Childhood Respiratory Disease

The dataset fev.sas7bdat contains determinants of FEV in 1980 on 654 children ages 3-19 who were seen in the Childhood Respiratory Disease Study in East Boston, MA. These data are part of a study to follow the change in pulmonary function over time in children. Data was collected for the following factors of interest: age in years, height in inches, FEV in one second in liters, sex (1 = M, 0 = F), and smoking status (0 = noncurrent, 1= current).
Question 1

Create a scatterplot of FEV versus height.
Question 2

Referencing the scatterplot you created, answer the following questions:
Does it look like there is a linear association between the two variables? Can we move forward with a linear regression? What other assumptions are required in order for us to perform a linear regression? Can we tell if these assumptions hold? Explain.
Question 3

Perform a simple linear regression of FEV on height. Write the estimated model using the information from the output. Interpret each coefficient.
Question 4

Now consider the hypothesis test testing the null hypothesis that the slope is 0. What does this test tell us?

Question 5

Finally, what is the R2 value and what does it tell you?

Question 6
A main reason for performing any type of modeling is to predict future values of the outcome given certain values for the explanatory variables. What is the estimated mean FEV for the group of children whose height is 53 inches?

Question 7

Using the 95% confidence interval for the mean FEV for all children whose height is 53 inches in the SAS output, give the endpoints of the 95% confidence interval.

Question 8
Suppose that a new child is randomly selected from the population and that her height is 53 inches. What would be the predicted value for this child)? Using the prediction interval in the output, give the values of the 95% prediction interval for this child. Explain why this interval is wider than the one you found in the previous question.
Question 9
Produce a residual plot and comment. Does it indicate any assumption violations of linearity or homoscedasticity (i.e., the vertical spread in the residuals as you go across the x-axis)?