Statistical Analysis of Depression & Smoking Effects on Health

In this comprehensive statistics homework, we venture into two distinct regression analysis scenarios. First, we explore the predictors of depression levels among low-income women using Multiple Regression. In the second part, we examine whether smoking status predicts health status after accounting for age and BMI through Logistic Regression. This analysis provides valuable insights into the factors influencing depression and health status among women.

Problem Description:

In this Statistical Analysis homework, we explore two different regression analysis scenarios: Multiple Regression and Logistic Regression. The first part aims to understand the predictors of depression levels among low-income women, while the second part investigates whether smoking status predicts health status after controlling for age and BMI. Below are the details and results for each part:

Part 1: Multiple Regression Analysis

• Research Question: What variables predict the level of depression among low-income women?
• Variables:

1. CESD: Depression Score
2. AGE: Chronological Age
3. EDUCATN: Educational Attainment
4. INCOME: Family Income Prior Month
5. WORKNOW: Current Employment Status
6. SF12PHYS: SF-12 Physical Health Component Score
7. SF12MENT: SF-12 Mental Health Component Score

• Analysis: Multiple regression analysis (with 'exclude cases PAIRWISE option').
• Results:

Table 1: Regression Model Predicting Depression in Low-Income Women

1. R2 = 0.465
2. Adjusted R2 = 0.461

Summary:

In this sample of low-income women, five of the six predictor variables examined were significant predictors of depression levels (F = 114.7, p < 0.001). Education (Beta = -0.06, p = 0.03), income (Beta = -0.08, p = 0.01), employment status (Beta = -0.06, p = 0.03), physical health score (Beta = -0.14, p < 0.01), and mental health score (Beta = -0.61, p < 0.01) were significant predictors of women’s depression levels. Higher education, higher income, being employed, and having better physical and mental health were associated with lower levels of depression. Age was not a significant predictor in this sample. Women's mental health score was the strongest predictor of depression. Slightly less than half of the variance (adjusted R2 = 0.461, p < 0.01) in depression levels was explained by this set of predictor variables.

Part 2: Logistic Regression Analysis

• Research Question: Does smoking status predict health status, after controlling for age and BMI?
• Variables:

1. Dependent Variable: HEALTH (0 = fair to poor health, 1 = good to excellent health)
2. Independent Variables: SMOKER (current smoker or not), BMI (respondent's BMI), AGE (chronological age)

1. Cases Included:933
2. Null Model (Block 0): 70.4% correctly classified.
3. Full Model (Block 1): 71.8% correctly classified (improved when 3 variables were included).
4. Misclassified Cases: 263

1. Predicted to be in fair/poor health but were observed in good/excellent health: 20 cases
2. Predicted to be in good/excellent health but were observed in fair/poor health: 243 cases
3. Most common misclassification: Women in poor health classified as good/excellent health.

Interpretation:

The logistic regression analysis aimed to determine if smoking predicted health status, after controlling for age and BMI. The results showed that the odds ratio for smoking was 0.55 (95% CI: [0.40, 0.74]), indicating a 45% reduction in the odds of being in good/excellent health for smokers. This reduction ranged from 60% at worst to 26% at best within the 95% CI, demonstrating statistical significance. Among the three predictor variables, smoking had the weakest effect on health status, with BMI (OR = 0.96) and AGE (OR = 0.92) having smaller effects. Each unit increase in BMI was associated with a 4% reduction in the odds of being in good health, while each year of advancing age resulted in an 8% reduction in the odds of being in good health.