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Read the following description of a data set. $\newline$ A professor wants to know if a student's first exam score can be used to accurately predict his or her final exam score. She looked at how some of her previous students did on their first exam, $x$ . She also looked at their final exam scores, $y$ . Both exams were graded out of $100$ . The least squares regression line of this data set is: $y = 0.259x + 54.179$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that if a student got an additional point on the first exam, their final exam score would be ___ points higher.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A professor wants to know if a student's first exam score can be used to accurately predict his or her final exam score. She looked at how some of her previous students did on their first exam,

x

. She also looked at their final exam scores,

y

. Both exams were graded out of

100

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

y = 0.259x + 54.179

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that if a student got an additional point on the first exam, their final exam score would be ___ points higher.

Identify Regression Line: The least squares regression line is given by the equation $y = 0.259x + 54.179$ . To find out how many additional points on the final exam score the line predicts for each additional point on the first exam, we need to look at the coefficient of $x$ in the equation.
Calculate Coefficient of $x$ : The coefficient of $x$ is $0.259$ . This means that for every additional point on the first exam ( $x$ ), the predicted final exam score ( $y$ ) increases by $0.259$ points.
Predict Additional Points: Therefore, if a student got an additional point on the first exam, the least squares regression line predicts that their final exam score would be $0.259$ points higher.

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