You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). x 3 4 12 16 26 36 y 37 46 77 100 150 200 Complete parts (a) through (e), given Σx = 97, Σy = 610, Σx2 = 2397, Σy2 = 81,914, Σxy = 13,919, and r ≈ 0.999. (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.) Σx = ? Σy = ? Σx2 = ? Σy2 = ? Σxy = ? r = ? (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) The calves you want to buy are 24 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) ?kg
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).
| x | 3 | 4 | 12 | 16 | 26 | 36 |
| y | 37 | 46 | 77 | 100 | 150 | 200 |
Complete parts (a) through (e), given Σx = 97, Σy = 610, Σx2 = 2397, Σy2 = 81,914, Σxy = 13,919, and r ≈ 0.999.
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample
| Σx = | ? |
| Σy = | ? |
| Σx2 = | ? |
| Σy2 = | ? |
| Σxy = | ? |
| r = | ? |
(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) The calves you want to buy are 24 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
?kg
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