Correlation Analysis
Assignment: (The topic of discussion is Logistic Regression)
Examine the results of Exercise 2 at the end of the chapter. (exercise 2 data attached).
Set up the 9-step hypothesis testing procedure for the analysis.
This is the format for the 9-step hypothesis I need to use:
Exercise 2
9-step Hypothesis Testing Procedure:
1. Evaluate the Data
2. Review Assumptions
3. State Hypotheses
4. Select the Test Statistic
5. Distribution of the Test Statistic
6. State the Decision Rule
7. Calculate the Test Statistic
8. Statistical Decision
9. Conclusion
Exercise 2:
Recode the depressed state of mind variable into a dichotomous variable with two groups: those who rated themselves as rarely depressed are scored 0, and those who rated themselves as sometimes to routinely depressed are scored 1. Using the new variable as the outcome measure, determine which of the following variables increase the odds of being depressed:
Smoking history: recoded into currently smoking = 1, and not currently smoking = 0.
2. Gender: Male = 0, Female = 1
3. Quality of life in the past month: recoded so that values 1 to 3 (sometimes to very unhappy) become 0, and 4 to 6 (sometimes to extremely happy) become 1.
4. Total score on the Inventory of Positive Psychological Attitudes scale (IPPA): Enter recoded smoking history and gender in the first block and recoded quality of life and total IPPA score in the second block.
Results for Exercise 2:
A logistic regression was run to answer the research question (n=653). The results are contained in Exercise Figure 13-1. The variables were entered in tow blocks. Smoking status and gender were entered in block 1, which was significant (p=.003), and accounted for 1.8 to 2.4 percent of the variance. The Hosmer and Lemeshow Test indicated a good fit (p=.808). Only smoking made a significant contribution (p=.001). Quality of life and total IPPA score were entered in block 2, which was significant (p=.000). The total model was significant (p=.000), and accounted for 34.3 to 45.7 percent of the variance. The model was a good fit. (Hosmer and Lemeshow, chi square = 4.068, df = 8, p = .851). The sensitivity of the model in predicting depression was 72.3 percent. The specificity in predicting those who were not depressed was 80. Three of the variables, smoking status (p=.032), quality of life (p=.000), and Total IPPA Score (p=.000) were significant predictors. The odds of being depressed were 2 times higher for those who smoked. Higher quality of life was related to lower probability of depression. The IPPA scale is scored from 30 to 210, therefore, a 1 point increase in that score would be of no practical interest. To calculate the effect of a 30 point change in IPPA, multiply the b-weight for TOTAL times 30 and raise 2.1718 to that power (.057 x 30 = 1.71), raising 2.1718 to the power of 1.71 = 5.53. So, for every 30 point increase in the IPPA score, the odds of being depressed go down (negative b-weight) 5.5 times.
Exercise Figure 13-1
LOGISTIC REGRESSION
Dependent Variable Encoding
|
Original Value |
Internal Value |
| Rarely |
0 |
|
Sometimes to routinely |
1 |
BLOCK 1: Method = Enter
Omnibus Tests of Model Coefficients
|
Chi Square |
df |
Sig | |
| Step 1 Step |
11.848 |
2 |
.003 |
| Block |
11.848 |
2 |
.003 |
| Model |
11.848 |
2 |
.003 |
Model Summary
|
Step |
-2Log likelihood |
Cox & Snell R Square |
Nagelkerke R Square |
|
1 |
892.445 |
.018 |
.024 |
Hosmer and Lemeshow Test
|
Step |
Chi Square |
Df |
Sig. |
| 1 |
.059 |
1 |
.808 |
Variables in the Equation
|
B |
S.E. |
Wald |
df |
Sig |
Exp(B) | |
|
Step 1(a) SMOKEREC |
.903 |
.273 |
10.978 |
1 |
.001 |
2.468 |
| Gender |
.169 |
.166 |
1.037 |
1 |
.309 |
1.184 |
| Constant |
-.275 |
.137 |
4.039 |
1 |
.044 |
.759 |
a Variables entered on step1: SMOKERERC, GENDER
Block 2: Method = Enter
Omnibus Tests of Model Coefficients
|
Chi Square |
df |
Sig. | |
| Step 1 Step |
262.275 |
2 |
.000 |
| Block |
262.275 |
2 |
.000 |
| Model |
274.123 |
4 |
.000 |
Model Summary
|
Step |
-2 Log likelihood |
Cox & Snell R Square |
Nagelkerke R Square |
| 1 |
630.170 |
.343 |
.457 |
Hosmer and Lemeshow Test
|
Step |
Chi Square |
df |
Sig. |
| 1 |
4.068 |
8 |
.851 |
Classification Table (a)
|
Observed |
Predicted Depression recoded rarely Sometimes to routinely |
Percentage correct |
|||
|
Step 1 Depression Rarely recoded Sometimes to routinely |
273 87 |
66 227 |
80.5 72.3 |
||
|
Overall percentage |
76.6 |
||||
a The cut value is .500
Variables in the Equation
|
B |
S.E. |
Wald |
df |
Sig |
Exp(B) | |
|
Step 1(a) SMOKEREC |
.771 |
.359 |
4.621 |
1 |
.032 |
2.162 |
| GENDER |
.225 |
.206 |
1.187 |
1 |
.276 |
1.252 |
| QOLREC |
-1.066 |
.292 |
13.320 |
1 |
.000 |
.344 |
| TOTAL |
-.057 |
.005 |
117.961 |
1 |
.000 |
.944 |
| Constant |
9.433 |
.832 |
128.681 |
1 |
.000 |
12499.450 |
a Variable(s) entered on step 1: QOLREC, TOTAL
