Q: Tests for Assumptions for Multiple Regression
APPENDIX Q (pp. 285-298)
Tests for Assumptions for Multiple Regression
There are four assumptions which need to be checked for violation in a linear regression analysis: 1) normality, 2) constant variance, 3) linearity, and 4) independence (Norusis, 1991). The first plot presented in Table 55 is a casewise plot of the residuals. The casewise plot provides an overview of the “fit” of the regression model. The observed value, the predicted value and the residual or difference between the predicted and observed values are presented for each tutor in the study. The “fit” is acceptable.
Two plots, Figures 32 and 33, test the normality of the sample using the residuals. Table 32 is a histogram plot of the residuals against a normal residual distribution curve for this sample. The distribution of residuals appears to be fairly normal. Table 33 compares each of the standardized residuals of this sample are compared for their “fit” against a predicted a regression line. The assumptions of normality have been met.
Scatterplots of the standardized residuals against the predicted values and against the values of each of the independent variables can provide a check that the variance appears to be constant. The first plot in Figure 34, checks the variance between the predicted values and the residuals. The variance appears to be constant. Figures 35-38 provide a plot of the standardized residuals against each of the four independent variables that were found to contribute to the tutor’s post-test score:
1) Prior related work experience in Figure 35,
2) Perceived reward of “Making money” in Figure 36,
3) Reason for becoming a tutor of “Other” in Figure 37, and
4) Perceived reward of “Giving something of self back” in Figure 38.
A major concern with each of the plots with the independent variable is that patterns emerge as a result of the many “0” values of each of the independent variables. When taking those scores into consideration, the variance of the plots appears to be acceptable.
To check the assumption of linearity, four scatterplots of the post-test score against each of the four independent variables that were found to contribute to the tutor’s post-test score:
1) Prior related work experience in Figure 39,
2) Perceived reward of “Making money” in Figure 40,
3) Reason for becoming a tutor of “Other” in Figure 41, and
4) Perceived reward of “Giving something of self back” in Figure 42.
The number of “0” values make it more difficult to examine these variables for linearity. However, no clearly defined curvilinear relationships were seen, thus the assumption of linearity has been met.
The casewise plot of the post-test scores, in Table 55, provides a test for independence if the plot is in sequence of occurrence, it is a check that the same subjects are not included in the data more than once as might be the case if later respondents did consistently better than the early respondents. The tutors’ responses were entered in the sequence with they were received by the researcher, not necessarily in the order in which they were taken. However, each tutor was assigned a case number. Each tutor’s name and case number was recorded in a separate file to eliminate any duplication. Thus the assumption of independence was met.
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