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Read the following description of a data set. For a project in her political science class, Becky researched approval ratings of previous mayors in her hometown. She wanted to see how closely the initial and final approval ratings of each mayor were related.Becky looked at the initial approval rating just after inauguration, $x$ , and the final approval rating immediately before leaving office, $y$ , of each mayor.The least squares regression line of this data set is: $y = 0.209x + 16.575$ $\newline$ Complete the following sentence: $\newline$ If a mayor's initial approval rating were one percentage point higher, the least squares regression line predicts that his or her final approval rating would have been ____ percentage points lower.

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Interpret regression lines

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Q. Read the following description of a data set. For a project in her political science class, Becky researched approval ratings of previous mayors in her hometown. She wanted to see how closely the initial and final approval ratings of each mayor were related.Becky looked at the initial approval rating just after inauguration,

x

, and the final approval rating immediately before leaving office,

y

, of each mayor.The least squares regression line of this data set is:

y = 0.209x + 16.575

\newline

Complete the following sentence:

\newline

If a mayor's initial approval rating were one percentage point higher, the least squares regression line predicts that his or her final approval rating would have been ____ percentage points lower.

Identify Slope: Identify the slope of the least squares regression line. The equation given is $y = 0.209x + 16.575$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.209$ . This slope indicates the change in the final approval rating ( $y$ ) for each one percentage point change in the initial approval rating ( $x$ ).
Interpret Slope: Interpret the slope. $\newline$ Since the slope is $0.209$ , this means that for each one percentage point increase in the initial approval rating, the final approval rating is predicted to increase by $0.209$ percentage points.
Check Question Prompt: Check the question prompt for the direction of the change. $\newline$ The question prompt asks for the predicted change in the final approval rating if the initial approval rating were one percentage point higher. Since the slope is positive, a higher initial approval rating would predict a higher final approval rating, not lower.

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