Computer lab 1: Simple linear regression – standard analyses
Simple linear regression models are used to examine the relationship between a response variable y
and an explanatory variable x, when we have made n independent observations (xi, yi), i = 1,2,…, n
of the two variables.
Learning objectives
After reading the recommended text and completing the computer lab the student shall be able to:
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Formulate a simple linear regression model and explain how the model parameters can be
interpreted;
Use a data set to make inference about the model parameters;
Compute a confidence interval for the expected response at a given level of the explanatory
variable;
Compute a prediction interval for a new observation of the response at a given level of the
explanatory variable;
Be familiar with the regression tools in Minitab or other statistical software of choice.
All datasets can be found at:
https://netfiles.umn.edu/users/nacht001/www/nachtsheim/5th/
Recommended reading
Chapter 1 – 2.10 in Kutner et al: Applied Linear Statistical Models
Exercise 1
Consider the data set in exercise 1.20 in the textbook and carry out the following:
a) Make a scatter plot of the observed service times versus the number of copying machines at
the 45 customers that have been visited.
b) Formulate a linear regression model of the observed data. How many parameters (unknown
constants) are there in the model?
c) Fit a straight line to the observed pairs of data. How can you interpret the estimated slope of
the fitted regression line? Has the intercept of the regression line a meaningful
interpretation?
d) Use the regression tools to estimate the parameters of the fitted regression model. How
large is the estimated standard deviation and variance of the error terms in the regression
model?
e) Compute a 95% confidence interval of the slope of the regression line. Check in the textbook
how the information in the output from the software can be combined with a suitable
t-value to compute the desired confidence interval.
f) Compute a 95% confidence interval for the expected service time for customers with six
copying machines.
g) A customer with six copying machines calls for service. Compute a 95% prediction interval
for the time it will take for that service.
h) Explain the difference between the computed confidence and prediction intervals.
i)
j)
Consider the ANOVA table in the regression output in Minitab. Which parameter is
estimated by MSE? How is MSE related to s?
Which hypothesis is tested in the F-test? How is the outcome of this test related to the
confidence interval computed in exercise 1.e?
To hand in
1. Answers to the questions d, h, j, k in exercise 1
2. Solutions to the following exercises in the textbook: 1.21; 2.6abcd; 2.15ab; 2.25ab
The lab report should be handed in no later than 5 days after the scheduled computer lab. Use Lisam
(lisam.liu.se) for handing in the assignments.