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Read the following description of a data set. $\newline$ Bob is an editor reviewing short story submissions for a literary magazine. He collected data showing that he's an efficient reviewer and wants to leverage this to get a raise.For a week, Bob recorded the number of words in each short story submission, $x$ , and how long it took him to review that story (in minutes), $y$ .The least squares regression line of this data set is: $y = 0.002x + 26.458$ $\newline$ Complete the following sentence: $\newline$ For each additional word in a story, the least squares regression line predicts that it would only take Bob ___ more minutes to review it.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Bob is an editor reviewing short story submissions for a literary magazine. He collected data showing that he's an efficient reviewer and wants to leverage this to get a raise.For a week, Bob recorded the number of words in each short story submission,

x

, and how long it took him to review that story (in minutes),

y

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

y = 0.002x + 26.458

\newline

Complete the following sentence:

\newline

For each additional word in a story, the least squares regression line predicts that it would only take Bob ___ more minutes to review it.

Identify slope: Identify the slope of the least squares regression line. The equation given is $y = 0.002x + 26.458$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.002$ . This slope represents the change in the dependent variable ( $y$ , the time to review) for each one-unit increase in the independent variable ( $x$ , the number of words).
Interpret slope: Interpret the slope. $\newline$ In the equation $y = 0.002x + 26.458$ , $x$ represents the number of words in the short story and $y$ represents the time it took Bob to review the story in minutes. The slope of $0.002$ indicates that for each additional word in a story, the least squares regression line predicts that it would take Bob $0.002$ more minutes to review it.

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