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Table and Symbols in a Logistic Regression

Table and Symbols in a Logistic Regression

Quantitative Results

Statistical Analysis

Source

B

SE B

Wald χ^{2}

p

OR

95% CIOR

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 χ^{2}, p, OR, 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 χ^{2}– 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 χ^{2} 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.