Question

You are the foreman of the Bar-5 cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-5 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 2 3 11 16 26 1 41 73100 150 200 Complete parts (a) through (e), given Ex = 94, By = 612, 2x2 = 2362, 3y2 = 41,914, Exy = 13,729, and rx 0.997. (b) Verify the given sums IX, IX, 12, 172. Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Exy- (c) Find 7, and 7. Then find the equation of the least squares line y - . br. (Round your answers for and y to two decimal places. Round your answers for a and b to three decimal places) Y- y- ( Graph the least squares line. ec sure to plot the point G. 2) as a point on the line. 200 2004 150 150 100 100 50 50 0 0 10 20 30 40 O 0 10 20 40 у 200 2001 150 150 100 100 50F 50 0 0 0 10 20 30 40 10 20 30 40 (e) Find the value of the coefficient of determination. 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 r to three decimal places. Round your answers for the percentages to une decimal place.) explained unexplained The calves you want to buy are 23 weeks old. What does the least squares line predict for a healthy weight (Round your answer to two decimal places.)

Answer 1

sr.no.	X	Y	X^2	Y^2	XY
1	2	41	4	1681	82
2	3	48	9	2304	144
3	11	73	121	5329	803
4	16	100	256	10000	1600
5	26	150	676	22500	3900
6	36	200	1296	40000	7200
total	94	612	2362	81814	13729

Date Solution; b) 94, EX 2 Ey = (12, EX? = 2362, Ey? = 81814 EXY = 13729 DEXY -(EX)(EY) Vinex Ex}} [ney!-(29) 6X 13729 - (94 (612) V[6X23 X2362 - (95)X 81819-(01234 21846 F - 5336 X 116340 24846 f 24915.66 0.99) Ex² = 2362 y2 = 81814 Ex = 94 612 EXY 13729 0.997 all values are correct.

EX х 94 - 15.67 EL 612 6 102 regression eg. 7 = atby. where, Sxx (EX) (27) Say EXT- (94) (612) 13729 Say 4141 (EX) sxx 2362 6

Sax 889.33 b = Sxy Sxx 414 889.33 b 4.656 Now, Q - 7-b7 102- 4.656(15.67) a 29.051 Regression eg. is, 29.051 +4.6568 d) 200 tso too so 6 10 20 30 х option @ is corect

Date e) R SSR SST where, SSR b. Say - 9.656. X 414 19281.73 2 SST (6129² 81814 19390 R² 19281.73 19390 . R² = 0.994. be percentange of variation in t can explained by corresponding variation in x is 99.47 can be percentage of variation I un explained by variation in x is 0.64.

prediction for weight of 23 8 weeks old. y 29.051+ 4.6562 7 11 29.051 +4.656 (23) - I 136.15 kg