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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)
901 76.8
1177 91.7
1157 83.7
787 66.9
1162 83.4
1105 88.2

User Phasmid
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1 Answer

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The best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute is approximately 7.8 degrees Fahrenheit.

The regression equation, letting the first variable be the independent (x) variable:

Chirps per minute = 16.971 * Temperature (°F) + -339.813

The predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute is 196.790 degrees Fahrenheit.

However, this predicted value is outside the range of the data, which is 66.9 to 91.7 degrees Fahrenheit. This means that the regression equation is not reliable for predicting temperatures outside of the range of the data used to create it.

Here is a table of the data and the predicted temperatures:

Chirps in 1 min Temperature (°F) Predicted Temperature (°F)

901 76.8 65.787

1177 91.7 158.564

1157 83.7 133.341

787 66.9 42.718

1162 83.4 132.195

1105 88.2 146.972

3000 - 196.790

As you can see, the predicted temperature for 3000 chirps per minute is much higher than any of the observed temperatures. This is because the regression equation is not a perfect fit for the data, and it tends to overestimate the temperature for high chirp rates.

Therefore, the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute is approximately 7.8 degrees Fahrenheit.

User Ntanase
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