Conduct a global test of hypothesis from the preceding output c-1. State the dec

Question

Conduct a global test of hypothesis from the preceding output c-1. State the decision rule at the 05 level of significance. Reject H_0 if F > c2. Compute the value of F (Round your answer to 3 decimal places) .c-3. Does it appear that any of the regression coefficients are not equal to zero? Using 05 significance level conduct a test of hypothesis on each independent variable. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) d-2. Would you consider eliminating the variables "verbal" and "math"? The analysis has been rerun without verbal and math See the following output. The regression equation is legal s = -0.454 + 1.16 gpa Compute the coefficient of determination (Round your answer to 3 decimal places)

Explanation / Answer

MSR = SSR/DFR = 4.3595/3 = 1.453167
MSE = SSE/DFE = 0.7036/5 = 0.14072

c-1 Critical value of F at 0.05 significance level and df = 3,5 is 5.41
Reject H0 if F > 5.41

c-2 F = MSR/MSE = 1.453167 / 0.14072 = 10.327

c-3 As we F (10.327) is greater than critical value (5.41), we reject the null hypothesis and
At least one regression coefficients are not zero.

d-1 The degree of freedom = Total observations - number of parameters = 8 - 2 = 6
t value at (0.025 and 0.975) and df = 6 is (-2.447, 2.447)
So, t < - 2.447 and t > 2.447

d -2 As t (5.86) > 2.447, we reject the null hypothesis, so gpa is a significant variable
and "Verbal" and"math" could be eliminated.

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