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I want to get verified if I can say like this.

here is the GLM output:

glm(formula = purchase ~ PC1 + month + weekday + job, 
  family = binomial(link = "logit"), data = data_train)

Deviance Residuals:
    Min      1Q  Median     3Q    Max
-2.4295 -0.8625 -0.5331 0.8478 2.1372

Coefficients:    
            Estimate Std. Error z value  Pr(>|z|)
(Intercept) -0.107928  0.117437  -0.919  0.358083
PC1          0.644329  0.023459  27.466  < 2e-16  ***
monthaug    -0.029188  0.117221  -0.249  0.803357
monthdec     1.120358  0.474668   2.360  0.018260 *
monthjul     0.469336  0.121083   3.876  0.000106 ***
monthjun     0.483871  0.126402   3.828  0.000129 ***
monthmar     0.873300  0.204628   4.268  1.97e-05 ***

Let's say if the base level is monthjan (i.e. January). Can you please verify if this interpretation for the selected feature is fine?

Given that we change from January (i.e. base level) to March, the predicted odds (i.e. $\frac{\hat{\mu}}{1-\hat{\mu}}$) will increase by 239% if all the other variables stay the same.

Also, "the predicted" is needed in the sentence?

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1 Answer 1

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This is technically correct, but it is preferred to express it in terms of an odds ratio. Also, this is more of an estimation not a prediction, so it would be better to use "estimated" odds. It's important because we don't exactly know the population odds ratio between these two groups, so we need to add a disclaimer that says that it's only an estimated relation of the odds.

I would write the interpretation as:

Given that we change from January (i.e. base level) to March, the odds of success (i.e. mu^/1-mu^) will be 2.39 times higher if all the other variables stay the same.

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  • $\begingroup$ thank you, Migs. Just wondering instead of saying '2.39times higher' in your answer, can I say like this? If we switch from January to March, the predicted odds of success will change by a factor of 239% if any other variable stays the same. $\endgroup$
    – user398060
    Commented Oct 16, 2023 at 4:46

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