Question

Analysis of Variance Source DF Regression Residual Error SS 20.8141 MS 10.4070 F 33.66 P .0013 2 5 1.5459 3092 Total 7 22.3600

Using the appropriate model, sample size n, and output:
Model:   
Sample: n=8 S=.5561, = 93.1% , adj = 90.3%

1. Report SSE, , and s as shown on the output. Calculate from SSE and other numbers. Report the total variation, unexplained variation, and explained variation as shown on the output. (Round answers to 4 decimal places.)
2. Report   and adjusted as shown on the output. Calculate the F statistic. (Round your answer to 3 decimal places.)
3. Find the p-value related to F on the output. Using the p-value, test the significance of the linear regression model by setting .  

Please show work step by step and explain! Thank you!

Answer 1

Given the appropriate model, sample size n, and output:

1) SSE = 1.5459

S² = MSE = SSE/df = 1.5459/5 = 0.30918 = 0.3092

S = 0.5561

^_​​Total variations = 22.360

Unexplained Variations = 1.546

Explained Variations = 22.360 - 1.546

= 20.814

2) R² = 93.1 % = 0.931

Adj. R² = 90.3 % = 0.903

F statistics = MSRegression/MSE

=( SSR / d.f. ) / ( SSE / d.f)

= 10.407 / 0.3092

= 33.657

3) p value = 0.0013

When $\alpha$ = 0.1 p value , so we reject H0 and concluded that model is significant.

When $\alpha$ = 0.5 p value , so we reject H0 and concluded that model is significant.

When $\alpha$ = 0.01 p value , so we reject H0 and concluded that model is significant

When $\alpha$ = 0.001 p value so we reject H0 and concluded that model is significant.