Question

In: Statistics and Probability

End of Section Problem 13.12 Your answer is partially correct. Try again. Use the following data...

End of Section Problem 13.12

Your answer is partially correct. Try again.

Use the following data to develop a regression model to predict y from x1 and x2. Comment on the output.
Develop a regression model to predict y from x1 only. Compare the results of this model with those of the model using both predictors.What might you conclude by examining the output from both regression models?

y x1 x2
28 12.6 134
43 11.4 126
45 11.5 143
49 11.1 152
57 10.4 143
68 9.6 147
74 9.8 128
81 8.4 119
82 8.8 130
86 8.9 135
101 8.1 141
112 7.6 123
114 7.8 121
119 7.4 129
124 6.4 135

(Round all answers to 4 decimal places.)


The regression equation for y from x1 and x2 is:

y=

+(

) x1 +(

) x2

F=

with p=

tx1=

with p=

tx2=

with p=


The regression equation for y from x1 only is:

y=

+(

) x1

F=

with p=

Solutions

Expert Solution

Using Excel, go to Data select Data Analysis, choose Regression. Put y values in Y input range. Put x1 and x2 values in X input range for first model and put x1 values in X input range for second model.

x1 and x2 model

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9814
R Square 0.9632
Adjusted R Square 0.9570
Standard Error 6.3334
Observations 15
ANOVA
df SS MS F Significance F
Regression 2 12586.3823 6293.1912 156.8882 0.0000
Residual 12 481.3510 40.1126
Total 14 13067.7333
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 243.4408 23.0195 10.5754 0.0000 193.2856 293.5961
X1 -16.6079 1.0312 -16.1047 0.0000 -18.8548 -14.3610
X2 -0.0732 0.1870 -0.3915 0.7023 -0.4806 0.3342

The regression equation for y from x1 and x2 is:

y = 243.4408 + (-16.6079)x1 +(-0.0732)x2

F = 156.8882

with p = 0.000

tx1 = -16.1047

with p = 0.000

tx2 = -0.3915

with p = 0.7023

x1 model

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9812
R Square 0.9627
Adjusted R Square 0.9598
Standard Error 6.1237
Observations 15
ANOVA
df SS MS F Significance F
Regression 1 12580.2357 12580.2357 335.4746 0.0000
Residual 13 487.4976 37.4998
Total 14 13067.7333
Coefficients Standard Error t Stat P-value
Intercept 235.1429 8.6775 27.0980 0.0000
X1 -16.7678 0.9155 -18.3160 0.0000

The regression equation for y from x1 and x2 is:

y = 235.1429 + (-16.7678)x1

F = 335.4746

with p = 0.000

orchestra answered 2 years ago
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