Question

5. Model Building: For the first three tests that you conducted (the Global F-test, the quadratics test, and the interaction test), provide the information that I ask for in the space below. In addition, for each test, include the printout used in the appropriate space.

A.) Global F-test (6 points) Complete 2nd-Order Model: E(y) = β0 + β1x1 + β2x12 + β3x2 + β4x1x2 + β5x12x2

Fill in the following information for your test: Test: Ho:__________ Ha: __________ Test Statistic: ____________ P-value: ____________ Conclusion:

Data

Least Squares Linear Regression of AskPrice Predictor Variables   Coefficient   Std Error       T        P   VIF Constant        16294.4   4351.49   3.74   0.0005   0.0 Mileage        -0.11543   0.07724   -1.49   0.1422   72.2 X1sq        2.238E-07   3.171E-07   0.71   0.4840   74.7 Model           3809.56   4978.46   0.77   0.4482   31.5 X1X2        3.645E-03   0.08877   0.04   0.9674   160.5 X1sqX2      -3.896E-08   3.611E-07   -0.11   0.9146   89.2 R²           0.6490     Mean Square Error (MSE) 9819818 Adjusted R² 0.6091     Standard Deviation       3133.66 AICc         815.27 PRESS        6.48E+08 Source       DF          SS          MS       F        P Regression   5   7.988E+08   1.598E+08   16.27   0.0000 Residual     44   4.321E+08   9819818 Total 49 1.231E+09 Cases Included 50    Missing Cases 0

Answer 1

H0: the model is not overall significant, that is, the model containing the intercept only is a good fit.
Ha: the model is overall significant, that is, the model fits the data better than the intercept-only model.

Statistic = F-value = 16.27
P-value (of the F test) = 0.0000
Conclusion = We reject H0 and conclude that there is enough evidence to suggest that the given model is overall significant.