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Read the following description of a data set. $\newline$ Researchers at a cognitive psychology lab are studying how children develop their color vocabulary. In a recent study, the researchers showed children of various ages different colored objects and asked them to name the colors.They recorded each child's age (in months), $x$ , and the number of colors the child could name, $y$ .The least squares regression line of this data set is: $y = 0.213x - 4.937$ $\newline$ $\newline$ Complete the following sentence: $\newline$ If a child were one month older, the least squares regression line predicts that he or she would be able to name $\_\_$ additional colors.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Researchers at a cognitive psychology lab are studying how children develop their color vocabulary. In a recent study, the researchers showed children of various ages different colored objects and asked them to name the colors.They recorded each child's age (in months),

x

, and the number of colors the child could name,

y

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

y = 0.213x - 4.937

\newline

\newline

Complete the following sentence:

\newline

If a child were one month older, the least squares regression line predicts that he or she would be able to name

\_\_

additional colors.

Identify Slope: Identify the slope of the regression line. The slope of the regression line is the coefficient of $x$ in the equation $y = 0.213x - 4.937$ . The slope represents the change in the dependent variable ( $y$ , the number of colors a child can name) for each one-unit increase in the independent variable ( $x$ , the child's age in months).
Interpret Slope: Interpret the slope. $\newline$ The slope of $0.213$ means that for each additional month of age, the regression line predicts an increase of $0.213$ in the number of colors a child can name.
Answer Question: Answer the question based on the slope. $\newline$ Since the slope is $0.213$ , if a child were one month older, the least squares regression line predicts that he or she would be able to name $0.213$ additional colors.

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