Solutions: https://www.paulamoraga.com/course-aramco/99-problems-4regression-solutions.html

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.

Estimate | Std. Error | t value | Pr(\(\geq \mid t\mid\)) | |
---|---|---|---|---|

(Intercept) | 123.05 | 0.65 | 189.60 | 0.0000 |

smoke | -8.94 | 1.03 | -8.65 | 0.0000 |

Write the equation of the regression model.

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?

The previous exercise Part I introduces a data set on birth weight of babies. Another variable we consider is `parity`

, which is 1 if the child is the first born, and 0 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(\(\geq \mid t\mid\)) | |
---|---|---|---|---|

(Intercept) | 120.07 | 0.60 | 199.94 | 0.0000 |

parity | -1.93 | 1.19 | -1.62 | 0.1052 |

Write the equation of the regression model.

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?

We considered the variables `smoke`

and `parity`

, one at a time, in modeling birth weights of babies in previous exercises Part I and II. 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`

).

Use the data `babies.csv`

(LINK) to answer the following questions.

- Write the equation of the regression model that relates birth weights of babies (
`bwt`

) to variables`gestation`

,`parity`

,`age`

,`height`

,`weight`

, and`smoke`

. - Interpret the slopes of
`gestation`

,`age`

and`parity`

in this context. - The coefficient for parity is different than in the linear model shown in exercise Part II. Why might there be a difference?
- Calculate the residual for the first observation in the data set.
- Interpret the adjusted \(R^2\).