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Crickets chirping The scatterplot shows the relationship between x = temperature in degrees Fahrenheit and y = chirps per minute for the striped ground cricket, along with the regression line y^=鈭0.31+0.212x

a. Calculate and interpret the residual for the cricket who chirped 20 times per minute when the temperature was 88.6掳F.

b. About how many additional chirps per minute do you expect cricket to make if the temperature increases by 10掳F?

Short Answer

Expert verified

Part (a) Residual is 1.5268

Part (b) 2.12 chirps per minute we expect a cricket to make.

Step by step solution

01

Part (a) Step 1: Given information

The regression line is given as follows in the question:

y= 鈭0.31 + 0.212x

02

Part (a) Step 2: Calculation

Also, when the temperature was 88.6degrees Fahrenheit, the insect chirped20 times per minute.

Thus,

x=88.6y=20

Thus, the predicted number of times cricket chirped is as:

y=0.31+0.212x=0.31+0.212(88.6)=18.4732

Thus, the residual will be calculated as:

Residual=yy=2018.4732=1.5268

This means that while using the regression line to make a prediction for the cricket, we underestimated the amount of chirps per minute by 1.5268chirps per minute.

03

Part (b) Step 1: Calculation

The regression line is given as follows in the question:

y=0.31+0.212x

The slope in the least square regression equation is the coefficient of xand it indicates the average rise or decrease of yper unit of xThus,

b1=0.212

As a result, the average number of chirps per minute increases by 0.212 per degree Fahrenheit. In this scenario, we raise the temperature by, and we anticipate an increase in the number of chirps per minute of:

100.212=2.12chirpsperminute

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