I am trying to predict a sale using a logit regression. My dependent variable is isSale and my dependent variables include only binary variables such as isHighSale_City, isHighSale_Domain, etc.

I have my regression output and converted the coefficients to odds and then to probability.

predicted_probability = odds_ratio / (1 + odds_ratio)

My question is can I sum the probabilities that I generated from the odds ratio to create a combined probability for the observation?


isHighSale_City: coef: 1.19; odds_ratio: 3.52; pred_probability: 0.779

isHighSale_Domain: coef: 0.61; odds_ratio: 1.83; pred_probability: 0.65

Intercept: coef: -6.88; odds_ratio: 0.00057; pred_probability: 0.00057

If I want to score an prospective sale in a high sale city and high sale domain, would it be:

0.779 + 0.65 + 0.00057 = 1.429

  • 2
    $\begingroup$ Could you explain how you would interpret a "probability" of $1.429$? $\endgroup$
    – whuber
    Commented Dec 13, 2017 at 20:17
  • $\begingroup$ For an observation where isHighSale_City=1 and isHighSale_Domain=1, the probability of it converting to a sale is 142% higher than if it isn't in a high sale city and a high sale domain? $\endgroup$
    – jonjon
    Commented Dec 13, 2017 at 21:40
  • 1
    $\begingroup$ @jonjon that is a probability ratio not a probability. The numbers should conform to the interpretation, not vice versa. $\endgroup$
    – AdamO
    Commented Dec 14, 2017 at 14:56

1 Answer 1


Your formula is incorrect. Odds can be converted to probability using the equation above. However, odds ratios are ratios of two different odds representing distinct probabilities. The model estimates from a logistic regression are additive on the log-odds scale. Create predictions on this scale using the appropriate coefficients, then transform the linear predictor using the inverse logit: $$\text{expit}(\alpha + x\beta) = (1+\exp(\alpha +x\beta))^{-1}$$.

This is the probabilistic prediction equation from a logistic regression. The intercept $\alpha$ is the log odds for response when all covariates are 0. The slope $\beta$ is the log odds ratio for adjacent groups in discrete or continuous $x$.

  • $\begingroup$ Ah, so i can create an additive probability and then take the inverse logit to get a more "readable" probability for the observation? $\endgroup$
    – jonjon
    Commented Dec 15, 2017 at 16:51
  • $\begingroup$ I don't understand what a readable probability is. The probability is not added. The inverse logit of a probability is a log-odds. Using logistic regression parameters, you can add up the log odds (intercept) and log odds ratios in the fashion you've shown, then reverse transform them (with inverse logit) to obtain a probability. Or fit an additive risk model. $\endgroup$
    – AdamO
    Commented Dec 15, 2017 at 17:40
  • $\begingroup$ Apologies if I'm not completely clear. I'm relatively new to this. $\endgroup$
    – jonjon
    Commented Dec 15, 2017 at 21:25
  • $\begingroup$ The resources I'm finding online mostly stop at an explanation of the odds ratio. I'm trying to create a probabilistic score. To find the probability of a sale, I can take: a + (x)HighSale_city + (x)HighSale_domain, then take the inverse logit to find the probability? $\endgroup$
    – jonjon
    Commented Dec 15, 2017 at 21:35
  • $\begingroup$ @jonjon yes! the value you use there is the one entitled "coef" and not "odds ratio". $\endgroup$
    – AdamO
    Commented Dec 15, 2017 at 22:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.