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The rst assumption was tested and validated using the F-test. The F-test was discussed in the previous section at the 95 percent con dence level. To access the assumptions of constant variance around the regression line, that residuals are randomly distributed, and residuals are normally distributed, residual plot analysis was conducted. A residual describes the error in the t of the model at the ith data point (Walpole and Myers, 1993) and is described in the following equation: ei = yi yi In a residual plot of ei versus an explanatory variable x, the residuals should appear scattered randomly about the zero line with no difference in the amount of variation in the residuals, regardless of the value of x (Dielman, 1996). If there appears to be a difference in variation (for example, if the residuals are more spread out for larger values of x than for small values), then the assumption of constant variance may be violated.

Table 10-1

The Corporate DPU is a measure of opportunities for improvement that exist for improving profitability and growth. Corporate DPU is calculated by using the formula DPU ln BPIn 100

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Figure 16.4 is an example of a residual plot for number of employees for the transportation equipment manufacturer s waste group. As shown by the residual plot, the residuals appear to be random and of equal variance, except for two outliers, which were removed and the model was recalculated. No patterns appear to be present. This validates the constant variance and random error assumptions of the regression model. The same tests were conducted for the other 19 waste groups as well. The nal assumption in a multiple regression model is that explanatory (independent) variables are not correlated with one another. When explanatory variables are correlated with one another, the problem of multicolinearity is said to exist. The presence of a high degree of multicolinearity among the explanatory variables will result in the following problems (Dielman, 1996):

The standard deviation of the regression coef cients will be disproportionately large. The regression coef cient estimates will be unstable, and the accuracy will vary

signi cantly for different independent variables. To detect multicolinearity, several methods have been developed. One method involves computing the pairwise correlations between explanatory variables. One rule of thumb suggested by some researchers is that mutlicolinearity may be a serious problem if any pairwise correlation is greater than 0.5 (Dielman, 1996). Multicolinearity was examined using this method and all pairwise correlation was below 0.5. The correlations between random variables are denoted by r and are calculated as: r = rx1x2 = S12 S11S22

S11, S12, and S22 may be found in the (X X) matrix in the off diagonals. All correlations between independent variables were less than 0.001.

This DPU is then converted to a Corporate DPMO. Corporate staff size represents the complexity of an organization and is given credit for the organization s success. Accordingly, any major error made in the business must be the responsibility of one of the executives. The formula for calculating Corporate DPMO is as follows: Corporate DPMO DPU 1,000,000 Number of executives reporting to CEO/COO

First of all, let s cover a little bit of the theory. Ordinary silicon forms into a regular crystalline structure. If you look at Figure 10-3, you can see the way that the silicon atoms align themselves into a regular array. To make silicon semiconducting, we can take a little bit of another chemical, in this case boron, and

This section discusses the results and ndings from the regression analysis conducted on the 20 waste groups. Included in this discussion are lists of the independent variables that are signi cant in predicting annual solid waste for each group, the full regression results (F-test, t-test, and R2-coef cient of determination), ANOVA, and correlation analysis. Table 16.3 and Fig. 16.5 display the signi cant variables that are

TABLE 16.3 SIGNIFICANT VARIABLES THAT INFLUENCE SOLID WASTE FOR THE 20 WASTE GROUPS LANDFILL DISPOSAL COST ($/TON)

The process may require a signi cant amount of time and resources to complete,

where the number of executives reporting to the CEO or COO represents opportunities to make mistakes in decision making.

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