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Read the following description of a data set. $\newline$ Savannah works with a property developer building houses close to the coastline in Italy. Her boss thinks that demand for the houses will be based primarily on their size. Savannah wants to show her boss that proximity to the ocean is also a big factor to consider.So, she looks at several houses of the same size in the area. She records the distance of each house from the ocean (in kilometers), $x$ . She also notes the number of people who offered to buy each house, $y$ , when it was last put up for sale.The least squares regression line of this data set is: $y = -1.687x + 17.915$ $\newline$ Complete the following sentence: $\newline$ For each additional kilometer away from the ocean, the least squares regression line predicts there will be $\_\_$ fewer offers.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Savannah works with a property developer building houses close to the coastline in Italy. Her boss thinks that demand for the houses will be based primarily on their size. Savannah wants to show her boss that proximity to the ocean is also a big factor to consider.So, she looks at several houses of the same size in the area. She records the distance of each house from the ocean (in kilometers),

x

. She also notes the number of people who offered to buy each house,

y

, when it was last put up for sale.The least squares regression line of this data set is:

y = -1.687x + 17.915

\newline

Complete the following sentence:

\newline

For each additional kilometer away from the ocean, the least squares regression line predicts there will be

\_\_

fewer offers.

Identify slope: Identify the slope of the least squares regression line. The equation given is $y = -1.687x + 17.915$ . The slope of the least squares regression line is the coefficient of $x$ , which is $-1.687$ .
Interpret slope: Interpret the slope. In the equation $y = -1.687x + 17.915$ , $x$ represents the distance of each house from the ocean in kilometers, and $y$ represents the number of offers each house received. The slope of $-1.687$ indicates that for each one kilometer increase in distance from the ocean, a house will receive $1.687$ fewer offers.

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