Concept explainers
a.
Write the fitted regression equation.
a.
Answer to Problem 67CE
The regression equation is,
Explanation of Solution
Calculation:
An output of a regression is given. The X variable is monthly maintenance spending and Y be the monthly machine downtime. The sample size is 15.
Regression:
Suppose
Where,
The total sum of squares is denoted as,
The regression sum of squares is denoted as,
The error sum of squares is denoted as,
From the regression the fitted line is denoted as,
From the output,
Hence, the regression equation is,
b.
Find the degrees of freedom for the two tailed-test.
Find the two-tailed critical value of t using Appendix D.
b.
Answer to Problem 67CE
The degree of freedom is 13 for the t-test.
The critical-value using Appendix D is 2.160.
Explanation of Solution
Calculation:
Critical value:
Here from the output, the sample size,
The degrees of freedom is,
For two tailed test, the critical value for t-test will be,
It is assumed that the level of significance,
From the Appendix D: STUDENT’S t CRITICAL VALUES:
- • Locate the value 13 in the column of degrees of freedom.
- • Locate the 0.025 in level of significance.
- • The intersecting value that corresponds to the degrees of freedom 13 with level of significance 0.025 is 2.160.
Thus, the critical-value using Appendix D is 2.160.
c.
Write the conclusion about the slope.
c.
Answer to Problem 67CE
There is an association between monthly machine downtime and monthly maintenance spending.
Explanation of Solution
Calculation:
Let
Hypotheses:
Null hypothesis:
That is, there is no association between X and Y.
Alternative hypothesis:
That is, there is an association between X and Y.
Decision rule:
If
If
From the output, the p-value for the t-test of slope is 0.0161.
The level of significance is 0.05.
Conclusion:
Here the p-value is less than the level of significance.
That is,
Hence, by the decision rule the null hypothesis will be rejected.
That is, the slope is significantly differs from zero.
Therefore, it can be concluded that there is an association between monthly machine downtime and monthly maintenance spending.
d.
Interpret the 95% confidence limits for the slope.
d.
Explanation of Solution
Interpretation:
From the given output, the 95% confidence interval for the slope is (–2.1671, –0.2656).
It can be said that there is 95% confident that the slope lies between –2.1671 and –0.2656. The interval does not contain zero. That is, all values are negative that implies a relationship between monthly maintenance spending and monthly machine downtime.
e.
Verify
e.
Explanation of Solution
Calculation:
From the output the F statistic is 7.64.
For the slope the t-statistic is –2.764.
Hence, it can be concluded that
f.
Describe the fit of the regression.
f.
Explanation of Solution
Calculation:
From the output, the R-squared value is 0.37.
The coefficient of determination (
The
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Chapter 12 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
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