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Read the following description of a data set. $\newline$ Stefan 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: $y = 7.833x - 11.618$ $\newline$ 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

Stefan 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 = 7.833x - 11.618

\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 Regression Line: The least squares regression line is given by the equation $y = 7.833x - 11.618$ . This equation predicts the height ( $y$ ) based on the length of the footprint ( $x$ ). To find out how much taller someone should be for each additional centimeter of footprint, we need to look at the coefficient of $x$ in the equation, which is $7.833$ .
Calculate Coefficient: The coefficient of $x$ ( $7.833$ ) represents the change in height for each one-centimeter increase in the length of the footprint. Therefore, if the length of the footprint increases by one centimeter, the predicted height increases by $7.833$ centimeters.

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