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	2	4	8	16	26	36
y	38	46	77	100	150	200

Complete parts (a) through (e), given Σx = 92, Σy = 611, Σx² = 2312, Σy² = 81,989, Σxy = 13,576, and r ≈ 0.997.

(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	=
	=	+   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 23 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
  kg

Answer 1

c)

sample size ,   n =   6          
here, x̅ =Σx/n =   15.33 , ȳ = Σy/n =   101.83
                  
SSxx =    Σx² - (Σx)²/n =   901.333          
SSxy=   Σxy - (Σx*Σy)/n =   4207.333          
SSyy =    Σy²-(Σy)²/n =   19768.833          
estimated slope , ß1 = SSxy/SSxx =   4207.333   /   901.333   =   4.6679
                  
intercept,   ß0 = y̅-ß1* x̄ =   30.2589          
                  
so, regression line is   Ŷ =   30.26   +   4.67   *x

d)

SSE=   (Sx*Sy - S²xy)/Sx =    129.4246
      
std error ,Se =    √(SSE/(n-2)) =    5.6882
      
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9967
      
R² =    (Sxy)²/(Sx.Sy) =    0.993

r2 =	.993
explained	99.3 %
unexplained	0.7 %

g)

Predicted Y at X=   23   is                  
Ŷ =   30.259   +   4.668   *   23   =   137.62

THANKS

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