Do a logistic regression that relates the probability of death penalty to Aggravation. In Minitab, use Stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model. Then Use Response in...

1. Do a logistic regression that relates the probability of death penalty to Aggravation. In Minitab, use Stat
   >
   Regression
   >
   Binary Logistic Regression > Fit Binary Logistic Model. Then

• Use Response in event/trial format


• Enter DeathPenalty in Number of events box.


• Enter cases in Number of trials box.


• Enter Aggravation in the Continuous Predictors box.


• Click Storage and request Fits (event probabilities). Click OK.

Write the sample logistic regression equation for this situation by filling in values for the coefficients b₀
and b₁
in the equation:

1. Plot the stored predicted probabilities of DeathPenalty occurrence versus Aggravation. [In Minitab, use Graph
   >
   Scatterplot and select “With Connect Line.” Use the column Fits as the
   y-variable and Aggravation as the
   x-variable.] Copy and paste the plot as part of your answer AND briefly describe what the plot shows about how the likelihood of DeathPenalty occurrence is related to Aggravation.


2. Using the output generated in part (a) find the odds ratio for Aggravation. Write a sentence that gives the value and interprets it in this situation. [If you're using software that does not give the odds ratio, calculate it using the formula
   e<sup>b
   
   1</sup>.]


3. Use the fitted sample logistic regression equation that you wrote in part (a) to predict the probability of death penalty for an individual with Aggravation = 2.0. (You can use the plot in part (b) to see if your answer is in the neighborhood of being correct.)


4. Now refit the model but enter the variable Victim in the Categorical Predictors box (along with Aggravation in the Continuous Predictors Box). Is there any statistical evidence that Victim is related to the odds of death penalty, and if so, which Victim has higher odds of death penalty?


5. Write down the logit regression equation in terms of the two predictors, Aggravation and Victim. Then plug in 1 and 0 for Victim to write two logit regression equations, one for White victims and one for Black victims. [Hint: the logit regression equation is of the form:

Logit() = constant1 + constant2 * Aggravation + constant3*Victim,
where, and the numerical values of constant1, constant2, and constant3 can be found in the Coefficients table of the Minitab output.]

1. The odds of death penalty in terms of both predictors can be computed directly from the equation:

Use the logit equation involving both predictors obtained in part (f) above to estimate the odds of death penalty for a White victim with Aggravation level equal to the sample White victim Aggravation average. [Remember that sample data is given as frequencies, so you will use:
The sample White victim Aggravation average = ]

1. Use the sample logit regression equation obtained in part (f) to express the estimated logit of the probability of no death penalty in terms of Aggravation and Victim.
   [Hints: The probability of no death penalty is 1–p, and log(1/a) = –log(a).]
   

Use the logit equation for White victims from part (f) to find the Aggravation at which death penalty probability is 0.85 for White victims.