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Read the following description of a data set. $\newline$ Jack 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: $y = 0.244x + 0.162$ $\newline$ 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

Jack 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 = 0.244x + 0.162

\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.

Regression Line Explanation: The least squares regression line provided is $y = 0.244x + 0.162$ . In this equation, $y$ represents the high jump (in meters) and $x$ represents the long jump (in meters). The coefficient of $x$ ( $0.244$ ) indicates the change in the high jump for each one-meter increase in the long jump.
Coefficient Interpretation: To find out how many extra meters a person can clear in the high jump for each additional meter in the long jump, we look at the coefficient of $x$ in the regression equation. The coefficient is $0.244$ , which means for each additional meter in the long jump, the regression line predicts an increase of $0.244$ meters in the high jump.

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