Question

In: Statistics and Probability

Supplementary Problem 14.27 (Essay) Given here are the data for a dependent variable, y, and independent...

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.)

x1 x2 x3 y
0 51 16.4 14
0 48 17.1 17
1 29 18.2 29
0 36 17.9 32
0 40 16.5 54
1 27 17.1 86
1 12 17.9 116
0 17 18.2 120
1 16 16.9 194
1 9 18.0 203
1 14 18.9 217
0 11 18.5 235

Solutions

Expert Solution

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


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