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Read the following description of a data set. $\newline$ Mariana 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. Mariana 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: $y = -3.234x + 33.499$ $\newline$ 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

Full solution

Q. Read the following description of a data set.

\newline

Mariana 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. Mariana 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 = -3.234x + 33.499

\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.

Understand slope of regression line: To solve this problem, we need to understand the slope of the least squares regression line, which is given by the coefficient of $x$ in the equation $y = -3.234x + 33.499$ . The slope represents the change in the dependent variable ( $y$ , the number of offers) for each unit increase in the independent variable ( $x$ , the distance from the ocean in kilometers).
Calculate slope value: The slope of the regression line is $-3.234$ . This means that for each additional kilometer away from the ocean, the number of offers decreases by $3.234$ according to the regression line.

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