Question

We give JMP output of regression analysis. Above output we give the regression model and the number of observations, n, used to perform the regression analysis under consideration. Using the model, sample size n, and output:

Model: y = β₀+ β₁x₁+ β₂x₂+ β₃x₃+ ε       Sample size: n = 30

Summary of Fit
RSquare	0.956255
RSquare Adj	0.951207
Root Mean Square Error	0.240340
Mean of Response	8.382667
Observations (or Sum Wgts)	30

Analysis of Variance
Source	df	Sum of Squares	Mean Square	F Ratio
Model	3	32.829545	10.94320	189.4492
Error	26	1.501842	0.05780	Prob > F
C. Total	29	34.331387	(1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.) Total variation unexplained variation explained variation (2) Report R2 and R¯¯¯2 as shown on the output. (Round your answers to 4 decimal places.) R^2 - R2 (3) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.) SSE S^2 (4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 2 decimal places.) F(model) (6) Find the p−value related to F(model) on the output. Using the p−value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001. What do you conclude? p-value =.0000. Since this p-value is less than α =.001, we have       evidence that H0: β1 = β2 = β3 =0 is false. That is, we have       evidence that at least one of x1, x2 ,and x3is significantly related to y.	<.0001*

Answer 1

(1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.)

Total variation:100%
unexplained variation:95.63%
explained variation:100-95.63=4.37%

2) Report R2 and R¯¯¯2 as shown on the output. (Round your answers to 4 decimal places.)
R^2=0.9563
-
R2=0.9512

3) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.)
SSE=1.5018
S^2=MSE=0.0578

s=sqrt(MSE)=0.2404

(4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 2 decimal places.)
F(model)=MS Square Error/MS Model=10.94320.05780=189.45

6) Find the p−value related to F(model) on the output. Using the p−value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001.

p-value =.0000. Since this p-value is less than α =0.1, we have       evidence
that H0: β1 = β2 = β3 =0 is false. That is, we have       evidence
that at least one of x1, x2 ,and x3is significantly related to y.

p-value =.0000. Since this p-value is less than α =0.05, we have       evidence
that H0: β1 = β2 = β3 =0 is false. That is, we have       evidence
that at least one of x1, x2 ,and x3is significantly related to y.

p-value =.0000. Since this p-value is less than α =0.01, we have       evidence
that H0: β1 = β2 = β3 =0 is false. That is, we have       evidence
that at least one of x1, x2 ,and x3is significantly related to y.

p-value =.0000. Since this p-value is less than α =0.001, we have       evidence
that H0: β1 = β2 = β3 =0 is false. That is, we have       evidence
that at least one of x1, x2 ,and x3is significantly related to y.