# Interpretation of logistic regression summary

I'm having trouble understanding how to interpret the results in this particular situation. The research topic is to understand how different cat species (Cats 1-3) get infected by a specific parasite.

In the table above, the base category is Cat1. The p-value for the intercept is high, so we cannot conclude Cat1 has a high/low probability of infection. But, we can say that Cat2 has significantly lower odds of infection than Cat1 since the odds ratio is exp(3.52) = 34 (approx.). In this situation what can I say about the odds (or probability) of infection for Cat2? (Although Cat1 has higher odds than Cat2, we can't say if Cat1 has a high/low probability of infection). This part seems confusing to me, so any help would be appreciated.

• Welcome to Cross Validated! When you sau that Cat1 does not have a higher/lower odds of infection, what if your reference? Higher or lower than what?
– Dave
Commented Mar 24, 2022 at 15:37
• that was a mistake, I corrected it. Commented Mar 24, 2022 at 15:42

You're right that there is uncertainty about whether the log-odds for $$\text{Cat1}$$ are greater than or less than zero, but we do have an estimate for the log-odds of $$\text{Cat1}$$: $$-0.19$$.

Then we have an estimate for the log-odds of $$\text{Cat2}$$, relative to $$\text{Cat1}$$: $$-3.52$$.

Consequently, the estimated log-odds for $$\text{Cat2}$$ are $$-0.19 - 3.52 = -3.71$$.

By similar logic, the log-odds for $$\text{Cat3}$$ are $$-0.22$$.

To get the odds, we can take $$\exp(\text{log-odds})$$.

$$\text{Cat2 odds: }\exp(-3.71) = 0.0245\\ \text{Cat3 odds: }\exp(-0.22) = 0.803$$

• So, would the conclusion be something like "although cat1 has a low probability of infection, cat2 has an even lower probability of infection than cat1"? Commented Mar 24, 2022 at 16:11
• $\text{Cat1}$ has an estimated probability of infection of about $45\%$. I am not sure that's a low probability of infection.
– Dave
Commented Mar 24, 2022 at 16:20