Question

Consider the following data for a dependent variable y and two independent variables, 21 and 22. 94 108 112 179 94 176 170 118 142 211 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y tox1. 21 y = Predict y if c1 = 35. b. Develop an estimated regression equation relating y to 22. Predict y if .22 = 15. y = c. Develop an estimated regression equation relating y to 21 and 22. Predict y if Xi = 35 and 22 = 15.

Answer 1

a.

X - My Y.M (X - MX) -46.4 (X - MNY - My 881.6 64.8 710 38.6 417.6 71.2 769.6 268.8 1976.8 SS: 2780 SP: 5215

Sum of X = 490
Sum of Y = 1404
Mean X = 49
Mean Y = 140.4
Sum of squares (SS_X) = 2780
Sum of products (SP) = 5215

Regression Equation = ŷ = bX + a

b = SP/SS_X = 5215/2780 = 1.88

a = M_Y - bM_X = 140.4 - (1.88*49) = 48.48

ŷ = 1.88X + 48.48

For x=38,

ŷ = (1.88*38) + 48.48=119.92

b.

X-M - 45.4 (X-M,)? 2.09 10.89 22.09 13.69 53.29 32.49 28.09 0.09 2.09 7.29 (X - MX/Y - My) 13.92 106.92 - 133.48 142.82 338.72 202.92 -156.88 6.72 -0.48 190.62 35.6 29.6 -22.4 70.6 SS: 168.1 SP: 711.8

Sum of X = 133
Sum of Y = 1404
Mean X = 13.3
Mean Y = 140.4
Sum of squares (SS_X) = 168.1
Sum of products (SP) = 711.8

Regression Equation = ŷ = bX + a

b = SP/SS_X = 711.8/168.1 = 4.23

a = M_Y - bM_X = 140.4 - (4.23*13.3) = 84.08

ŷ = 4.23X + 84.08

For x=15,

ŷ = (4.23*15) + 84.08=147.53

c.

X1-M 1 X2-MX2 Y.My (X1-MX1)? SPxty 881.6 SPx1x2 -32.4 (x2-M/2)2 e.e9 10.89 22.09 13.69 53.29 32.49 28.09 0.09 e.e9 7.29 ต่ ง - ก ก 5 6 65.7 SPx2y 13.92 106.92 - 133.48 142.82 338.72 202.92 -156.88 6.72 -0.48 190.62 710 38.6 417.6 71.2 769.6 268.8 16 1976.8 - 137.8 3.6 -22.4 1.6 70.6 23 180 784 75.6 SSX1: 2780 SSX2: 168.1 SPX1Y: 5215 SPX2Y: 711.8 SPX1X2: -86

Sum of X₁ = 490
Sum of X₂ = 133
Sum of Y = 1404
Mean X₁ = 49
Mean X₂ = 13.3
Mean Y = 140.4
Sum of squares (SS_X1) = 2780
Sum of squares (SS_X2) = 168.1
Sum of products (SP_X1Y) = 5215
Sum of products (SP_X2Y) = 711.8
Sum of products (SP_X1X2) = -86

Regression Equation = ŷ = b₁X₁ + b₂X₂ + a

b₁ = ((SP_X1Y)*(SS_X2)-(SP_X1X2)*(SP_X2Y)) / ((SS_X1)*(SS_X2)-(SP_X1X2)*(SP_X1X2)) = 937856.3/459922 = 2.04

b₂ = ((SP_X2Y)*(SS_X1)-(SP_X1X2)*(SP_X1Y)) / ((SS_X1)*(SS_X2)-(SP_X1X2)*(SP_X1X2)) = 2427294/459922 = 5.28

a = M_Y - b₁M_X1 - b₂M_X2 = 140.4 - (2.04*49) - (5.28*13.3) = -29.71

ŷ = 2.04X₁ + 5.28X₂ - 29.71

For x1=35 and x2=15

ŷ = (2.04*35)+ (5.28*15)- 29.71=120.89