# Probability from Logit Regression

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?

Example:

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

• Could you explain how you would interpret a "probability" of $1.429$?
– whuber
Dec 13, 2017 at 20:17
• 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? Dec 13, 2017 at 21:40
• @jonjon that is a probability ratio not a probability. The numbers should conform to the interpretation, not vice versa. Dec 14, 2017 at 14:56

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 $x$.