In: Statistics and Probability
Supplementary Problem 14.27 (Essay)
Given here are the data for a dependent variable, y,
and independent variables. Use these data to develop a regression
model to predict y. Discuss the output. Which variable is
an indicator variable? Was it a significant predictor of
y? (Set the alpha level of significance at 0.10.)
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SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.890429 | |||||||
R Square | 0.792864 | |||||||
Adjusted R Square | 0.715188 | |||||||
Standard Error | 44.69014 | |||||||
Observations | 12 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 3 | 61158.58 | 20386.19 | 10.20735 | 0.004137 | |||
Residual | 8 | 15977.67 | 1997.208 | |||||
Total | 11 | 77136.25 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 553.8005 | 441.438 | 1.254537 | 0.245058 | -464.157 | 1571.758 | -464.157 | 1571.758 |
x1 | -28.2439 | 31.8106 | -0.88788 | 0.400513 | -101.599 | 45.11149 | -101.599 | 45.11149 |
x2 | -6.03901 | 1.471032 | -4.10529 | 0.003413 | -9.43122 | -2.64681 | -9.43122 | -2.64681 |
x3 | -15.5343 | 23.29371 | -0.66689 | 0.523609 | -69.2496 | 38.18114 | -69.2496 | 38.18114 |
variable x1 is indicator variable, and it is not significant because p value for x1 = 0.400 < α=0.10
X2 is significant predictor
x3 is not significant predictor