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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: $y = 12.085x - 97.998$ $\newline$ 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 = 12.085x - 97.998

\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.

Interpreting Regression Equation: To answer the question prompt, we need to look at the coefficient of the variable $x$ in the least squares regression line equation. The equation given is $y = 12.085x - 97.998$ , where $y$ represents the maximum recording length in minutes, and $x$ represents the thickness of the device in millimeters.
Understanding Coefficient of $x$ : The coefficient of $x$ , which is $12.085$ , represents the slope of the regression line. This slope tells us how much the dependent variable ( $y$ , the recording length) changes for each unit increase in the independent variable ( $x$ , the thickness of the device). Therefore, for each additional millimeter of thickness, the recording length increases by $12.085$ minutes.
Conclusion: There is no need for further calculations as the coefficient directly answers the question prompt. We can conclude that the least squares regression line predicts that for each additional millimeter of thickness, a device can record $12.085$ additional minutes.

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