Question

In: Math

Consider the following data for a dependent variable y and two independent variables, x1 and x2....

Consider the following data for a dependent variable y and two independent variables, x1 and x2.

x1 x2 y
30 13 95
46 10 108
25 18 113
50 16 179
40 5 95
51 20 176
74 7 170
36 12 117
59 13 142
77 16 211

Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.

a. Develop an estimated regression equation relating y to x1.

ŷ =_________ +___________ x1

Predict y if x1 = 45.

ŷ = ____________

b. Develop an estimated regression equation relating y to x2.

ŷ =__________ +____________ x2


Predict y if x2 = 15.

ŷ = ___________

c. Develop an estimated regression equation relating y to x1 and x2.

ŷ =________ +___________ x1________ +____________ x2

Predict y if x1 = 45 and x2 = 15.

ŷ = __________

Solutions

Expert Solution

a)

Regression Statistics
Multiple R 0.8090
R Square 0.6545
Adjusted R Square 0.6113
Standard Error 25.5286
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 9876.7 9876.7 15.16 0.0046
Residual 8 5213.7 651.7
Total 9 15090.4
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 47.4305 25.2577 1.8779 0.0972 -10.8139 105.6748
X 1.9092 0.4904 3.8930 0.0046 0.7783 3.0401

Ŷ =   47.43   +   1.91   *x

Predicted Y at X=   45   is                  
Ŷ =   47.4305   +   1.9092   *   45   =   133.35

b)

Regression Statistics
Multiple R 0.4273
R Square 0.1826
Adjusted R Square 0.0804
Standard Error 39.2673
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 2755.0 2755.0 1.79 0.2181
Residual 8 12335.4 1541.9
Total 9 15090.4
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 92.5901 38.0028 2.4364 0.0408 4.9554 180.2248
X 3.6931 2.7628 1.3367 0.2181 -2.6780 10.0642

Ŷ =   92.59   +   3.69   *x

Predicted Y at X=   15   is                  
Ŷ =   92.5901   +   3.6931   *   15   =   147.99

c)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.957381
R Square 0.916579
Adjusted R Square 0.892744
Standard Error 13.41035
Observations 10
ANOVA
df SS MS F Significance F
Regression 2 13831.54 6915.769 38.45567 0.000168
Residual 7 1258.862 179.8374
Total 9 15090.4
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -16.3966 19.00773 -0.86263 0.416915 -61.3427 28.54957 -61.3427 28.54957
x1 2.03232 0.258959 7.848043 0.000103 1.419979 2.64466 1.419979 2.64466
x2 4.447643 0.948435 4.689455 0.002236 2.204951 6.690336 2.204951 6.690336

Y^ = -16.40+2.03*X1 + 4.45*X2

Y^ = -16.40+2.03*45 + 4.45*15 = 141.70


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