Table and Symbols in a Logistic Regression

Quantitative Results
Statistical Analysis
Source
B
SE B
Wald χ2
p
OR
95% CI OR
       
Variable 1
1.46
0.12
7.55
.006
4.31
Variable 2
-0.43
0.15
6.31
.012
0.65

Note. OR = odds ratio. CI = confidence interval

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The table for a typical logistic regression is shown above.  There are six sets of symbols used in the table (B, SE B,Wald χ2pOR, 95% CI OR).  The main variables interpreted from the table are the p and the OR.  However, it can be useful to know what each variable means.

B – This is the unstandardized regression weight. It is measured just a multiple linear regression weight and can be simplified in its interpretation. For example, as Variable 1 increases, the likelihood of scoring a “1” on the dependent variable also increases.  As Variable 2 increases, the likelihood of scoring a “1” on the dependent variable decreases.

SE B – Like the multiple linear regression, this is how much the unstandardized regression weight can vary by. It is similar to a standard deviation to a mean.

Wald χ2– This is the test statistic for the individual predictor variable.  A multiple linear regression will have a t test, while a logistic regression will have a χ2 test.  This is used to determine the p value.

p – this is used to determine which variables are significant.  Typically, any variable that has a p value below .050 would be significant.  In the table above, Variable 1 and Variable 2 are significant.

OR – this is the odds ratio.  This is the measurement of likelihood.  For every one unit increase in Variable 1, the odds of a participant having a “1” in the dependent variable increases by a factor of 4.31.  However, for Variable 2, this doesn’t make a lot of sense (for every one unit increase in Variable 2, the odds of a participant having a “1” in the dependent variable increases by a factor of 0.65).  Any significant variable with a negative B value will be easier to interpret in the opposite manner.  Therefore for every one unit increase in Variable 2, the odds of a participant being a “0” in the dependent variable increases by a factor of (1 / 0.65) 1.54.  To interpret in the opposite direction, simply take one divided by that odds ratio.

95% CI OR – this is the 95% confidence interval for the odds ratio.  With these values, we are 95% certain that the true value of the odds ratio is between those units.  If the confidence interval does not contain a 1 in it, the pvalue will end up being less than .050.