Let’s consider the logistic regression model, which we will refer to as Model 1,

Question

Let’s consider the logistic regression model, which we will refer to as Model 1, given by

                                    Logit_Y = 0.25 + 0.32*X1 + 0.70*X2 + 0.50*X3

In the above formula, X3 is an indicator variable with X3=0 if the observation is from Group A and X3=1 if the observation is from Group B.

1. For X1=2 and X2=1 compute the log-odds for each group, i.e. X3=0 and X3=1.

2. For X1=2 and X2=1 compute the odds for each group, i.e. X3=0 and X3=1.

3. For X1=2 and X2=1 compute the probability of an event for each group, i.e. X3=0 and X3=1.

4. Using the equation for Model 1, compute the relative odds associated with X3, i.e. the relative odds of Group B compared to Group A.

5. Use the odds that you found in QUESTION 2 to compute the relative odds of Group B to Group A.   How does this number compare to the result in Question #4. Does this make sense?

Explanation / Answer

Logit_Y = 0.25 + 0.32*X1 + 0.70*X2 + 0.50*X3

1. For X1=2 and X2=1 compute the log-odds for each group, i.e. X3=0 and X3=1.

With x1 = 2 and x2 = 1, logit_y = 0.25+0.64+0.7 + 0.5x3 = 1.59 + 0.5x3. When x3= 0, the logit is 1.59 and x3=1, it is 2.09. Hence, the log-odds is 1.59/2.09 = 0.7608.

2. For X1=2 and X2=1 compute the odds for each group, i.e. X3=0 and X3=1, the answer is exp(0.7608) = 2.14.

3. For X1=2 and X2=1 compute the probability of an event for each group, i.e. X3=0 and X3=1 are respectively 0.8306161 and  0.8899274.

4. The relative odds associated with X3, i.e. the relative odds of Group B compared to Group A, is exp(1.59)/exp(2.09) = 0.6065307.

5. The odds and relative odds are different metrics and a comparison between them is not appropriate.

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