9.3: Baby Weights, Part III

The Child Health and Development Studies investigate a range of topics. One study, in particular, considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. The goal is to model the weight of the infants (bwt, in ounces) using variables including length of pregnancy in days (gestation), mother’s age in years (age), mother’s height in inches (height), whether the child was the first born (parity), mother’s pregnancy weight in pounds (weight), and whether the mother was a smoker (smoke).

9.3

(a) Write the equation of the regression model that includes all of the variables.

Multiple Linear Regression

Predicted Average Birth Weight = -80.41 + 0.44(gestation) -3.33 (parity) -0.01 (age) + 1.15(height) + 0.05(weight) -8.40 (smoke)

(b) Interpret the slopes of gestation and age in this context.

The average predicted birth rate for a baby increases by 0.44% the longer the gestation period and decreases by 0.01% the older the mother is.

(c) Calculate the residual for the first observation in the data set.

Actual <- 120
Predicted <- -80.41 +0.44*284-3.33*0-0.01*27+1.15*62+0.05*100-8.40*0
Residual <- Actual-Predicted
Predicted
## [1] 120.58
Residual
## [1] -0.58

The actual weight for baby 1 is 120 ounces and the predicted birth weight is 120.58. Our residual is -0.58.

(d) The variance of the residuals is 249.28, and the variance of the birth weights of all babies in the dataset is 332.57. Calculate the R2 and the adjusted R2. Note that there are 1,236 observations in the dataset.

R2

Var1<-249.28
Var2 <- 332.57
n<-1236
k <- 6
R2 <- 1-(Var1/Var2)
R2
## [1] 0.2504435

Adjusted R2

x<- (n-k-1)
y<- (n-1)
Adj <- 1-((Var1/Var2)*(y/x))
Adj
## [1] 0.2467842