Anyone who has been outdoors on a summer evening has probablyheard crickets. Did you know that it is possible to use the cricketas a thermometer? Crickets tend to chirp more frequently astemperatures increase. This phenomenon was studied in detail byGeorge W. Pierce, a physics professor at Harvard. In the followingdata, x is a random variable representing chirps persecond and y is a random variable representing temperature(°F).
| x | 20.5 | 15.5 | 18.8 | 17.5 | 16.3 | 15.5 | 14.7 | 17.1 |
| y | 87.8 | 70.4 | 92.9 | 83.5 | 81.2 | 75.2 | 69.7 | 82.0 |
| x | 15.4 | 16.2 | 15.0 | 17.2 | 16.0 | 17.0 | 14.4 |
| y | 69.4 | 83.3 | 79.6 | 82.6 | 80.6 | 83.5 | 76.3 |
Complete parts (a) through (e), given Σx = 247.1,Σy = 1198, Σx2 = 4107.43,Σy2 = 96,302.7, Σxy = 19,855.58, andr ≈ 0.796.
(b) Verify the given sums Σx, Σy,Σx2, Σy2, Σxy, andthe value of the sample correlation coefficient r. (Roundyour value for r to three decimal places.)
| Σx = | |
| Σy = | |
| Σx2 = | |
| Σy2 = | |
| Σxy = | |
| r = | |
(c) Find x, and y. Then find the equation of the least-squaresline  = a + bx. (Round your answers forx and y to two decimal places. Round your answers for aand b to three decimal places.)
(e) Find the value of the coefficient of determinationr2. What percentage of the variation iny can be explained by the corresponding variationin x and the least-squares line? What percentage isunexplained? (Round your answer for r2to three decimal places. Round your answers for the percentages toone decimal place.)
| r2 = | |
| explained    | % |
| unexplained    | % |
(f) What is the predicted temperature when x = 19.0 chirpsper second? (Round your answer to two decimal places.)
°F
