a)
SUMMARY OUTPUT | |||||
Regression Statistics | |||||
Multiple R | 0.416053663 | ||||
R Square | 0.173100651 | ||||
Adjusted R Square | 0.168725522 | ||||
Standard Error | 0.242952779 | ||||
Observations | 191 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 2.335347946 | 2.335348 | 39.5647 | 2.15E-09 |
Residual | 189 | 11.15592396 | 0.059026 | ||
Total | 190 | 13.49127191 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 0.779935051 | 0.424394376 | 1.83776 | 0.067668 | -0.05722 |
GIR | 0.041106819 | 0.006535216 | 6.290048 | 2.15E-09 | 0.028215 |
y^= 0.7799 + 0.0411 GIR
b)
SUMMARY OUTPUT | |||||
Regression Statistics | |||||
Multiple R | 0.83765946 | ||||
R Square | 0.70167337 | ||||
Adjusted R Square | 0.69688738 | ||||
Standard Error | 0.14670728 | ||||
Observations | 191 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 3 | 9.466466271 | 3.155489 | 146.6099 | 7.04E-49 |
Residual | 187 | 4.024805635 | 0.021523 | ||
Total | 190 | 13.49127191 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 7.2217 | 0.71175534 | 10.14634 | 1.5E-19 | 5.817611 |
GIR | 0.0755 | 0.004906387 | 15.38117 | 4.88E-35 | 0.065787 |
DriveDist | 0.0125 | 0.001310586 | 9.545474 | 7.68E-18 | 0.009925 |
PPR | -0.4211 | 0.026581946 | -15.8423 | 2.12E-36 | -0.47356 |
y^= 7.2217 + 0.0755 GIR + 0.0125 DriveDist -0.4211 PPR
c)
SSE(reduced) = 11.1559
SSE (full) = 4.0248
MSE(full) = 0.02152
F = ((11.1559 - 4.0248)/2)/( 0.02152 )
=165.6854
p-value = =F.DIST.RT(165.6854,2,187)
=0.0000
the addition is statistically signifcant
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