Question

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 1 5 8 16 26 36 y 42 52 71 100 150 200 Complete parts (a) through (e), given Σx = 92, Σy = 615, Σx2 = 2318, Σy2 = 82,009, Σxy = 13,570, 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 y hat = 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 hat = + 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 13 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) kg

Answer 1

Answer a:

The Scatter Plot is given below -

( where X- Axis represents the age of the calf and Y- Axis represents the weight of the calf (in kgs))

X-Axis : 2 cm = 5 units , Y - Axis : 2 cm = 20 kgs

Answer b:

The following table shows the calculations -

	x	y	x2	y2	xy
	1	42	1	1764	42
	5	52	25	2704	260
	8	71	64	5041	568
	16	100	256	10000	1600
	26	150	676	22500	3900
	36	200	1296	40000	7200
Total	92	615	2318	82009	13570

which verifies that all the data given in the question is true

Answer c:

Answer d:
The least squares line in the graph is given below -

The (X , Y) point on the graph is (12 , 80)

(NOTE THAT : The first four parts of the question are attempted)