Question

interpret the least squares regression line of this data set.
dan is a professional dancer booked for a major event. although he has a rigorous practice schedule, he sometimes has to end a practice session when he begins to experience stiffness. he wonders if stretching more before starting a session will allow him to practice for a longer time.
over the next few days dan varies the number of minutes he stretches before the start of his session, x, and notes the number of minutes he can practice before experiencing stiffness, y.
the correct least squares regression line for the data set is:
y = 3.014x + 194.191
use it to complete the following sentence:
for each additional minute of stretching, the least squares regression line predicts he will be able to practice \boxed{} minutes longer.

Explanation:

Step1: Recall the form of a regression line

The general form of a linear regression line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Identify the slope

In the given regression line \(y = 3.014x+194.191\), the coefficient of \(x\) is \(m = 3.014\). The slope \(m\) represents the change in \(y\) (minutes of practice) for a unit change in \(x\) (minutes of stretching).

Answer:

\(3.014\)