Module 14: Multiple and Logistic Regression
Exercises
Barbara Illowsky & OpenStax et al.
Introduction to Multiple Regression
Exercise 1: Baby Weights, Part I
The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. Here, we study the relationship between smoking and weight of the baby. The variable smoke is coded 1 if the mother is a smoker, and 0 if not. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, based on the smoking status of the mother.[1]
| Estimate | Std. Error | t-value | Pr(> |t|) | |
| (Intercept) | 123.05 | 0.65 | 189.60 | 0.0000 |
| smoke | –8.94 | 1.03 | –8.65 | 0.0000 |
The variability within the smokers and non-smokers are about equal and the distributions are symmetric. With these conditions satisfied, it is reasonable to apply the model. (Note that we don’t need to check linearity since the predictor has only two levels.)
- Write the equation of the regression line.
- Interpret the slope in this context, and calculate the predicted birth weight of babies born to smoker and non-smoker mothers.
- Is there a statistically significant relationship between the average birth weight and smoking?
Exercise 2: Baby weights, Part II
Exercise 1 introduces a data set on birth weight of babies. Another variable we consider is parity, which is 0 if the child is the first born, and 1 otherwise. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, from parity.
| Estimate | Std. Error | t-value | Pr(> |t|) | |
| (Intercept) | 120.07 | 0.60 | 199.94 | 0.0000 |
| parity | –1.93 | 1.19 | –1.62 | 0.1052 |
- Write the equation of the regression line.
- Interpret the slope in this context, and calculate the predicted birth weight of first borns and others.
- Is there a statistically significant relationship between the average birth weight and parity?
Exercise 3: Baby weights, Part III
We considered the variables smoke and parity, one at a time, in modeling birth weights of babies in Exercises 1 and 2. A more realistic approach to modeling infant weights is to consider all possibly related variables at once. Other variables of interest include length of pregnancy in days (gestation), mother’s age in years (age), mother’s height in inches (height), and mother’s pregnancy weight in pounds (weight). Below are three observations from this data set.
| bwt | gestation | parity | age | height | weight | smoke | |
| 1 | 120 | 284 | 0 | 27 | 62 | 100 | 0 |
| 2 | 113 | 282 | 0 | 33 | 64 | 135 | 0 |
| [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] | [latex]vdots[/latex] |
| 1236 | 117 | 297 | 0 | 38 | 65 | 129 | 0 |