The theoretical model of a set of data with three independent variables is given by Y...

 

Transcribed Image Text:

The theoretical model of a set of data with three independent variables is given by Y = B,X, + B2X2 + B3X3 + E. The ANOVA table of all possible combination is shown below. Model Regression (Constant) X1 Source Regression Residual Sum of squares 4789.896 7854.344 df Mean Square 1 -22.849 4789.896 17.420 23 341.493 Total 12644.240 6392.471 6251.769 12644.240 5404.650 7239.590 12644.240 24 (Constant) X2 Regression Residual Total Regression 6392.471 271.816 2 -49.962 24.652 23 24 3 (Constant) -46.776 1 5404.650 X3 22.225 Residual 23 24 2 22 24 2 22 24 314.765 Total Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual Total (Constant) 3196.853 284.115 4 -49.865 6393.707 X1 0.546 24.079 -46.571 6250.533 12644.240 5745.176 6899.064 12644.240 X2 (Constant) X1 X3 (Constant) X2 X3 (Constant) 2872.588 313.594 5. 7.518 15.124 -61.042 17.465 6. 6823.250 5820.990 2 22 24 3 3411.625 264.590 9.436 -64.009 -4.629 20.942 12644.240 6896.088 5748.152 12644.240 7 2298.696 273.722 X1 21 X2 24 X3 11.261 a) Calculate MSR(X,X, X, ). b) Performa Backward Elimination to find the final appropriate regression reduced model for the data. Use a = 0.05. The theoretical model of a set of data with three independent variables is given by Y = B,X, + B2X2 + B3X3 + E. The ANOVA table of all possible combination is shown below. Model Regression (Constant) X1 Source Regression Residual Sum of squares 4789.896 7854.344 df Mean Square 1 -22.849 4789.896 17.420 23 341.493 Total 12644.240 6392.471 6251.769 12644.240 5404.650 7239.590 12644.240 24 (Constant) X2 Regression Residual Total Regression 6392.471 271.816 2 -49.962 24.652 23 24 3 (Constant) -46.776 1 5404.650 X3 22.225 Residual 23 24 2 22 24 2 22 24 314.765 Total Regression Residual Total Regression Residual Total Regression Residual Total Regression Residual Total (Constant) 3196.853 284.115 4 -49.865 6393.707 X1 0.546 24.079 -46.571 6250.533 12644.240 5745.176 6899.064 12644.240 X2 (Constant) X1 X3 (Constant) X2 X3 (Constant) 2872.588 313.594 5. 7.518 15.124 -61.042 17.465 6. 6823.250 5820.990 2 22 24 3 3411.625 264.590 9.436 -64.009 -4.629 20.942 12644.240 6896.088 5748.152 12644.240 7 2298.696 273.722 X1 21 X2 24 X3 11.261 a) Calculate MSR(X,X, X, ). b) Performa Backward Elimination to find the final appropriate regression reduced model for the data. Use a = 0.05.