QuestionConsider the following two Minitab regression outputs:* Regression Analysis: Y versus X1, X2, X3Analysis of VarianceSource DF Seq SS Seq MSF-Value P-ValueRegression 3 250.574 83.525 115.12 0.000 X1 1228.998 228.998 315.63 0.000 X2 1 11.712 11.712 16.14 0.000 X3 1 9.865 9.865 13.60 0.001Error 46 33.375 0.726Total 49 283.949CoefficientsTerm Coef SE Coef T-ValueP-ValueConstant 2.029 0.312 6.51 0.000X1 -0.068 0.219 -0.31 0.757X2 0.501 0.131 3.84 0.000X3 0.560 0.152 3.69 0.001Regression Equation: Y = 2.029 -0.068X1 +0.501X2 +0.560X3* Regression Analysis: Y versus X3Analysis of VarianceSource DF Seq SS Seq MSF-Value P-ValueRegression 1 234.135 234.135 225.61 0.000 X3 1234.135 234.135 225.61 0.000Error 48 49.814 1.038Total 49 283.949CoefficientsTerm Coef SE Coef T-ValueP-ValueConstant 2.118 0.321 6.59 0.000X3 0.9877 0.0658 15.02 0.000Regression Equation: Y = 2.118 +0.9877X3Test H0: 1 = 0 vs. Ha: 1?0 in the model E(Y) = 0 + 1X1 + 2 X2 + 3 X3? Write the value of the test statistic, the p-value and your conclusion. [There is no need to write out the calculation of the test statistic here.]Show how to calculate the value of the F-statistic for testing H0: 1 = 2 = 0 in the model E(Y) = 0 + 1 X1 + 2 X2 + 3 X3, where the X variables are defined in the order given above. [Hint: Calculate the numerator of the F-statistic from the difference in SSE between the full and reduced models.]Propose a model to test H0 in part (b) by using a partial F-statistic using sequential sums of squares. Remember to specify the order of the predictors in your model. Write out the formula for the F-statistic in this case using symbols (you won’t be able to calculate the actual value of this F-statistic). [Hint: For a partial F-statistic we would calculate the numerator of the F-statistic from the sum of two appropriate sequential sums of squares.]Write an interpretation of the significance of the test results given for the predictor variable X3 within the three-predictor model (the first output). Contrast this interpretation with the interpretation of the results for X3 in the one-predictor model in which X3 is the only predictor (the second output)?MathStatistics and Probability STAT 501
