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  3. consider the following data for a dependent variab

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...

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Basic Math

Consider the following data for a dependent variable yand two independent variables, x1 andx2.

x1x2y
301395
4610108
2518113
5016179
40595
5120176
747170
3612117
5913142
7716211

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

a. Develop an estimated regression equationrelating y to x1.

? =_________ +___________ x1

Predict y if x1 = 45.

? = ____________

b. Develop an estimated regression equationrelating y to x2.

? =__________ +____________ x2


Predict y if x2 = 15.

? = ___________

c. Develop an estimated regression equationrelating y to x1 andx2.

? =________ +___________ x1________ +____________ x2

Predict y if x1 = 45 andx2 = 15.

? = __________

Answer & Explanation Solved by verified expert
4.3 Ratings (619 Votes)

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

Y? =   47.43   +   1.91   *x

Predicted Y at X=   45   is                  
Y? =   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

Y? =   92.59   +   3.69   *x

Predicted Y at X=   15   is                  
Y? =   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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