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Read the following description of a data set. $\newline$ Percy is packing for vacation and is wondering how many books to bring. He wants to make sure he does not run out of reading material, so he looks at his reading journal to see how many books he read on past vacations.For each vacation, he records the vacation's length (in days), $x$ , and how many books he read, $y$ .The least squares regression line of this data set is: $y = 0.756x + 2.093$ $\newline$ Complete the following sentence: $\newline$ If Percy stays on vacation for one extra day, the least squares regression line predicts that he would have read ___ additional books.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Percy is packing for vacation and is wondering how many books to bring. He wants to make sure he does not run out of reading material, so he looks at his reading journal to see how many books he read on past vacations.For each vacation, he records the vacation's length (in days),

x

, and how many books he read,

y

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

y = 0.756x + 2.093

\newline

Complete the following sentence:

\newline

If Percy stays on vacation for one extra day, the least squares regression line predicts that he would have read ___ additional books.

Regression Line Equation: The least squares regression line provided is $y = 0.756x + 2.093$ . This equation predicts the number of books, $y$ , that Percy reads based on the number of days, $x$ , he is on vacation. To find out how many additional books Percy would read if he stays one extra day, we need to look at the coefficient of $x$ , which represents the slope of the line.
Interpreting Slope: The slope of the regression line is $0.756$ . This means that for each additional day Percy stays on vacation, he is predicted to read $0.756$ more books. Since we are only adding one extra day, we can directly use the slope to determine the additional number of books read.
Calculating Additional Books: We calculate the additional books read by multiplying the slope $0.756$ by the number of extra days $1$ . So, $0.756 \times 1 = 0.756$ . This is the predicted number of additional books Percy would read if he stays one extra day on vacation.

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