Logistic Worksheet
We will be using Minitab to study data on the performance of the O-ring seals on the space shuttle Challenger. Data on temperature and seal incidents appears below. You can enter the data in three columns of your Minitab worksheet (it actually takes two columns to construct the response variable: number of incidents and number of trials).
| c | ||
| Temperature | Seal Incidents | No. of Seals |
| 54 | 3 | 3 |
| 57 | 1 | 1 |
| 58 | 1 | 1 |
| 63 | 1 | 1 |
| 66 | 0 | 1 |
| 67 | 0 | 3 |
| 68 | 0 | 1 |
| 69 | 0 | 1 |
| 70 | 2 | 4 |
| 73 | 0 | 1 |
| 75 | 2 | 3 |
| 76 | 0 | 2 |
| 78 | 0 | 1 |
| 79 | 0 | 1 |
| 81 | 0 | 1 |
After entering this data in the worksheet, select Stat>Regression>Binary Logistic Regression. There are several different ways the response can be encoded so the response formatting is confusing. Click on Success and select the column in which the number of seal incidents was entered then click on Trial and select the column in which the number of trials at each temperature was entered.
The model is simple; enter the column containing the temperatures in the Model dialog box. At this point, we could run a simple logistic regression though there are options we need to explore. Note that Minitab has Options, Storage, Results and Graphs buttons. Results controls the screen output and isn't relevant for this course. Likewise, Graphs produces influence and leverage plots which we won't have time to explore in this class-you can look at the options at your own risk. Under Storage, I would encourage you to save Event probability and Pearson residuals (note the other types of residuals). You could use Options for a probit or Gompit model. The output contains much of the information you would find in SAS. In the table of regression coefficients, the odds-ratio refers to the odds of a success when the independent variable is incremented by 1. Minitab conducts a likelihood ratio test, a Pearson Chi-square test, a deviance test and a Hosmer-Lemeshow test, but doesn't compute score tests, Wald tests, the Akaike Information Criterion and Schwartz' Criterion. The display of assocation measures is similar to SAS.
Print the output and we will discuss is briefly in class. What would be the probability of a seal incident at 32 degrees? What is the threshold value at which 50% failure would be predicted?