Question

The following table is the output of simple linear regression analysis. Note that in the lower right hand corner of the output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H₀: β₁ = 0 versus H_a: β₁ ≠ 0.

ANOVA	df	SS	MS	F	Significance F
Regression	1	61,091.6455	61,091.6455	.69	.4259
Residual	10	886,599.2711	88,659.9271
Total	11	947,690.9167		(n = 12; t = .8301)

(a)	Use the explained variation and the unexplained variation as given on the computer output to calculate the F(model) statistic. (Round your answer to 2 decimal places.)

F

(b)	Utilize the F(model) statistic and the appropriate critical value to test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .05. What do you conclude about the regression relationship between y and x?

  (Click to select)Do not rejectReject H₀ with (Click to select)no evidencestrong evidence of a significant relationship between x and y.

(c)	Utilize the F(model) statistic and the appropriate critical value to test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .01. What do you conclude about the regression relationship between y and x?

  (Click to select)Do not rejectReject H₀ with (Click to select)very strong evidenceno evidence of a not significant relationship between x and y.

(d)	Find the p-value related to F(model) on the computer output and report its value. Using the p-value, test the significance of the regression model at the .10, .05, .01, and .001 levels of significance. What do you conclude? (Round your answer to 4 decimal places.)

  p-value = ; Reject H₀ at α = (Click to select)0.05 and 0.10none0.01 and 0.050.001.

  (Click to select)Very strong evidenceNo evidenceStrong evidenceExtremely strong evidenceSmall evidence of a significant relationship between x and y.

I need help finding the F value and the p-value?

Answer 1

You want to find  the F value and the p-value

Let's find F value using by the explained variation and the unexplained variation as given on the computer output to calculate the F(model) statistic.

The formula of explained variation(r²) is as follow:

So the unexplained variation = 1 - r² = 1 - 0.064464 = 0.935536

Sample size = n = 12

k = 1 ( because for simple linear regression there is only one independent (regressor ) variable ).

The formula of F test statistics based on the explained variation and the unexplained variation is as follow:

Let's find p-value:

Degrees of freedom for numerator = 1

Degrees of freedom for denominator = n -2 = 10

Let's use excel:

F = "=FDIST(0.689056,1,10)" = 0.4259