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Read the following description of a data set. $\newline$ Executives at A+ Mart grocery stores would like to expand to the rapidly growing town of Milford. Company analysts are trying to estimate future demand for grocery stores in Milford by looking at data from nearby cities.The analysts note the population of nearby cities (in thousands), $x$ , and compare it to the number of grocery stores in each city, $y$ .The least squares regression line of this data set is: $y = 0.184x - 3.772$ $\newline$ Complete the following sentence: $\newline$ If a city has one thousand additional people, the least squares regression line predicts it will have ___ more grocery stores.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Executives at A+ Mart grocery stores would like to expand to the rapidly growing town of Milford. Company analysts are trying to estimate future demand for grocery stores in Milford by looking at data from nearby cities.The analysts note the population of nearby cities (in thousands),

x

, and compare it to the number of grocery stores in each city,

y

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

y = 0.184x - 3.772

\newline

Complete the following sentence:

\newline

If a city has one thousand additional people, the least squares regression line predicts it will have ___ more grocery stores.

Identify Slope: Identify the slope of the least squares regression line. The equation given is $y = 0.184x - 3.772$ . The slope of the least squares regression line is the coefficient of $x$ , which is $0.184$ . This slope indicates the change in the number of grocery stores for each additional thousand people in the population.
Interpret Slope: Interpret the slope in the context of the problem. $\newline$ Since the slope is $0.184$ , this means that for every increase of one thousand people in the population ( $x$ ), the number of grocery stores ( $y$ ) is predicted to increase by $0.184$ .
Answer Prompt: Answer the question prompt based on the slope. $\newline$ If a city has $1000$ additional people, the least squares regression line predicts it will have $0.184$ more grocery stores.

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