3.10 Using the Supervisor Performance data, test the hypothesis Ho B B3 - - 0.5

Question

3.10 Using the Supervisor Performance data, test the hypothesis Ho B B3 - - 0.5 in each of the following models:

Explanation / Answer

Equation of the model (Y:X1,X3) Y = 9.87+0.6435*X1+0.2112*X3+7.061 Model parameters (Y): Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%) Intercept 9.871 7.061 1.398 0.174 -4.618 24.359 X1 0.644 0.118 5.432 < 0.0001 0.400 0.887 X3 0.211 0.134 1.571 0.128 -0.065 0.487 Standardized coefficients (Y): Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%) X1 0.704 0.130 5.432 < 0.0001 0.438 0.970 X2 0.000 0.000 X3 0.204 0.130 1.571 0.128 -0.062 0.470 Analysis of variance (Y): Source DF Sum of squares Mean squares F Pr > F Model 2 3042.318 1521.159 32.735 < 0.0001 Error 27 1254.649 46.468 Corrected Total 29 4296.967 Goodness of fit statistics (Y): Observations 30.000 Sum of weights 30.000 DF 27.000 R² 0.708 Adjusted R² 0.686 MSE 46.468 RMSE 6.817 MAPE 9.478 DW 1.958 Cp 3.000 AIC 118.002 SBC 122.206 PC 0.357 Given the R2, 71% of the variability of the dependent variable Y is explained by the 2 explanatory variables. Given the p-value of the F statistic computed in the ANOVA table, and given the significance level of 5%, the information brought by the explanatory variables is significantly better than what a basic mean would bring. Based on the Type III sum of squares, the following variables bring significant information to explain the variability of the dependent variable Y: X1. Based on the Type III sum of squares, the following variables do not bring significant information to explain the variability the dependent variable Y: X3. You might want to remove them from the model. Among the explanatory variables, based on the Type III sum of squares, variable X1 is the most influential. Equation of the model (Y:X1,X2,X3) Y = 9.87+0.6435*X1+0.2112*X3+7.061 Model parameters (Y): Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%) Intercept 9.871 7.061 1.398 0.174 -4.618 24.359 X1 0.644 0.118 5.432 < 0.0001 0.400 0.887 X2 0.000 0.000 X3 0.211 0.134 1.571 0.128 -0.065 0.487 Standardized coefficients (Y): Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%) X1 0.704 0.130 5.432 < 0.0001 0.438 0.970 X3 0.204 0.130 1.571 0.128 -0.062 0.470 Analysis of variance (Y): Source DF Sum of squares Mean squares F Pr > F Model 2 3042.318 1521.159 32.735 < 0.0001 Error 27 1254.649 46.468 Corrected Total 29 4296.967 Goodness of fit statistics (Y): Observations 30.000 Sum of weights 30.000 DF 27.000 R² 0.708 Adjusted R² 0.686 MSE 46.468 RMSE 6.817 MAPE 9.478 DW 1.958 Cp 2.638 AIC 118.002 SBC 122.206 PC 0.357 Given the R2, 71% of the variability of the dependent variable Y is explained by the 2 explanatory variables. Given the p-value of the F statistic computed in the ANOVA table, and given the significance level of 5%, the information brought by the explanatory variables is significantly better than what a basic mean would bring. Based on the Type III sum of squares, the following variables bring significant information to explain the variability of the dependent variable Y: X1. Based on the Type III sum of squares, the following variables do not bring significant information to explain the variability the dependent variable Y: X3. You might want to remove them from the model. Among the explanatory variables, based on the Type III sum of squares, variable X1 is the most influential.

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