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Read the following description of a data set. $\newline$ Chad is a crime scene investigator. He found a footprint at the site of a recent murder and believes the footprint belongs to the culprit. To help identify possible suspects, he is investigating the relationship between a person's height and the length of his or her footprint.He consulted his agency's database and found cases in which detectives had recorded the length of people's footprints, $x$ , and their heights (in centimeters), $y$ .The least squares regression line of this data set is: $y = 2.256x + 107.341$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that someone whose footprint is one centimeter longer should be ___ centimeters taller.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Chad is a crime scene investigator. He found a footprint at the site of a recent murder and believes the footprint belongs to the culprit. To help identify possible suspects, he is investigating the relationship between a person's height and the length of his or her footprint.He consulted his agency's database and found cases in which detectives had recorded the length of people's footprints,

x

, and their heights (in centimeters),

y

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

y = 2.256x + 107.341

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that someone whose footprint is one centimeter longer should be ___ centimeters taller.

Identify Coefficient: To find out how much taller someone is predicted to be for each additional centimeter of footprint length, we need to look at the coefficient of $x$ in the regression equation, which represents the change in height for each unit change in footprint length.
Regression Equation: The regression equation is $y = 2.256x + 107.341$ . The coefficient of $x$ is $2.256$ , which means for every additional centimeter in footprint length, the height is predicted to increase by $2.256$ centimeters.
Predicted Height Increase: Therefore, the least squares regression line predicts that someone whose footprint is $1$ centimeter longer should be $2.256$ centimeters taller.

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