A psychologist examined the regression relationship between anxiety level (Y)€” measured on a scale ranging from 1 to 50, as the average of an index determined at three points in a 2-week period€”and the following three independent variables: X1 = systolic blood pressure; X2 = IQ; and X3 = job satisfaction (measured on a scale ranging from 1 to 25). The following ANOVA table summarizes results obtained from a variables-added-in-order regression analysis on data involving 22 outpatients who were undergoing therapy at a certain clinic.

a. Test for the significance of each independent variable as it enters the model. State the null hypothesis for each test in terms of regression coefficient parameters.
b. Test for the significance of adding both X2 and X3 to a model already containing X1. State the null hypothesis in terms of regression coefficient parameters.
c. In terms of regression sums of squares, identify the test that corresponds to comparing the two models
Y = β0 + β1X1 + β2X2 + β3X3 + E
and
Y = β0 + β3X3 + E
Why can't this test be done by using the ANOVA table? Describe the appropriate test procedure.
d. Based on the tests made, what would you recommend as the most appropriate statistical model? Use α = .05.

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Source d.f. (Xi) (XIX,) 981.326 190.232 129.431 442.292 Regression Residual 18