Page images
PDF
EPUB

the standardized residuals by observation.

In addition,

the program automatically prints the following:

For each step in the regression:

(1)

(2)

[blocks in formation]

for each variable included in the regression
equation at each step

(a) regression coefficient

[blocks in formation]

(3) for each variable not included in the regression equation at each stage

[blocks in formation]

After the stepwise procedure is completed:

(1) a summary table containing, for each variable included in the regression equation, its

(a) regression coefficient

[blocks in formation]

e. Limitations.

When interpreting the results of an analytical study, the limitations of the study must be borne carefully in mind. In this correlation analysis, the first and most obvious limitation is the relatively small number of observations (817) as compared to the number of DOL employees (10,700). The number of observations, as mentioned earlier, was determined by the size of the education sample. While a larger number of employees might have given better regression results, it should be noted that the sample was carefully chosen to be statistically valid with respect to all measureable aspects (e.g., salary, age, and experience by race and sex). Still, the large number of variables used in the regression could result in cells with too few observations to allow any valid conclusions re

garding those cells.

A second limitation derives from other factors that

influence salary but which were not included in this analysis. Such excluded factors are: (1) ability measures, (2) quality measures for education and experience, (3) non-government experience, (4) job classification series, (5) personal mannerisms (e.g., appearance and

personality), and (6) number and quality of personal

contacts. Inclusion of some of these would have improved the regression and reduced some of the unexplained variation in salary. Also, the addition of time series data might have been significant.

The last set of limitations represents the nemesis

of all regression and correlation analyses: that is, the many ways in which the practical problem fails to satisfy all of the theoretical assumptions underlying correlation. First, the relationship between many of the independent variables and salary is not really linear. The age and experience factors have already been discussed in this light. Second, there existed relatively high correlation among some of the independent variables again, particularly among age, age-squared, and years of service. And third, quite a large number of dummy variables had to be used, relative to the number of continuous variables.

[ocr errors]

f. The results. As listed in the table in Section C above, salary models were developed for twelve different employee groupings. The regression equation was statistically significant at a one percent alpha-level in each of the twelve models. In fact, the F-statistics were

extremely large for most of the models (e.g., 26.89,

studies.

40.39, 17.96, 38.77; the smallest F-statistic was 12.43, an F-ratio of 16/162 degrees of freedom, where the tabled value of F(6, 162, .01) is approximately 6.81). This indicates very strong results. Also, the R-squared values were relatively high for all of the models, particularly considering the complexity of the salary determination process and the R-squared values obtained in other similar 31/ The R-squared value indicates the amount of variation of the dependent variable explained by the regression equation. For example, an R-squared of .659 means that 65.9 percent of the variation in salary is explained by the regression equation; 34.1 percent of the variation remains unexplained. The table on the following page gives the R-squared values for the twelve models developed in this study.

In addition to testing the statistical significance

of the overall regression fit as in the F-statistics discussed above, t-tests were used to evaluate the statistical significance of the individual regression coefficients in

31/ For example, in the research of George F. Travers, Jr. of the Office of Federal Contract Compliance; and others.

[blocks in formation]
« PreviousContinue »