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Read the following description of a data set. $\newline$ Every summer, the Greenville Fair has a grasshopper catching contest. Grasshoppers are released into a fenced area, and participants are given five minutes to catch as many as they can. To even the playing field, the organizers developed a handicap system based on the results of this year's competition. The system takes into account the different experience levels of the contest participants.To create the system, the organizers recorded the number of times each contestant had previously participated, $x$ , and the number of grasshoppers each contestant had caught this year, $y$ .The least squares regression line of this data set is: $y = 3.378x - 11.215$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that a participant would have caught $\_\_$ more grasshoppers for each additional year of participation.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Every summer, the Greenville Fair has a grasshopper catching contest. Grasshoppers are released into a fenced area, and participants are given five minutes to catch as many as they can. To even the playing field, the organizers developed a handicap system based on the results of this year's competition. The system takes into account the different experience levels of the contest participants.To create the system, the organizers recorded the number of times each contestant had previously participated,

x

, and the number of grasshoppers each contestant had caught this year,

y

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

y = 3.378x - 11.215

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that a participant would have caught

\_\_

more grasshoppers for each additional year of participation.

Identify Slope: Identify the slope of the least squares regression line. $\newline$ The equation given is $y = 3.378x - 11.215$ . The slope of the least squares regression line is the coefficient of $x$ , which is $3.378$ . This slope represents the change in the number of grasshoppers caught for each additional year of participation.
Interpret Slope: Interpret the slope. $\newline$ In the equation $y = 3.378x - 11.215$ , $x$ represents the number of times each contestant had previously participated, and $y$ represents the number of grasshoppers each contestant had caught this year. The slope of $3.378$ indicates that for each additional year of participation, a contestant is predicted to catch $3.378$ more grasshoppers.

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