**Logistic regression** is a type of regression analysis we use when the response variable is binary.

We can use the following general format to report the results of a logistic regression model:

Logistic regression was used to analyze the relationship between [predictor variable 1], [predictor variable 2], … [predictor variable

n] and [response variable].

It was found that, holding all other predictor variables constant, the odds of [response variable] occurring [increased or decreased] by [some percent] (95% CI [Lower Limit, Upper Limit]) for a one -unit increase in [predictor variable 1].

It was found that, holding all other predictor variables constant, the odds of [response variable] occurring [increased or decreased] by [some percent] (95% CI [Lower Limit, Upper Limit]) for a one -unit increase in [predictor variable 2].

…

We can use this basic syntax to report the odds ratios and corresponding 95% confidence interval for the odds ratios of each predictor variable in the model.

The following example shows how to report the results of a logistic regression model in practice.

**Example: Reporting Logistic Regression Results**

Suppose a professor wants to understand whether or not two different studying programs (program A vs. program B) and number of hours studied affect the probability that a student passes the final exam in his class.

He fits a logistic regression model using hours studied and studying program as the predictor variables and exam result (pass or fail) as the response variable.

The following output shows the results of the logistic regression model:

Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.415 0.623 -3.876 <0.000 program_A 0.344 0.156 2.205 0.027 hours 0.006 0.002 3.000 0.003

Before we report the results of the logistic regression model, we should first calculate the odds ratio for each predictor variable by using the formula e^{β}.

For example, here’s how to calculate the odds ratio for each predictor variable:

- Odds ratio of Program: e
^{.344}= 1.41 - Odds ratio of Hours: e
^{.006}= 1.006

We should also calculate the 95% confidence interval for the odds ratio of each predictor variable using the formula e^{(β +/- 1.96*std error)}.

For example, here’s how to calculate the odds ratio for each predictor variable:

- 95% C.I. for odds ratio of Program: e
^{.344 +/- 1.96*.156}= [1.04 , 1.92] - 95% C.I. for odds ratio of Hours: e
^{.006 +/- 1.96*.002}= [1.002 , 1.009]

Now that we’ve calculated the odds ratio and corresponding confidence interval for each predictor variable, we can report the results of the model as follows:

Logistic regression was used to analyze the relationship between studying program and hours studied on the probability of passing a final exam.

It was found that, holding hours studied constant, the odds of passing the final exam increased by 41% (95% CI [.04, .92]) for students who used studying program A compared to studying program B.

It was also found that, holding studying program constant, the odds of passing the final exam increased by .6% (95% CI [.002, .009]) for each additional hour studied.

Note that we reported the odds ratios for the predictor variables as opposed to the beta values from the model because the odds ratios are easier to interpret and understand.

**Additional Resources**

The following tutorials offer additional information on logistic regression:

Introduction to Logistic Regression

How to Perform Logistic Regression in R

How to Perform Logistic Regression in Python

4 Examples of Using Logistic Regression in Real Life

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