# Odds Ratio

**ADM 7213**

**Homework Assignment 6**

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**Coefficients**

Now let’s do the simple interpretation, since that is more intuitive.

- If the regression coefficient is
, this means that an increase in__positive__

the independent variable ___________ the probability that Y=1

*If a coefficient is positive, then its odds ratio will always be greater than __*- If the regression coefficient is
, this means that an increase in__negative__

the independent variable ___________ the probability that Y=1

*If a coefficient is negative, then its odds ratio will always be less than ____**The odds ratio for negative coefficients is bounded by zero and ___**The odds ratio for positive coefficients is bounded by one and positive _________________*

**Rules for Odds Ratio Interpretation**

**Rules for Interpreting Odds Ratios on Dummy Variables**

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The mantra is this: *The odds of the numerator case are OR times the odds of the denominator case*.

__ __

- If OR>1: For example, OR=1.2. We would say that the odds of the outcome are
**(OR-1)*100**= 20%**larger**in for the numerator group. - If OR<1: For example, an OR=0.2. We would say that the odds of the outcome are
**(1-OR)*100**=80%**smaller**in the numerator group compared to another.

**Rules for Interpreting Odds Ratios on Continuous Variables**

The mantra is this: *A one unit change in X is associated with a OR change in the odds of the outcome*

- If OR>1: For example, OR=1.2. We would say that a one unit change in x is associated with a (OR-1)*100= 20%
**increase in the odds of the outcome.** - If OR<1: For example, OR=0.95. We would say that a one unit change in x is associated with a (1-OR)*100=5%
**decrease in the odds of the outcome.**

**Titanic Data**

Here are estimates for the following using logistic regression using Odds Ratios

Survived = b_{0} + b_{1} male +b_{2} fare + b_{3} age + b_{4} fam_size

For this regression, Odds Ratios are reported instead of raw coefficients.

- Interpretation of odds ratio b
_{1 }(male)

- Is this a dummy variable or continuous variable? So, you should use the

interpretation for a ______________ variable.

- Is the odds ratio greater than 1 or less than 1? So, you should use the

interpretation for an odds ratio _____ ________ 1.

- What is the interpretation of the odds ratio b
_{1}?

- What is the p value for b
_{1}?

- How many stars for b
_{1}?

- Interpretation of odds ratio b
_{2}(fare)

- Is this a dummy variable or continuous variable? So, you should use the

interpretation for a ______________ variable.

- Is the odds ratio greater than 1 or less than 1? So, you should use the

interpretation for an odds ratio _____ ________ 1.

- What is the interpretation of the odds ratio b
_{2}?

- What is the p value for b
_{2}?

- How many stars for b
_{2}?

**Logistic Regression in Real Research**

Please download and read the following article:

David J. Houston, “Walking the Walk” of Public Service Motivation: Public Employees and Charitable Gifts of Time, Blood, and Money, *Journal of Public Administration Research and Theory*, Volume 16, Issue 1, January 2006, Pages 67–86, https://doi.org/10.1093/jopart/mui028

Note that in the logistic regression tables, odds ratios are reported in parenthesis to the right of the raw coefficients)

Look at __Table 3, Model 1__.

- According to model 1, the odds ratio for public employees is 1.372.

- Is this a dummy variable or continuous variable? So, you should use the

interpretation for a ______________ variable.

- Is the odds ratio greater than 1 or less than 1? So, you should use the

interpretation for an odds ratio _____ ________ 1.

- What is the interpretation of the odds ratio?

* *

* *

* *

* *

- According to model 1, the odds ratio for years of education is 1.086

- Is this a dummy variable or continuous variable? So, you should use the

interpretation for a ______________ variable.

- Is the odds ratio greater than 1 or less than 1? So, you should use the

interpretation for an odds ratio _____ ________ 1.

- What is the interpretation of the odds ratio?

- According to model 1, the odds ratio for church attendance is 2.481

- Is this a dummy variable or continuous variable? So, you should use the

interpretation for a ______________ variable.

- Is the odds ratio greater than 1 or less than 1? So, you should use the

interpretation for an odds ratio _____ ________ 1.

- What is the interpretation of the odds ratio?