Question

coach leonard is responsible for recruiting male athletes to join the european masters track and field team. to improve his recruitment strategies, he wants to investigate the connection between an athletes height and 3000 - meter run time. coach leonard has recorded the heights of the men on the track and field team (in centimeters), x, and their best 3000 - meter times (in minutes), y. the correct least squares regression line for the data set is: y = - 0.041x + 15.039 use it to complete the following sentence: according to the least squares regression line, a one centimeter increase in height corresponds to minutes off the 3000 - meter run.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the regression line \(y=-0.041x + 15.039\), \(x\) is height (in centimeters) and \(y\) is the 3000 - meter run time (in minutes).

Step2: Interpret the slope

The slope \(m=-0.041\). The slope represents the change in \(y\) (dependent variable) for a unit change in \(x\) (independent variable). Here, for a 1 - centimeter increase in \(x\) (height), the change in \(y\) (3000 - meter run time) is given by the slope.

Answer:

\(0.041\)