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Hi there I have currently been running a stepwise multiple linear regression in SPSS and have been having trouble interpreting the results. I have attached a link to the results below:

Regression Results

More specifically I set my regression to produce a correlation matrix which can be seen in the folder above. It is my understanding that a stepwise regression will add the most statistically significant variables one at a time until it produces the best result. However I can't understand why it is adding variables that do not exhibit the strongest correlations or significance with the dependent variable(height). Surely the model should add the variables that the variables that have the highest correlation and significance?

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    $\begingroup$ Apologies for a not complete answer, as I have not worked with SPSS for a long time. However, may it be that the step-wise procedure estimates partial correlations for newly added variable following the first one? In this way you may look at the general correlation matrix expecting its order of correlation, but the procedure operates the different coefficients. $\endgroup$ – Alexey Burnakov Oct 10 '17 at 11:04
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First off, stepwise does not produce "best" models for most definitions of best. It is not a recommended method and this has been discussed extensively here and elsewhere. See e.g. Frank Harrell's book Regression Modeling Strategies.

But, to your question, there's no conflict. Stepwise adds variables that are most significant given the existing model. There is no reason that these have to be the variables that correlate most highly with the dependent variable, unless all the independent variables are orthogonal.

For and extreme example, suppose your dependent variable is weight in a sample of adult humans. Your independent variables are height, age, sex and leg length. Now, stepwise might add height to the model as a first step. After this, it won't add leg length to the model even though its correlation with weight will be almost exactly the same as that of height, because, after height is in the model, leg length doesn't add very much.

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  • $\begingroup$ Thank you for your response, but how would you suggest I explain how variables are added to the model? $\endgroup$ – user4144725 Oct 10 '17 at 11:41
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    $\begingroup$ Unless your signal:noise ratio is very high and the sample size is huge, you could say that the variables are added randomly to the model. Stepwise regression is to be avoided. $\endgroup$ – Frank Harrell Oct 10 '17 at 12:16
  • $\begingroup$ The thing is the sample size is not very large at only 58 samples $\endgroup$ – user4144725 Oct 10 '17 at 13:55
  • $\begingroup$ If you insist on using stepwise, you can just say you used stepwise. But you shouldn't do that. All the results from stepwise are incorrect. $\endgroup$ – Peter Flom Oct 10 '17 at 17:34

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