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Read the following description of a data set. $\newline$ 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: $y = 70.381x - 1,042.356$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that, for each additional millimeter of thickness, a device can record $\_\_$ additional minutes.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

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 = 70.381x - 1,042.356

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that, for each additional millimeter of thickness, a device can record

\_\_

additional minutes.

Interpret slope change: To answer the question prompt, we need to interpret the slope of the least squares regression line. The slope represents the change in the dependent variable ( $y$ , which is the maximum recording length in minutes) for each unit increase in the independent variable ( $x$ , which is the thickness in millimeters).
Calculate regression line slope: The slope of the regression line is the coefficient of $x$ in the equation $y = 70.381x - 1,042.356$ . This means that for each additional millimeter of thickness, the maximum recording length increases by $70.381$ minutes.
No further calculations needed: There is no need for further calculations as the slope directly gives us the answer to the question prompt.

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