# Logistic Regression Interpretation

#### smw10c

##### New Member
I hope you are all having a good day. How would I interpret the coefficient on age in the following logistic regression (note that the coefficients are the marginal effects at the mean)? Would it be: as age increases by 1 unit, the probability of cancer survival decreases by 0.023% or would it be that it decreases by 2.3%? I don't know if I am supposed to multiply the slope coefficient by 100.

cancer_survival=0.761-0.023age

#### gianmarco

##### TS Contributor
Hello,
the estimated coefficients can be meaningful interpreted if you exponentiate them, thus expressing them in terms of odds ratio.
An exponentiated coefficient of 1 leaves the odds for the positive outcome of the dependent variable unchanged, while a coefficient greater or smaller than 1 increases or decreases the odds respectively.

In your case, exp(-0.023)=0.9772625.

Therefore, 1-unit increase in age decreases the odds for cancer survival by 0.977.

Hope this makes sense.
Gm

#### smw10c

##### New Member
Hello,
the estimated coefficients can be meaningful interpreted if you exponentiate them, thus expressing them in terms of odds ratio.
An exponentiated coefficient of 1 leaves the odds for the positive outcome of the dependent variable unchanged, while a coefficient greater or smaller than 1 increases or decreases the odds respectively.

In your case, exp(-0.023)=0.9772625.

Therefore, 1-unit increase in age decreases the odds for cancer survival by 0.977.

Hope this makes sense.
Gm
Thank you for your response. I am a bit confused because my econometrics professor and my microeconomics professor instructed us to find the marginal effects at the mean or the average marginal effects and just to interpret that number. Is that a method as well?

#### hlsmith

##### Omega Contributor
I might add a little more info; a one unit increase in age results in 2.3% lower odds for cancer survival, you may want to evaluate the respective confidence intervals to see whether this is a significant change. This is given that your dependent variable group of interest was survived.

#### smw10c

##### New Member
I might add a little more info; a one unit increase in age results in 2.3% lower odds for cancer survival, you may want to evaluate the respective confidence intervals to see whether this is a significant change. This is given that your dependent variable group of interest was survived.
Thank you so much!

#### hlsmith

##### Omega Contributor
Most estimate effects are considered the marginal effects. I believe it is when you look at interactions or sub-analyses when you get off the margins.

#### ondansetron

##### TS Contributor
Hello,
the estimated coefficients can be meaningful interpreted if you exponentiate them, thus expressing them in terms of odds ratio.
An exponentiated coefficient of 1 leaves the odds for the positive outcome of the dependent variable unchanged, while a coefficient greater or smaller than 1 increases or decreases the odds respectively.

In your case, exp(-0.023)=0.9772625.

Therefore, 1-unit increase in age decreases the odds for cancer survival by 0.977.

Hope this makes sense.
Gm
I think you may have made a typo or may have been a bit unclear for my understanding. The odds ratio of 0.977 would indeed indicate that increasing age will tend to decrease the odds of survival, but the decrease would be 2.3% (0.023) as pointed out by hlsmith. You could say that the odds of survival change by a factor of 0.977 for each additional year of age, but this doesn't sound as intuitive as just saying the odds of survival decrease by 2.3%, on average, for each additional year of age.

I felt it might be a bit unclear since it's not obvious whether you mean by a multiplicative factor of 0.977 versus a linear decrease of 0.977%. Feel free to clarify if I missed something!

#### smw10c

##### New Member
I think you may have made a typo or may have been a bit unclear for my understanding. The odds ratio of 0.977 would indeed indicate that increasing age will tend to decrease the odds of survival, but the decrease would be 2.3% (0.023) as pointed out by hlsmith. You could say that the odds of survival change by a factor of 0.977 for each additional year of age, but this doesn't sound as intuitive as just saying the odds of survival decrease by 2.3%, on average, for each additional year of age.

I felt it might be a bit unclear since it's not obvious whether you mean by a multiplicative factor of 0.977 versus a linear decrease of 0.977%. Feel free to clarify if I missed something!
Now it makes sense. Thank you so much!