Regression Essay

727 words - 3 pages

A) Estimated regression equation – First Order: y = β0 + β1x1 + β2x2 + ε
Output of 1st Model | | | | | | |
| | | | | | |
Regression Statistics | | | | | |
Multiple R | 0.763064634 | | | | | |
R Square | 0.582267636 | SSR/SST | | ̂̂̂ | | |
Adjusted R Square | 0.512645575 | | | | | |
Standard Error | 547.737482 | | | | | |
Observations | 15 | | | | | |
| | | | | | |
ANOVA | | | | | | |
  | df | SS | MS | F | Significance F | |
Regression | 2 | 5018231.543 | 2509115.772 | 8.363263464 | 0.005313599 | |
Residual | 12 | 3600196.19 | 300016.3492 | | | |
Total | 14 | 8618427.733 |   |   |   | |
| | | ...view middle of the document...

543/2= 2509115.772
MSE = SSE/n-(k+1) = 3600196.19/15-(2+1) = 300016.3492
F = MSR/MSE = 8.363263464
Critical Value = 3.885293835 (Fα 0.05 df1 = 1, df2 = 12)
So F > Critical value, we reject the null hypothesis and conclude that the fitted model is useful.
p- value = 0.005313599
E) Interpretation of Ra2 (Adjusted R2) = 1-(1-R2). (n-1)/ n-(k+1) = 1-(1- 0.582267636). (15-1)/15-(2+1) = 0.512645575
F) Interpretation of S, The estimated standard deviation of the error term = √MSE = 547.737482
G) Testing for the significance for x1, using α = .01
H0 = β1 = 0 is not useful
H1 = β1 ≠ 0 is useful
Test Statistic t= 1.740225432, P Value = 0.107375657
Critical value tα/2, df =12 = 2.680997993
Since t< critical value 2.680997993, we reject the alternative hypothesis and conclude that having x1 in the model is not useful
H) 95% Confidence interval estimate for β2
β̂2 ± tα/2 = 0.05/2=0.025 df= 15-(2+1). S β2
Upper Limit = 382.0946511
Lower Limit = 105.334278
I)Comparing the 1st model with y = β0 + β1x1 + β2x2 + β1x12 + β2x22 +ε
Output of 2nd model
Regression Statistics | | | | | |
Multiple R | 0.860329337 | | | | | |
R Square | 0.740166568 | | | | | |
Adjusted R Square | 0.636233195 | | | | | |
Standard Error | 473.2183068 | | | | | |
Observations | 15 | | | | | |
| | | | | | |
ANOVA | | | | | | |
  | df | SS | MS | F | Significance F | |
Regression | 4 | 6379072.074 | 1594768.018 | 7.121548611 | 0.005567368 | |
Residual | 10 |...

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