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Read the following description of a data set. $\newline$ The operator of an electric plant was concerned about the performance of some of its wind turbines.He consulted the manuals to find the rotor diameter of each turbine (in meters), $x$ . Then, on a day with steady wind, he checked the control panel and noted each turbine's power output (in kilowatts), $y$ .The least squares regression line of this data set is: $y = 182.615x - 9,027.874$ $\newline$ Complete the following sentence: $\newline$ For each additional meter of rotor diameter, the least squares regression line predicts the power output of a turbine would increase by $\_\_\_\_$ kilowatts.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

The operator of an electric plant was concerned about the performance of some of its wind turbines.He consulted the manuals to find the rotor diameter of each turbine (in meters),

x

. Then, on a day with steady wind, he checked the control panel and noted each turbine's power output (in kilowatts),

y

.The least squares regression line of this data set is:

y = 182.615x - 9,027.874

\newline

Complete the following sentence:

\newline

For each additional meter of rotor diameter, the least squares regression line predicts the power output of a turbine would increase by

\_\_\_\_

kilowatts.

Identify slope: Identify the slope of the least squares regression line. The equation given is $y = 182.615x - 9,027.874$ . The slope of the least squares regression line is the coefficient of $x$ , which is $182.615$ . This slope indicates the change in power output ( $y$ ) for each additional meter of rotor diameter ( $x$ ).
Interpret slope: Interpret the slope. $\newline$ Since the slope is $182.615$ , this means that for each additional meter of rotor diameter, the least squares regression line predicts an increase in power output of $182.615$ kilowatts.

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