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Read the following description of a data set. $\newline$ A publishing company is interested in the relationship between a customer's educational background and book-buying habits. As part of her summer internship at the company, Maggie designed a survey to investigate this relationship.The survey asked each person how many years of education they had completed, $x$ , and how many books they had purchased last year, $y$ .The least squares regression line of this data set is: $y = 1.206x + 42.766$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts a person would have bought $\_\_$ additional books last year, for each additional year of education.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

A publishing company is interested in the relationship between a customer's educational background and book-buying habits. As part of her summer internship at the company, Maggie designed a survey to investigate this relationship.The survey asked each person how many years of education they had completed,

x

, and how many books they had purchased last year,

y

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

y = 1.206x + 42.766

\newline

Complete the following sentence:

\newline

The least squares regression line predicts a person would have bought

\_\_

additional books last year, for each additional year of education.

Identify Slope: Identify the slope of the regression line. $\newline$ The slope of the regression line is the coefficient of $x$ in the equation $y = 1.206x + 42.766$ . The slope represents the change in the dependent variable ( $y$ , number of books purchased) for each unit increase in the independent variable ( $x$ , years of education).
Interpret Slope: Interpret the slope. $\newline$ The slope of $1.206$ means that for each additional year of education, the number of books purchased increases by $1.206$ , according to the least squares regression line.
Check for Errors: Check for any mathematical errors. There are no calculations to perform in this step, as the slope is given directly in the equation. Therefore, there is no math error.

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