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Read the following description of a data set. $\newline$ A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.For each town in the sample, the report recorded its population (in thousands), $x$ , and its number of schools, $y$ .The least squares regression line of this data set is: $y = 0.119x - 18.064$ $\newline$ Complete the following sentence: $\newline$ If a town had one thousand more people, the least squares regression line predicts that it would have $\_$ more schools.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.For each town in the sample, the report recorded its population (in thousands),

x

, and its number of schools,

y

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

y = 0.119x - 18.064

\newline

Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_

more schools.

Identify Slope: Identify the slope of the least squares regression line. The equation given is $y = 0.119x - 18.064$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.119$ . This slope indicates the change in the number of schools for each additional thousand people in the town's population.
Interpret Slope: Interpret the slope in the context of the problem. $\newline$ Since the slope is $0.119$ , this means that for every increase of one thousand in the population (since $x$ is in thousands), the number of schools ( $y$ ) is predicted to increase by $0.119$ .
Calculate Predicted Increase: Calculate the predicted increase in the number of schools for an increase of one thousand people. Using the slope, we can predict that if a town had $1000$ more people, it would have $0.119$ more schools according to the least squares regression line.

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