Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that

Question:

Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (oF). These data are also available for download at www.cengagebrain.com.

Complete parts (a) through (e), given ˆ‘x = 249.8, ˆ‘y = 1200.6, ˆ‘x2 = 4200.56, ˆ‘y2 = 96,725.86, ˆ‘xy = 20,127.47, and r ‰ˆ 0.835.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line Å· = Î± + bx.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?
(f) What is the predicted temperature when x = 19 chirps per second?