Solved – Interpreting logistic regression output in R

interpretationlogisticp-valuer

I'm working on a multiple logistic regression in R using glm. The predictor variables are continuous and categorical. An extract of the summary of the model shows the following:

Coefficients:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)   2.451e+00  2.439e+00   1.005   0.3150
Age           5.747e-02  3.466e-02   1.658   0.0973 .
BMI          -7.750e-02  7.090e-02  -1.093   0.2743
...
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Confidence intervals:

                  2.5 %       97.5 %
(Intercept)  0.10969506 1.863217e+03
Age          0.99565783 1.142627e+00
BMI          0.80089276 1.064256e+00
...

Odd ratios:

                 Estimate Std. Error   z value Pr(>|z|)
(Intercept)  1.159642e+01  11.464683 2.7310435 1.370327
Age          1.059155e+00   1.035269 5.2491658 1.102195
B            9.254228e-01   1.073477 0.3351730 1.315670
...

The first output shows that $Age$ is significant. However, the confidence interval for $Age$ includes the value 1 and the odds ratio for $Age$ is very close to 1. What does the significant p-value from the first output mean? Is $Age$ a predictor of the outcome or not?

Best Answer

There are a host of questions here on the site that will help with the interpretation of the models output (here are three different examples, 1 2 3 , and I am sure there are more if you dig through the archive). Here is also a tutorial on the UCLA stats website on how to interpret the coefficients for logistic regression.

Although the odds-ratio for the age coefficient is close to one it does not necessarily mean the effect is small (whether an effect is small or large is frequently as much a normative question as it is an empirical one). One would need to know the typical variation in age between observations to make a more informed opinion.

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