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Read the following description of a data set. $\newline$ Naomi is a food scientist interested in whether bitter flavors, like coffee, become more tolerable as people get older. She sets up a study in which subjects taste cups of coffee with varying intensities.Naomi then writes down the age of each subject, $x$ , as well as the weight of the coffee (in grams), $y$ , used to make the cup he or she liked best.The least squares regression line of this data set is: $y = 0.743x + 36.386$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that if a subject is one year older, he or she prefers an additional ___ grams of coffee in their ideal cup.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Naomi is a food scientist interested in whether bitter flavors, like coffee, become more tolerable as people get older. She sets up a study in which subjects taste cups of coffee with varying intensities.Naomi then writes down the age of each subject,

x

, as well as the weight of the coffee (in grams),

y

, used to make the cup he or she liked best.The least squares regression line of this data set is:

y = 0.743x + 36.386

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that if a subject is one year older, he or she prefers an additional ___ grams of coffee in their ideal cup.

Identify Slope: Identify the slope of the regression line. The slope of the regression line is the coefficient of the independent variable $x$ , which represents age in this case. The slope indicates how much the dependent variable $y$ , which represents the weight of the coffee, changes for each unit increase in $x$ . In the equation $y = 0.743x + 36.386$ , the slope is $0.743$ .
Interpret Slope: Interpret the slope. $\newline$ The slope of $0.743$ means that for each additional year of age (each increase by $1$ in $x$ ), the weight of the coffee ( $y$ ) that the subject prefers increases by $0.743$ grams.
Check for Errors: Check for any mathematical errors. $\newline$ There are no mathematical errors in the interpretation of the slope as the change in $y$ for each unit increase in $x$ .

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