I need to see the steps so that I may understand my own mistakes. Thank you! The data are from n = 900 students at Penn State, surveyed in February of 2007. We will use logistic regression to predict...

I need to see the steps so that I may understand my own mistakes. Thank you!
The data are from
n
= 900 students at Penn State, surveyed in February of 2007. We will use logistic regression to predict the probability that a student says they have ever cheated on a college exam. The
y-variable is ChtdExam and possible responses are Yes and No.

1. Do a logistic regression that relates the probability of having ever cheated on an exam to GPA. In Minitab, use Stat>Regression>Binary Logistic Regression > (Fit) Binary Logistic Model. Take the following actions:

• Enter ChtdExam as Response.


• Enter GPA 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 having ever cheated on an exam versus GPA. [In Minitab, use Graph>Scatterplot and select “With Connect Line.” Use the column Fits1 as the
   y-variable and GPA as the
   x-variable.] Copy and paste the plot as part of your answer AND briefly describe what the plot shows about how the probability of having ever cheated on an exam is related to GPA.


2. Examine the results that were generated in part (a) in order to find the odds ratio for GPA. 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. Refer to the equation that you wrote in part (a). Use it to estimate the probability of having ever cheated on an exam for a student with a GPA = 3.0. (You can use the plot in part (b) to see if your answer is in the neighborhood of being correct.)


4. Calculate the odds of having ever cheated on an exam for a student with a GPA = 4.0. [Hint: You can calculate this two different ways. Use the equation from part (a) and the fact that the odds of an event are p/(1–p). Alternatively, use the answers to parts (c) and (d) and the fact that the odds ratio multiplies the odds each time
   x
   is increased by one unit.]


5. Now add the variable SkipClass as a predictor variable in the model (along with GPA). SkipClass is the number of classes student says he or she misses in a typical week. What is the evidence in the output that SkipClass is related to the probability of having ever cheated on an exam?


6. For the model with two
   x-variables, write a sentence that gives the odds ratio for SkipClass and interprets it in the context of this situation.


7. In the logistic model with two
   x
   variables, the odds of an event can be computed directly from the equation:

Use this equation to estimate the odds of having ever cheated on an exam for students with a 3.5 GPA who typically miss one class per week.

1. In part (g) you wrote the odds ratio for SkipClass and in part (h) you found the odds of having ever cheated on an exam for students with a 3.5 GPA who typically skip one class per week. Use only the answers to parts (g) and (h) to determine the odds of having ever cheated on an exam for students with a 3.5 GPA who typically skip two classes per week.


2. Four more variables in the dataset are the following:

• FakeID = whether student has ever used a fake id in order to be served alcohol.


• ChtdSO = whether student has ever cheated on another person with whom they were having a romantic relationship.


• SmokeCig = whether student smokes cigarettes.


• SmokeMJ = whether student has ever smoked marijuana.

All four of these variables are coded as either Yes or No. In the multiple logistic regression model for predicting the probability of ever having cheated on an exam, add the four variables just listed to the model along with GPA and SkipClass.
[In Minitab17, list these variables in the “Categorical Predictors.” In Minitab16, list these variables in the Model box and also in the Factors box. Minitab will create indicator variables for variables in the Factors box. In this case, each indicator variable created will equal 1 for Yes and 0 for No.]
Discuss the results with respect to these added variables only. Which variables are significant, which are not? Interpret the significant odds ratios.