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4. DATA ANALYSIS The Minitab regression computer program outputs are given below. The paragraphs that follow explain the computer program outputs.
4.1. Minitab Regression Computer Program Output: Analysis of Variance 4.1.1. Regression Analysis: Y versus X1, X2, X3 The regression equation is Y = 8.98 + 0.247 X1 + 0.338 X2 + 0.290 X3 Predictor Coef SE Coef Constant 8.978 9.737 X1 0.2466 0.1456 X2 0.3384 0.1202 X3 0.2899 0.1146 S = 13.1376
T 0.92 1.69 2.82 2.53
R-Sq = 53.3%
PRESS = 7229.35
P 0.363 0.099 0.008 0.016
VIF 1.6 1.5 1.1
R-Sq(adj) = 49.3%
R-Sq(pred) = 44.09%
Analysis of Variance Source Regression Residual Error Total Source X1 X2 X3
DF 1 1 1
DF 3 35 38
SS MS F P 6890.6 2296.9 13.31 0.000 6040.8 172.6 12931.4
Seq SS 4251.7 1534.1 1104.8
Unusual Observations Obs X1 Y Fit 13 59.0 85.00 58.42 38 78.0 45.00 72.63
SE Fit Residual St Resid 3.69 26.58 2.11R 2.37 -27.63 -2.14R
R denotes an observation with a large standardized residual.
4.1.2. Interpreting the Results I. From the Analysis of Variance table, we observe that the p-value is (0.000). This implies that that the model estimated by the regression procedure is significant at an Îą -level of 0.05. Thus at least one of the regression coefficients is different from zero.