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Read the following description of a data set. $\newline$ Layla 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: $y = -1.685x + 42.681$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line indicates that Layla'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

Layla 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 = -1.685x + 42.681

\newline

Complete the following sentence:

\newline

The least squares regression line indicates that Layla's commute would be ___ minutes shorter if the morning temperature increases one degree Celsius.

Identify slope: Identify the slope of the regression line. The slope of the regression line is the coefficient of $x$ , which represents the change in the dependent variable ( $y$ , the time of Layla's commute) for each one-unit change in the independent variable ( $x$ , the morning temperature). In the equation $y = -1.685x + 42.681$ , the slope is $-1.685$ .
Interpret slope: Interpret the slope. $\newline$ The negative sign of the slope ( $-1.685$ ) indicates that there is an inverse relationship between the temperature and the duration of Layla's commute. This means that as the temperature increases, the time taken for Layla's commute decreases.
Calculate change: Calculate the change in commute time for a one-degree increase in temperature. $\newline$ Since the slope is $-1.685$ , a one-degree increase in temperature would result in a $-1.685$ minute change in the duration of Layla's commute. This means her commute would be $1.685$ minutes shorter for each degree Celsius increase in temperature.

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