - 9.82x$