Stat 401B
Lab 7
Fall 2006
1
Due October 24, 2006
1. Earlier in the semester in Labs 1 and 2 you analyzed data on Forced Expiratory Volume
(FEV) of youths in the East Boston area who participated in a study of lung function.
Along with FEV, the Age and Height of those youths were also measured. Use the
data from Lab 1 (it is still on the course web site) to look at the relationship between
Age and Height.
(a) Plot Height vs. Age. Describe the general pattern.
(b) Fit a simple linear model relating Height to Age.
i. Give the equation of the least squares line.
ii. Interpret both the estimated intercept and the estimated slope within the
context of the problem.
iii. Comment on how well the simple linear model fits the data. Be sure to
mention the R2 value, M SError , model utility, significance of variables in the
model, and the plot of residuals versus Age.
(c) Fit a polynomial regression (degree=2) model with Age and Age2 as the explanatory variables.
i. Give the equation of the least squares line.
ii. Why is it difficult to interpret the parameter estimates for this model?
iii. Comment on how well the model fits the data. Be sure to mention the R 2
value, M SError , model utility, significance of variables in the model, and the
plot of residuals versus Age.
(d) Fit a polynomial regression (degree=3) with Age, Age2 and Age3 as the explanatory variables.
i. Give the equation of the least squares line.
ii. Comment on how well the model fits the data. Be sure to mention the R 2
value, M SError , model utility, and the significance of variables in the model.
(e) Use Analysis - Multivariate Methods - Multivariate to look at the correlations
between Age, Age2 , and Age3 . What does this say about multicollinearity?
(f) Which model (b), (c) or (d) does a better job of predicting the Height of youths?
For this model analyze the residuals and comment on the condition of normally
distributed errors.
(g) Write a brief (about two or three paragraphs) summary of what you have learned
about the relationship between Age and Height of youths from this analysis. This
part of the lab will be turned in to Dr. Stephenson on a separate sheet
of paper. A word processed copy printed on a laser printer is required.