The coefficient returned by a logistic regression in r is a logit, or the log of the odds. To convert logits to odds ratio, you can exponentiate it, as you've done above. To convert logits to probabilities, you can use the function exp(logit)/(1+exp(logit)) .
How do you use odds in logistic regression?
[3] log(p/q) = a + bX
This means that the coefficients in a simple logistic regression are in terms of the log odds, that is, the coefficient 1.694596 implies that a one unit change in gender results in a 1.694596 unit change in the log of the odds. Equation [3] can be expressed in odds by getting rid of the log.
How do you calculate odds in R?
In a 2by2 table with cells a, b, c, and d (see figure), the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or nonexposure group (c/d). Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc.
What are the odds of an event in logistic regression?
The odds that an event occurs is the ratio of the number of people who experience the event to the number of people who do not. The coefficients in the logistic regression model tell you how much the logit changes based on the values of the predictor variables.
Can you get odds ratio from logistic regression?
Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest.
What is the interpretation of R2 in logistic regression?
In logistic regression, there is no true R2 value as there is in OLS regression. However, because deviance can be thought of as a measure of how poorly the model fits (i.e., lack of fit between observed and predicted values), an analogy can be made to sum of squares residual in ordinary least squares.
How to interpret odds ratio in logistic regression in R?
An odds ratio of 1 indicates no change, whereas an odds ratio of 2 indicates a doubling, etc. Your odds ratio of 2.07 implies that a 1 unit increase in 'Thoughts' increases the odds of taking the product by a factor of 2.07.
Frequently Asked Questions
Is the R2 a good measure for logistic regression?
“Unfortunately, low R2 values in logistic regression are the norm and this presents a problem when reporting their values to an audience accustomed to seeing linear regression values… Thus we do not recommend routine publishing of R2 values from fitted logistic regression models.”
How should you interpret an odds ratio or in the context of logistic regression?
The interpretation of the odds ratio depends on whether the predictor is categorical or continuous. Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.
How do you interpret an ordinal regression model?
For an ordinal regression, what you are looking to understand is how much closer each predictor pushes the outcome toward the next “jump up,” or increase into the next category of the outcome.
How do you find the odds ratio in logistic regression?
Introduction
 P = .8. Then the probability of failure is.
 Q = 1 – p = .2.
 Odds(success) = p/(1p) or p/q = .8/.2 = 4,
 Odds(failure) = q/p = .
 P = 7/10 = .7 q = 1 – .7 = .3.
 P = 3/10 = .3 q = 1 – .3 = .7.
 Odds(male) = .7/.3 = 2.33333 odds(female) = .3/.7 = .42857.
 OR = 2.3333/.42857 = 5.44.
How to get odds ratio from logistic regression in Stata?
You can obtain the odds ratio from Stata either by issuing the logistic command or by using the or option with the logit command.
What is the interpretation of odds in logistic regression?
Odds ratios greater than 1 correspond to "positive effects" because they increase the odds. Those between 0 and 1 correspond to "negative effects" because they decrease the odds. Odds ratios of exactly 1 correspond to "no association." An odds ratio cannot be less than 0.
FAQ
 How do you interpret odds ratios?
 Important points about Odds ratio: OR >1 indicates increased occurrence of an event. OR <1 indicates decreased occurrence of an event (protective exposure) Look at CI and Pvalue for statistical significance of value (Learn more about p values and confidence intervals here) In rare outcomes OR = RR (RR = Relative Risk)
 What is the assumption of proportional odds in ordinal logistic regression?
 A major assumption of ordinal logistic regression is the assumption of proportional odds: the effect of an independent variable is constant for each increase in the level of the response.
 What does odds ratio of 1.5 mean?
 As an example, if the odds ratio is 1.5, the odds of disease after being exposed are 1.5 times greater than the odds of disease if you were not exposed another way to think of it is that there is a 50% increase in the odds of disease if you are exposed.
 When we have to choose between two logistic regression models based on AIC which one will we choose?
 If we are choosing between two models, a model with less AIC is preferred. AIC is an estimate of the information lost when a given model is used to represent the process that generates the data.
 Why use odds ratio instead of relative risk?
 The relative risk (RR) is the risk of the event in an experimental group relative to that in a control group. The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control group. An RR or OR of 1.00 indicates that the risk is comparable in the two groups.
 What is confidence interval for odds ratio?
 The confidence interval gives an expected range for the true odds ratio for the population to fall within. If estimating the odds of lung cancer in smokers versus nonsmokers of the general population based on a smaller sample, the true population odds ratio may be different than the odds ratio found in the sample.
How to get odds column in logistic regression analysis in r
Does the odds ratio give a good approximation to the relative risk for these data why OR why not?  Odds ratios often are mistaken for relative risk ratios. 2,3 Although for rare outcomes odds ratios approximate relative risk ratios, when the outcomes are not rare, odds ratios always overestimate relative risk ratios, a problem that becomes more acute as the baseline prevalence of the outcome exceeds 10%. 
Why use AIC for model selection?  With AIC, the risk of selecting a very bad model is minimized. If the "true model" is not in the candidate set, then the most that we can hope to do is select the model that best approximates the "true model". AIC is appropriate for finding the best approximating model, under certain assumptions. 
How do you interpret ordinal regression results?  Interpreting and Reporting the Ordinal Regression Output

What is the proportional odds ratio?  Or log odds ratio = β(x2 − x1). The log cumulative odds ratio is proportional to the difference (distance) between x1 and x2. Since the proportionality coefficient β is constant, this model is called the “Proportional Odds Model”. Since β is constant, curves of cumulative probabilities plotted against x are parallel. 
What is the difference between logistic and ordinal regression?  Logistic regression is usually taken to mean binary logistic regression for a twovalued dependent variable Y. Ordinal regression is a general term for any model dedicated to ordinal Y whether Y is discrete or continuous. 
How do you interpret odds ratio for categorical variables?  The interpretation of the odds ratio depends on whether the predictor is categorical or continuous. Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases. 
 How do you interpret odds ratio in ordinal regression?
 The interpretation of an OR of 1.50 in an ordinal logistic regression is that those with a 1unit greater X have 50% greater odds of having a greater outcome – 50% greater odds of Y>1 compared to Y≤1 Y ≤ 1 , 50% greater odds of Y>2 compared to Y≤2 Y ≤ 2 , …, and 50% greater odds of Y>L−1 Y > L − 1 compared to Y≤L−1 Y ≤
 How do you interpret odds ratio in logistic regression?
 The interpretation of the odds ratio depends on whether the predictor is categorical or continuous. Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.
 What is the score test for proportional odds assumption?
 The standard test is a Score test that SAS labels in the output as the “Score Test for the Proportional Odds Assumption.” A nonsignificant test is taken as evidence that the logit surfaces are parallel and that the odds ratios can be interpreted as constant across all possible cut points of the outcome.
 What is the proportional odds assumption in ordered logistic regression?
 A major assumption of ordinal logistic regression is the assumption of proportional odds: the effect of an independent variable is constant for each increase in the level of the response.
 What is a violation of the proportional odds assumption?
 The proportional odds assumption in ordered logit models is a restrictive assumption that is often violated in practice. A violation of the assumption indicates that the effects of one or more independent variables significantly vary across cutpoint equations in the model.