Question

The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min Temperature (F) 894 965 83 856 949 1233 69.9 81 74.3 77 75 88.3 What is the regression equation? (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.)

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Answer #1
X Y XY X2
894 69.9 62490.6 799236
965 81 78165 931225
893 74.3 66349.9 797449
856 77 65912 732736
949 75 71175 900601
1233 88.3 108873.9 1520289
Total = 5790 465.5 452966.4 5681536

a=rac{sum Ysum X^{2}-sum Xsum XY}{nsum X^{2}-(sum X)^{2}}

(465.5 × 568 1536)-(5790 × 452966.4) (6 × 568 1536)-57902 39.071

b=rac{nsum XY-sum Xsum Y}{nsum X^{2}-(sum X)^{2}}

=rac{(6 imes 452966.4)-(5790 imes 465.5)}{(6 imes 5681536)-5790^{2}}=0.0399

So,

the Regression Equation is:

y = 39.0T+ 0.03992.

For x = 3000:

hat{y}=39.07+(0.0399 imes 3000)=358.7980

The wrong in the predicted value is that x = 3000 is an extrapolation i.e., beyond the given range of values of x and so the predicted value is not reliable.

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