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Read the following description of a data set. $\newline$ Regan has noticed that her bike ride to work takes longer on some days than others. She is curious to see how the morning temperature is related to the duration of her commute.For the past several mornings, she measured the temperature (in Celsius), $x$ , and the time her commute had taken (in minutes), $y$ .The least squares regression line of this data set is: $y = -18.522x + 194.485$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line indicates that Regan's commute would be $\_\_$ minutes shorter if the morning temperature increases one degree Celsius.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

Regan has noticed that her bike ride to work takes longer on some days than others. She is curious to see how the morning temperature is related to the duration of her commute.For the past several mornings, she measured the temperature (in Celsius),

x

, and the time her commute had taken (in minutes),

y

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

y = -18.522x + 194.485

\newline

Complete the following sentence:

\newline

The least squares regression line indicates that Regan's commute would be

\_\_

minutes shorter if the morning temperature increases one degree Celsius.

Regression Equation Analysis: To find out how much shorter Regan's commute would be with a one degree Celsius increase in temperature, we need to look at the coefficient of $x$ in the regression equation, which represents the change in the commute time ( $y$ ) for each one-unit change in temperature ( $x$ ). $\newline$ The regression equation is $y = -18.522x + 194.485$ .
Coefficient of $x$ : The coefficient of $x$ is $-18.522$ . This means that for each one degree Celsius increase in temperature, the commute time decreases by $18.522$ minutes, because the coefficient is negative.
Calculation of Shorter Commute: Therefore, if the morning temperature increases by one degree Celsius, Regan's commute would be $18.522$ minutes shorter.

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