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Shown below is the output of two regression analyses on the same problem. The first output was done on a full model. In the second

Shown below is the output of two regression analyses on the same problem. The first output was done on a "full" model. In the second output, the variable with the highest p-value was removed and the regression has been rerun. Examine the two outputs.

Independent Variables Coefficients p-value
Intercept 336.790 0.012
X1 1.650 0.363
X2 -5.630 0.680
X3 0.260 0.878
X4 185.500 0.010

Independent Variables Coefficients p-value
Intercept 342.919 0.006
X1 1.834 0.174
X2 -5.749 0.667
X4 181.220 0.005

  1. Is Model 2 better than Model 1? Explain why. What is the most significant variable in the regression?
  2. Suppose we continue with this process of backward elimination where we remove the variable with the highest p-value. Which variable is likely to become newly significant as a result of this step? Does this imply that we have a better model?

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