Question

interpret the least squares regression line of this data set.
paula 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 correct least squares regression line for the data set is:
y = -1.747x + 54.374
use it to complete the following sentence:
the least squares regression line indicates that paulas commute would be minutes shorter if the morning temperature increases one degree celsius

Explanation:

Step1: Recall the form of a linear regression equation

The general form of a linear regression equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(y=-1.747x + 54.374\), \(x\) represents the temperature (in Celsius) and \(y\) represents the commute time (in minutes).

Step2: Interpret the slope

The slope \(m=-1.747\). In the context of a regression line \(y = mx + b\), the slope \(m\) represents the change in \(y\) for a one - unit change in \(x\). Here, when \(x\) (temperature) increases by 1 degree Celsius, \(y\) (commute time) changes by \(m\) minutes.

Answer:

\(1.747\)