Stat 401B Lab 7: Due October 28 Fall 2008
1. Dugongs are large aquatic mammals similar to manatees but native to the Indian and Pacific
Oceans. Data was collected on the age (years) and length (meters) of 27 dugongs captured near
Townsville in north Queensland, Australia. The data are given below.
Age Length Age Length Age Length
1 1.80 8 2.47 13 2.47
1.5 1.85 8.5 2.19 14.5 2.56
1.5 1.87 9 2.26 15.5 2.65
1.5 1.77 9.5 2.4 15.5 2.47
2.5 2.02 9.5 2.39 16.5 2.64
4 2.27 10 2.41 17 2.56
5 2.15 12 2.50 22.5 2.70
5 2.26 12 2.32 29 2.72
7 2.35 13 2.43 31.5 2.57
a) Plot Length versus Age. Describe the general pattern.
b) Fit a simple linear model relating Length 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, RMSE, 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. Do not center 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 R2 value, RMSE,
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. Do not center 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 R2 value, RMSE,
model utility, and the significance of variables in the model.
e) For the model with Age, Age2 and Age3 as the explanatory variables, look at the distribution
of residuals. Comment on the conditions of identically and normally distributed errors. Be
sure to refer to the appropriate plots in your comments.
f) Which model b), c) or d) does a better job of predicting the lengths of dugongs? To answer
this question you should look at the predictions especially for older dugongs. Note: This
question is not asking which model is the best statistical model.
g) Report the correlations between Age and Age2, Age and Age3, Age2 and Age3. Is there
statistically significant multicollinearity?
(OVER)
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