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Read the following description of a data set. $\newline$ Charlie is a kinesiologist and is interested in how different athletic abilities are related. He selected several subjects with similar athletic backgrounds and compared their abilities in the long jump and the high jump.He measured how far, $x$ , and how high, $y$ , each subject could jump (in meters).The least squares regression line of this data set is: $y = 0.312x + 0.067$ $\newline$ Complete the following sentence: $\newline$ For each additional meter in a person's long jump, the least squares regression line predicts that he or she can clear an extra ___ meters in the high jump.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Charlie is a kinesiologist and is interested in how different athletic abilities are related. He selected several subjects with similar athletic backgrounds and compared their abilities in the long jump and the high jump.He measured how far,

x

, and how high,

y

, each subject could jump (in meters).The least squares regression line of this data set is:

y = 0.312x + 0.067

\newline

Complete the following sentence:

\newline

For each additional meter in a person's long jump, the least squares regression line predicts that he or she can clear an extra ___ meters in the high jump.

Identify the slope: Identify the slope of the regression line. The slope of the regression line is the coefficient of $x$ in the equation $y = 0.312x + 0.067$ . This coefficient represents the change in the dependent variable ( $y$ , the high jump) for each unit increase in the independent variable ( $x$ , the long jump).
Interpret the slope: Interpret the slope. $\newline$ The slope of $0.312$ means that for each additional meter in the long jump, the regression line predicts an increase of $0.312$ meters in the high jump.
Check for errors: Check for any mathematical errors. $\newline$ There are no mathematical errors in the interpretation of the slope as the change in $y$ for each unit change in $x$ .

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