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 |...

Beat writer's block and start your paper with the best examples