Please interpret the SPSS printout below, and answer the following questions.
Suppose we regress the dependent variable y on the four independent variables x, x, x, x. After running this regression, on sixteen observations, the SPSS printout provides the following information about the ANOVA table: Regression Sum of Squares, 946.181; Residual Sum of Squares, 49.773. For (a), (b), and (c) below, please provide numerical answers.
(a) What is the coefficient of determination?
(b) What is the correlation between the actual dependent variable and the predicted dependent variable?
(c) What is the adjusted coefficient of determination?
(d) Test the overall significance of the regression model at α = .05 level. Please use the six-step hypothesis-testing framework we employed in class, and write out the last three steps in this table:
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H0: r = 0
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Ha: r 0
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n = 16, α = .05
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(e) The SPSS printout also provides the following information about the partial regression coefficients:
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Independent variables
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Unstandardized coefficients
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Standard error
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x
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-0.0008155
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0.003
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x
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-2.484
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0.960
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x
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0.05901
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0.015
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x
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0.06928
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0.038
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Test the significance of each of the four independent variables, one at a time, at α = .05 level. Please use the six-step hypothesis-testing framework we employed in class, and write out the last three steps in this table.
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H : β1 = 0
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H : β1 ≠ 0
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n = 16, α = .05
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H : β2 = 0
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H : β2 ≠ 0
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n = 16, α = .05
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H : β3 = 0
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H : β3 ≠ 0
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n = 16, α = .05
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H : β4 = 0
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H : β4 ≠ 0
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n = 16, α = .05
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(f) What is your conclusion? That is, is the overall regression model significant? Why or why not? Which, if any, of the independent variables are significant? Why or why not?