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Read the following description of a data set. $\newline$ Jim is a programmer in Silicon Valley and spends most of his day typing and drinking coffee. He wants to know if drinking coffee makes him type faster.Over the next few days, Jim varies the number of cups of coffee he drinks, $x$ , and measures the average number of words typed per minute on each day, $y$ .The least squares regression line of this data set is: $y = 0.325x + 105.824$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts Jim's average daily typing speed will increase by ___ words per minute for each additional cup of coffee.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Jim is a programmer in Silicon Valley and spends most of his day typing and drinking coffee. He wants to know if drinking coffee makes him type faster.Over the next few days, Jim varies the number of cups of coffee he drinks,

x

, and measures the average number of words typed per minute on each day,

y

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

y = 0.325x + 105.824

\newline

Complete the following sentence:

\newline

The least squares regression line predicts Jim's average daily typing speed will increase by ___ words per minute for each additional cup of coffee.

Analyze regression equation: Analyze the given regression equation $y = 0.325x + 105.824$ . Here, the coefficient of $x$ , which is $0.325$ , represents the slope of the line.
Interpret slope meaning: The slope of the regression line ( $0.325$ ) indicates the change in the dependent variable ( $y$ , average words typed per minute) for each one-unit increase in the independent variable ( $x$ , number of cups of coffee). Therefore, for each additional cup of coffee Jim drinks, his typing speed is predicted to increase by $0.325$ words per minute.

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