APSC 3115, Uncertainty Analysis for Engineers
Lecture 12 In-Class Example—Regression Analysis
EXERCISE 1.
A plant distills liquid air to produce oxygen, nitrogen, and
argon. The percentage of impurity in the oxygen is thought to be linearly
related to the amount of impurities in the air as measured by the “pollution
count” in parts per million (ppm). A sample of plant operating data is shown
in the worksheet titled “Distillation Data”:
a)
Fit a linear regression model to the data.
b)
Test for significance of regression
c)
Find a 95% confidence interval on beta 1.
d)
Plot the residuals and comment on model adequacy.
EXERCISE 2.
The brake horsepower developed by an automobile engine on
a dynamometer is thought to be a function of the engine speed in
revolutions per minute (rpm), the road octane number of the fuel, and the
engine compression. An experiment is run in the laboratory and the data are
shown in the “Brake Horsepower Data” worksheet:
a)
Fit a multiple regression model to these data.
b)
Test for significance of regression. What conclusions can you draw?
c)
Based on t-tests, do you need all three regressor variables in the
model?
d)
Analyze the residuals and comment on model adequacy.
