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The list of mistakes presented in this section leads to the checklist presented in Box 15.2. The list is organized as a series of questions that should all be answered in the affirmative.

Box 15.2 Checklist For Regression Analyses

1.  Have you plotted and visually verified that the relationship is linear?
2.  Are all predictors in appropriate units so that regression coefficients are comparable?
3.  Has the coefficient of determination been specified?
4.  Is the coefficient of determination high enough?
5.  Have the confidence intervals for regression parameters been specified?
6.  Are all regression parameters statistically significant?
7.  If there are several predictors, has an F-test been performed?
8.  Does the F-test show that regression parameters are statistically significant?
9.  Has the correlation among predictor variables been computed?
10.  Is the correlation negligible?
11.  Is the regression being used for predictions close to the measured range?
12.  Is the confidence interval for predictions specified?
13.  Are all predictor variables required?
14.  Has the normality assumption been verified using a quantile-quantile plot of errors?
15.  Have all the outliers in the quantile-quantile plot of errors been explained?
16.  If the quantile-quantile plot of errors is different from a straight line, have the transformations been investigated?
17.  Has the homoscedasticity assumption been verified using an error versus predicted mean plot?

EXERCISES

15.1  The results of a multiple regression based on nine observations are shown in Table 15.11. Based on these results answer the following questions:
a.  What percentage of variance is explained by the regression?
TABLE 15.11 Results of a Multiple Regression Analysis

j bj sbj

1 1.3 3.6
2 2.7 1.8
3 0.5 0.6
4 5.0 8.3
Intercept = 75.3
Coefficient of multiple correlation = 0.95
Standard deviation of errors = 12.0
F-value = 14.1

b.  Is the regression significant at the 90% confidence level?
c.  Which variable has the highest coefficient?
d.  Which variable is most significant?
e.  Which parameters are not significant at 90%?
f.  What is the problem with this regression?
g.  What would you try next?
15.2  The time to encrypt or decrypt a k-bit record was measured on a uniprocessor as well as on a multiprocessor. The times in milliseconds are shown in Table 15.12. Using a log transformation and the method for categorical predictors, fit a regression model and interpret the results.
TABLE 15.12 Time to Encrypt a k-bit Record

k Uniprocessor Multiprocessor

128 93 67
256 478 355
512 3,408 2,351
1024 25,410 17,022

FURTHER READING FOR PART III

There are a number of good books on statistics and probability theory. For example, see Levin (1981), Trivedi (1982), King and Julstrom (1982), and Papoulis (1965).

Those readers who want a basic nonmathematical treatment of statistics may want to read Haack (1981) or Runyon (1977).

Discussion on misuse of statistics can be found in Hooke (1983), Huff (1954), and Reichmann (1961).

For arguments in favor of geometric means, see Fleming and Wallace (1986). Smith (1988) refutes those arguments. Chambers et al. (1983) discuss quantile-quantile plots.

Natrella (1966) presents a variety of statistical tests and examples of their applications.

The formula for the general transformation technique using integration, first derived by Bartlett in 1947, is discussed in Das and Giri (1986).

The data for Case Study 12.1 is from Gross et al. (1988).


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