barcode generator in vb net free download Stepwise Regression Methodology in Software

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16.3 Stepwise Regression Methodology
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Multivariable stepwise regression analysis was conducted on each of the 20 waste group data sets to determine the signi cant independent variables that in uence the annual solid generation. The multivariable stepwise regression analysis of the integrated environmental model functioned to predict and evaluate annual solid waste quantity means and variances of the individual companies in each of the 20 waste groups. Linear, nonlinear, indicator (binary), and interaction variables were considered and statistically tested as potential independent variables. These variables were gathered during the data collection phase. A ve-step procedure was utilized to conduct the multivariable stepwise regression analysis and each step is discussed in the following paragraphs. The ve-step regression procedure is listed below:
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Consolidate data for each of the 20 waste groups Determine the multiple regression mathematics and procedure Conduct regression procedure and select independent variables Evaluate results and determine nal models Validate regression assumptions
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16.3.1 STEP 1: CONSOLIDATE DATA FOR EACH WASTE GROUP
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This step prepared the waste records in each of the 20 waste groups for the regression analysis by separating waste records for each waste group and arranging the values in a matrix. The rows of each matrix represented each waste record and the columns represented potential independent variables to be investigated. The value to be predicted was: y = total annual waste generation (tons/year) for each waste group The potential independent variables to be investigated were x1 = number of employees at the facility x2 = ISO 9000 certi cation duration (months)
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STEPWISE REGRESSION METHODOLOGY
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x3 = ISO 14001 certi cation duration (months) x4 = land ll disposal fee per ton in area (dollars) x5 = recycling level (percentage of total waste generation) x6 = days open per year Nonlinear variables to be investigated were x12 = number of employees at the facility squared x42 = land ll disposal fee per ton in area (dollars) squared x52 = recycling level (percentage of total waste generation) squared Several indicator variables to be investigated were x7 = indictor variable code 1 non ISO 9000 certi cation and code 0 for certi cation x8 = indictor variable code 1 non ISO 14000 certi cation and code 0 for certi cation Indicator variables were used to investigate the effects of company location. The variables were investigated based on the U.S. state in which the company operated: x9 through x38 = indictor variable for U.S. state of operation with code 1 for operation in state i and code 0 for operation in a different state Several interaction variables to be investigated were x1x2 = interaction variable between number of employees and ISO 9000 duration x1x3 = interaction variable between number of employees and ISO 14000 duration x1x4 = interaction variable between number of employees and disposal cost x1x5 = interaction variable between number of employees and recycling level x1x6 = interaction variable between number of employees and days open per year x1x7 = interaction variable between number of employees and ISO 9000 indicator x1x8 = interaction variable between number of employees and ISO 14000 indicator
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16.3.2 STEP 2: DETERMINE THE MULTIPLE REGRESSION MATHEMATICS AND PROCEDURE
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In tting a multivariable regression model and when the number of variables exceeds two, as in the case of these models, matrix theory can facilitate the mathematical manipulations considerably (Walpole and Myers, 1993). Minitab was used as the software program to conduct the regression analyses.
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SOLID WASTE ESTIMATION AND PREDICTION
For the general model, there are k independent variables, denoted as x1, x2, . . ., xk and n observations denoted as y1, y2, . . ., yn. Each variable is expressed by the equation yi = 0 + 1 x1i + 2 x 2i + + k x ki + i
The model represents n equations describing how the dependent variables (annual solid waste generation per company) are generated. Using matrix notation, the equations can be written as y = X + where y1 y y = 2 yn 1 x11 1 x12 X= 1 x1n x 21 x 22 x2n x k1 xk 2 x kn 0 1 = 2 k
The least squares solution for estimation of involves nding for which SSE = (y X ) (y X ) is minimized. The minimization process involves solving for the equation (SSE ) = 0 b The result reduces to the solution of in (X X) = X y Apart from the initial element, the ith row represents x-values that give rise to the response yi. Writing n n x A = X X = i =1 1i n x ki i =1
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