Question

3. Naturalists have long known that you can use the rate at which crickets chirp to predict the temperature. Below are some data. Enter them in your trusty T Chirps in 1 minutes 882 1188 | 1104864 1200 ) 1032 1960 9oo Temperature (F69.7 93.3 84.3 76.3 88.6 82.6 716 79.6 a) What would be a good window for a scatter plot? b) Using that window, sketch the scatter plot. c). Find the equation of the regression bie d). Is the line a very good fit for the data? Explain. e). Suppose a cricket is chirping at 1000 chirps per minute. What do you predict the temperature to be?

Answer 1

a. Excel

b.

c.

$Let ~X=Chips~in~1~minutes,~Y=Temperature~(^0F)\\ Regression~equation~of~Y~on~X~is\\ \hat{Y}=27.6284+0.0523X\\ d.~R^2=0.7633~i.e.~76.33\%~of~total~variation~in~the~sample~of~temperature\\ is~explained~by~this~regression~equation.~Hence~the~line~is~a~good~fit~for~the~data.\\ e.~For~X=1000,~\hat{Y}=27.6284+0.0523*1000=79.9284\approx 79.9^0F.$