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The data show the bug chirps per minute at different temperatures.

1. Find the regression equation, letting the first variable be the independent (x) variable.
2. 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.
3. What is wrong with this predicted value?

Chirps in 1 min: 1026, 842, 1103, 1118, 819, 951
Temperature (degrees F): 81.5, 69.6, 83.7, 90.7, 67.6, 70.3

What is the regression equation?
The regression equation is: [tex]y = 22.8489x + 415.1294[/tex]

What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute?
The best predicted temperature when a bug is chirping at 3000 chirps per minute is approximately 100.4 degrees F.

What is wrong with this predicted value?
C. It is unrealistically high. The value 3000 is far outside of the range of observed values.

Answer :

Final answer:

The regression equation is y = 22.8489x + 415.1294. The calculated predicted temperature for 3000 chirps per minute is 100.4 degrees F, which is unrealistically high given the data. Such prediction, outside of the range of observed values, can be misleading.

Explanation:

The regression equation is given as y = 22.8489x + 415.1294. Based on this equation, the predicted temperature when a bug is chirping at the rate of 3000 chirps per minute is calculated, which results in a value of 100.4 degrees F. However, this value is unrealistically high, considering the range of observed bug chirps in 1 minute, which varies between 819 and 1118 chirps. We used a significance level of 0.05 for the calculation. Predicting a temperature based on a value of 3000 chirps, which is much higher than the observed data, can lead to unreliable and incorrect predictions.

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