STA2020F
Class Test 2
Date:
16 April 2008
Time:
1 hour
SECTION A (20)
Question 1.
In multiple regression, why is it necessary to test the hypothesis that at least one of the
β
’s differs from 0 before testing each individual
β
for difference from 0?
[2]
Question 2.
Suppose that you have at your disposal the information below for each of 30 drivers.
Propose a model (including a very brief indication of notation used to represent the
variables) to explain how fuel consumption varies from driver to driver on the basis of
the factors measured.
Information:
1.
km driven per day
2.
mass of car
3.
number of cylinders in car
4.
average speed
5.
fuel consumption (litres per 100 km)
6.
number of passengers
[3]
Question 3.
It is believed that the production rate Y in an industrial process is linearly related to
the amount of salt X
1
and the amount of chlorine dioxide X
2
used during a critical part
of the process. Production rates (in litres per minute) were recorded along with the
values of X
1
and X
2
on eight occasions:
Rate (Y)
Salt (X
1
)
Chlorine Dioxide (X
2
)
5.0
9.6
1.5
3.5
9.4
2.3
2.0
9.0
2.0
2.5
9.4
4.2
4.0
9.5
1.5
3.0
9.4
2.5
2.5
9.2
2.5
3.0
9.5
3.3
A portion of computer output is given below:
ANOVA
df
SS
MS
F
Pvalue
Regression
2
6.1070
3.0535
42.20
0.001
Residual
5
0.3618
0.0724
Total
7
6.4687
Coefficient
SE
tstat
Pvalue
Intercept
33.023
5.009
6.59
0.001
SALT
4.0128
0.5328
7.53
0.001
CLDIOX
0.5696
0.1116
5.11
0.004
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View Full Documenta) Write down the equation of the fitted model.
(1)
b) Find the
standard error of the estimate
and explain what this number means.
(2)
c) What is R
2
? How do we interpret this figure?
(2)
d) What conclusion can be drawn about the overall fit of the model?
(2)
e) What conclusions can be drawn about the individual variables in the model?
(3)
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 Spring '11
 
 Linear Regression, Regression Analysis, 1 Hour, 8 weeks, important null hypothesis

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