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Now we can relate the odds for males and females and the output from the logistic regression. The intercept of -1. Using the odds we calculated above for males, we can confirm this: log(. The coefficient for female is the log of odds ratio between the female group and male group: log(1. So we can get the odds ratio by exponentiating the coefficient for female.

Most statistical packages display both the raw regression coefficients and the exponentiated coefficients for logistic regression models. The table below is created by Stata. In other words, the odds of being in an honors class when the math score is zero is exp(-9.

These odds are very low, but if we look at the distribution of the variable math, we will see that no one in the sample has math score lower than 30. In fact, all the test scores in the data set were standardized around mean of 50 and standard deviation of 10. So the intercept in this model corresponds to the log odds of being in an honors class when math is at the hypothetical value of zero. How do we interpret the coefficient for math.

We will use 54. Then the conditional logit of being in an honors class when the math score is held at 54 isWe can examine the effect of a one-unit increase in math score. When the math score is held at 55, the conditional logit of being in an honors class isWe can say now that the coefficient for math is the difference in the log odds. In other words, for a one-unit increase in the math score, the expected change in log odds is. Can we translate this change in log odds to the change in odds.

Recall that logarithm converts multiplication and division to addition and subtraction. Its inverse, the exponentiation converts addition and subtraction back to multiplication and division. Applying such a model to our example dataset, each estimated coefficient is the expected change in the log odds of being in an honors class for a unit increase in the corresponding predictor variable holding the other predictor variables constant at certain value.

Each exponentiated coefficient is the ratio of two odds, or the change in odds in the multiplicative scale for a unit increase in the corresponding predictor variable holding other variables at certain value. Here is an example. In all the previous examples, we have said that the regression coefficient of a variable corresponds to the change in log odds and its exponentiated form corresponds to the odds ratio. This is only true when our model does not have any interaction terms.

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