A multiple regression analysis produced the following tables: Using $\alpha$= 0.01 to test the null hypothesis H₀: $\beta$₁ = $\beta$₂ = 0, the critical F value is ___. A)8.68 B)6.36 C)8.40 D)6.11 E)3.36

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From the tables, we can see that the regression equation is: Y = 76.02 + 1.42X1 - 0.68X2 - 2.15X3 + 0.95X4 To test the null hypothesis H₀: F1F1F1S1F1F1F10₁ = F1F1F1S1F1F1F10₂ = 0, we can use the F test with the following formula: F = (SSR1 - SSR2) / q / SSE where SSR1 is the sum of squares due to regression for the full model, SSR2 is the sum of squares due to regression for the reduced model, q is the number of restrictions on the regression coefficients, and SSE is the error sum of squares for the full model. In this case, the full model has four regression coefficients, while the reduced model has two restrictions, so q = 2. We can obtain the values for SSR1, SSR2, and SSE from the ANOVA table: SSR1 = 445.48, SSR2 = 85.52, SSE = 214.16 Plugging in these values, we get: F = (445.48 - 85.52) / 2 / 214.16 = 5.905 To find the critical F value, we need to look up the F distribution table with degrees of freedom (2, 61) at a significance level of 0.01. The closest value is 6.36, so the critical F value is 6.36. Since the calculated F value (5.905) is less than the critical F value (6.36), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that F1F1F1S1F1F1F10₁ and F1F1F1S1F1F1F10₂ are significantly different from zero.

A Multiple Regression Analysis Produced the Following Tables α\alphaα = 001 to Test the Null Hypothesis H0

A Multiple Regression Analysis Produced the Following Tables $\alpha$ = 001 to Test the Null Hypothesis H₀