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Read the following description of a data set. $\newline$ Jeanette is a math teacher at a large school. She wonders if her test problems are too wordy. Jeanette is curious whether the wordiness is affecting student performance.For the last several tests, Jeanette computes the average number of words in each question, $x$ , as well as the average percentage scores on the tests, $y$ .The least squares regression line of this data set is: $y = -1.436x + 107.874$ $\newline$ Complete the following sentence: $\newline$ If the average question length increased by one word, the least squares regression line predicts that the average percentage score would decrease by ___.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Jeanette is a math teacher at a large school. She wonders if her test problems are too wordy. Jeanette is curious whether the wordiness is affecting student performance.For the last several tests, Jeanette computes the average number of words in each question,

x

, as well as the average percentage scores on the tests,

y

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

y = -1.436x + 107.874

\newline

Complete the following sentence:

\newline

If the average question length increased by one word, the least squares regression line predicts that the average percentage score would decrease by ___.

Understand Equation: To solve this problem, we need to understand the equation of the least squares regression line, which is given as: $\newline$ $y = -1.436x + 107.874$ $\newline$ Here, $y$ represents the average percentage score, and $x$ represents the average number of words in each question. The coefficient of $x$ ( $-1.436$ ) indicates how much $y$ changes for each one-unit increase in $x$ .
Calculate Predicted Change: If the average question length $x$ increases by one word, we can find the predicted change in the average percentage score $y$ by multiplying the coefficient of $x$ by $1$ . $\newline$ Change in $y$ = $-1.436 \times 1$
Calculate Change in y: Now, we calculate the change in y: $\newline$ Change in y = $-1.436 \times 1 = -1.436$ $\newline$ This means that if the average question length increases by one word, the least squares regression line predicts that the average percentage score would decrease by $1.436$ .

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