Shown below is output from two Excel regression analyses on the same problem. Th

Question

Shown below is output from two Excel regression analyses on the same problem. The first output was done on a “full” model. In the second output, the vari- able with the smallest absolute t value has been removed, and the regression has been rerun as a second step of a backward elimination process. Examine the two outputs. Explain what happened, what the results mean, and what might happen in a third step.

FULL MODEL
Regression Statistics

Multiple R = 0.567, R Square = 0.321, Adjusted R Square = 0.208, Standard Error = 159.681, Observations = 29

ANOVA

df SS MS F Significance F

Regression 4 289856.08 72464.02 2.84 0.046   

Residual 24 611955.23 25498.13

Total 28 901811.31

Coefficients Standard Error t Stat P-value

Intercept 336.79 124.0800 2.71 0.012

X1 1.65 1.7800 0.93   0.363

X2 5.63 13.4700 0.42 0.680

X3 0.26 1.6800 0.16   0.878

X4 185.50 66.2200 2.80   0.010

SECOND MODEL

Regression Statistics

Multiple R = 0.566, R Square = 0.321, Adjusted R Square = 0.239, Standard Error = 156.534, Observations = 29

ANOVA

df SS MS F Significance F

Regression 3 289238.10 96412.70     3.93 0.020

Residual 25 612573.20 24502.90

Total 28 901811.30

Coefficients Standard Error t Stat P-value

Intercept 342.92 115.34 2.97 0.006

X1 1.83 1.31 1.40 0.174

X2 5.75 13.18    0.44 0.667

X4 181.22 59.05 3.07 0.005

Explanation / Answer

In the second model X3 was eliminated, the correlation determination R2 = 0.566 is close to that of first model is 0.567. There is no change in correlation determination. But SE of Second model is 156.534 which is less than that of first model 159.681, ,

Therefore, Second model is appropriate model compare to first model.

But we can eliminate the variable X1 and X2 since p-value of those variables are > alpha 0.05, if done, the Standard error will be reduce and R2 will be increase. Thus the model is best fit to the given data

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