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 810 1149 841 1013 863 930 Temperature ​(degrees​F) 68.2 88.3 73.5 84.6 75.6 74.3 What is the regression​ equation? ModifyingAbove y with caretequals nothingplus nothingx ​(Round the​ x-coefficient to four decimal places as needed. Round the constant to two decimal places as​ needed.) 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 nothingdegreesF. ​(Round to one decimal place as​ needed.) What is wrong with this predicted​ value? Choose the correct answer below. A. It is unrealistically high. The value 3000 is far outside of the range of observed values. B. It is only an approximation. An unrounded value would be considered accurate. C. The first variable should have been the dependent variable. D. Nothing is wrong with this value. It can be treated as an accurate prediction.

Answer 1

Using Simple linear regression, our objective is to model the dependent variable (here, Temperature) based on the independent variable (Chirps in 1 min.)

We need to fit a regression equation of the form:

where y = Temperature, x = Chirps in 1 min., = estimated intercept, = estimated slope

The slope can be estimated using the formula:

Substituting the values,

= 0.0559......................(1)

Substituting the values,

= 25.1875........................(2)

Hence, from (1) and (2), the fitted regression equation can be expressed as:

...........................(3)

To obtain the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per​ minute, we may substitute x = 3000 in (3)

= 192.9

The predicted value definitely has something wrong with it, since, the surrounding temperature for living inhabitants can never be 192.9, in practice.

Yes, the value is unrealistically high, but the real reason behind this is that C. The first variable should have been the dependent variable.

Since, temperature is an independent phenomenon, which definitely does not depend on Chirping of a bug. It should, in actual, be the other way round; Temperature being the independent variable / predictor and Chirps in min., the dependent one. This would provide a meaningful result.