Concept explainers
a.
State whether the given statement is true or false.
a.
Answer to Problem 88E
The given statement is false.
Explanation of Solution
The statement is, if Model I is fit, the estimate for
Model I is as follows:
An unbiased estimator of
According to this, the estimate for
It is given that
From Model I, the value of
The degrees of freedom is as follows:
This indicates that the estimate for
Since the estimate for
b.
Explain whether the given statement is true or false.
b.
Answer to Problem 88E
The given statement is true.
Explanation of Solution
The fitted Model II is as follows:
To determine whether
The significance level is 0.01.
The test statistic is as follows:
Where,
Here,
Also, it is noticed that
Where,
The rejection region for this test is as follows:
Where,
The value of
According to this, if
If
Thus, the given statement is true.
c.
Check whether
c.
Answer to Problem 88E
The given statement is true.
Explanation of Solution
If there are k independent variables, then the fitted model is as follows:
It is known that
Where
Here, Model I contains four independent variables
Also Model II contains two independent variables
This indicates that the predicted value for
Where,
This means that
According to this, the given statement is true.
d.
Check whether
d.
Answer to Problem 88E
The given statement is false.
Explanation of Solution
It is known that an unbiased estimator for
Where,
Also
For Model I, it is seen that
Now, compute the values of
From Part (c), it is seen that
Therefore, the given statement is false.
e.
Check whether Model II is a reduction of Model I.
e.
Answer to Problem 88E
The statement istrue.
Explanation of Solution
Models I and II are as follows:
It is observed that Model II is a subset of Model I.
That is,
Therefore, the given statement is true.
f.
Check whether Model III is a reduction of Model I.
f.
Answer to Problem 88E
The given statement isfalse.
Explanation of Solution
Models I and III are as follows:
Here, Model III contains
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Chapter 11 Solutions
Mathematical Statistics with Applications
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