Question

read the following description of a data set. the design team at an electronics company is evaluating its new prototype for a miniature recording device. as part of this evaluation, designers at the company gathered data about competing devices already on the market. among other things, the designers recorded the thickness of each recording device (in millimeters), x, and its maximum recording length (in minutes), y. the least - squares regression line of this data set is: y = 15.869x - 41.814. complete the following sentence: the least squares regression line predicts that, for each additional millimeter of thickness, a device can record additional minutes.

Explanation:

Step1: Identify the slope of the regression line

The least - squares regression line is given by $y = 15.869x-41.814$. In a linear regression equation of the form $y = mx + b$, the slope $m$ represents the change in $y$ for a unit change in $x$. Here, $m = 15.869$.

Step2: Interpret the slope in context

The variable $x$ is the thickness of the device in millimeters and $y$ is the recording length in minutes. So, for each additional millimeter of thickness, the regression line predicts an additional $15.869$ minutes of recording length.

Answer:

15.869