Concept explainers
The following is the quadratic regression equation for a sample of
a. Predict
b. Suppose that the computed
c. Suppose that the computer
d. Suppose the regression coefficient for the linear effect is
a.
Determine the predicted value of Y.
Answer to Problem 1PS
The predicted value of Y is 17.
Explanation of Solution
The quadratic regression equation is given as:
For predicting the value of Y for
Thus, the predicted value can be calculated as:
Therefore, the predicted value of Y is 17.
b.
Test whether a quadratic model is better than linear model, if the test statistics for quadratic regression coefficient is 2.35
Answer to Problem 1PS
The quadratic model is better than linear model.
Explanation of Solution
It is given that the value of the test statistics
The null and alternative hypotheses can be constructed as:
The degrees of freedom
This is a two tailed test. So, the upper critical region will be
The critical value of t statistics from t distribution table, which is given in appendix table E.3 at
The decision rule on the basis of the critical value approach:
If,
If,
Since,
Therefore, there is a sufficient evidence to conclude that quadratic model is better than linear model.
c.
Test whether a quadratic model is better than linear model, if the test statistics for quadratic regression coefficient is 1.17
Answer to Problem 1PS
The quadratic model is not better than linear model.
Explanation of Solution
It is given that the value of the test statistics
The hypothesis and the critical value of test statistics is same as above.
Since,
Therefore, there is a sufficient evidence to conclude that quadratic model is not better than the linear model.
d.
Predict Y, when coefficient for the linear effect is
Answer to Problem 1PS
The predicted value of Y is 5.
Explanation of Solution
The regression coefficient for the linear model is given as
Thus, the quadratic regression equation for 25 sample will change to:
For predicting the value of Y for
Thus, the required predicted value is,
Therefore, the predicted value of Y is 5.
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Chapter 15 Solutions
Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
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