9.2
1)
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 | 19.1 | 16.1 | 19.2 | 18.1 | 17.2 | 15.5 | 14.7 | 17.1 |
| y | 90.2 | 72.4 | 93.3 | 85.1 | 82.0 | 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 = 248.2,Σy = 1205.2, Σx2 = 4137.66,Σy2 = 97,490.3, Σxy = 20,063.68, andr ≈ 0.856.
(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 = 19.4 chirpsper second? (Round your answer to two decimal places.)
°F
2)
(a) Suppose you are given the following (x, y)data pairs.
Find the least-squares equation for these data (rounded to threedigits after the decimal).
Å· =Â Â +Â Â Â x
(b) Now suppose you are given these (x, y) datapairs.
Find the least-squares equation for these data (rounded to threedigits after the decimal).
Å· =Â Â Â +Â Â Â x
(c) In the data for parts (a) and (b), did we simply exchange thex and y values of each data pair?
YesNo  Â
(d) Solve your answer from part (a) for x (rounded tothree digits after the decimal).
x =Â Â Â +Â Â Â y
3)
You are the foreman of the Bar-S cattle ranch in Colorado. Aneighboring ranch has calves for sale, and you are going to buysome calves to add to the Bar-S herd. How much should a healthycalf weigh? Let x be the age of the calf (in weeks), andlet y be the weight of the calf (in kilograms).
| x | 3 | 4 | 12 | 16 | 26 | 36 |
| y | 42 | 54 | 70 | 100 | 150 | 200 |
Complete parts (a) through (e), given Σx = 97,Σy = 616, Σx2 = 2397,Σy2 = 82,080, Σxy = 13,882, andr ≈ 0.993.
(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.)
(d) Graph the least-squares line. Be sure to plot the point (x, y)as a point on the line.
(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) The calves you want to buy are 22 weeks old. What does theleast-squares line predict for a healthy weight? (Round your answerto two decimal places.)
kg
