Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 26 45 34 47 23 40 34 52 y 31 20 22 13 29 17 21 14 Complete parts (a) through (e), given Σx = 301, Σy = 167, Σx2 = 12,055, Σy2 = 3781, Σxy = 5854, and r ≈ −0.926. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x =? y =? y = ?+? x (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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = ? explained ?% unexplained ?% (f) Suppose a car weighs x = 43 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) mpg
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).
| x | 26 | 45 | 34 | 47 | 23 | 40 | 34 | 52 |
| y | 31 | 20 | 22 | 13 | 29 | 17 | 21 | 14 |
Complete parts (a) through (e), given Σx = 301, Σy = 167, Σx2 = 12,055, Σy2 = 3781, Σxy = 5854, and
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample
(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
| x | =? | |
| y | =? | |
| y | = | ?+? x |
(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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
| r2 = | ? |
| explained | ?% |
| unexplained | ?% |
(f) Suppose a car weighs x = 43 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg
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