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 9 16 26 36 y 43 46 79 100 150 200 Complete parts (a) through (e), given Σx = 94, Σy = 618, Σx2 = 2334, Σy2 = 82,706, Σxy = 13,724, and r ≈ 0.998. (a) Draw a scatter diagram displaying the data.(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 (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 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 21 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 | 9 | 16 | 26 | 36 |
y | 43 | 46 | 79 | 100 | 150 | 200 |
Complete parts (a) through (e), given Σx = 94, Σy = 618, Σx2 = 2334, Σy2 = 82,706, Σxy = 13,724, and r ≈ 0.998.
(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
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
r2 = | |
explained | % |
unexplained | % |
(f) The calves you want to buy are 21 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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