Econometrics Assignment 1
Professor: Kenneth Mackenzie
Course: Econ 337

1a) Check Appendix A and B at the end.

b) Partial F-Test for unemp = (t stat for unemp)2
∴ Partial F-Test Statistic for unemp= (-5.44259121)2 = 29.62179908
The p-value is the same, and ∴ = 0.00096358

c) We reject H0 that unemp is not significant for predicting cpi and accept the Ha . Meaning unemp is a significant predictor of cpi. This is because the p-value is smaller than 0.05.

d)
=920.9-857.37965114=63.52034834

e) where Rj2 is the R2 value when burger is regressed onto unemp.
We regress burger onto unemp, and since in simple regression (r)2= R2, we can find the R2 valueto be:

=(-0.3750362919)2 = 0.1406522202 VIFburger= 1.163673222
1<VIF<5 ∴ the two variables are moderately correlated.

f) The equation to calculate the standard error of the coefficient burger is:
Where D2 is the second diagonal value in (XtX)-1

Sb1= 4.252227717
g) To test whether the R2 value for the second model (with only burger) is significantly smaller than the first model (with both burger and unemp) we construct a test statistic. This can also be written as: is the R2 value for the first model significantly bigger than the second model?
H0: R12 = R22
Ha: R12 > R22

Test Statistic:

=
= 4.231685687*7=29.62179981
This is equivalent to the t-stat2 for burger.
∴ we can use the p-value for burger in the first model to determine whether R12 is significantly larger than R22 and thus R22 being significantly smaller than R12.
Since the p-value is 0.00098216 and this is < 0.05, we reject H0 and accept that R12 is significantly larger than R22 and so R22 is significantly smaller.
h) There is a possible outlier line of data if hii > p/n according to A.J.’s rule.
For this model, p=3 and n=10.
For the 3rd last line of data:
0.209377028 <0.3 ∴ A.J would not count this line as an outlier.
For the 2nd last line of data:
0.422487658>0.3 ∴ A.J would count this line as an outlier.
For the last line of data:
0.380685174>0.3 A.J would count this line as an outlier.
2a) We can use SSTotal from model 1 to calculate the R2 value for this model as the SSTotal is the same for all models as it only uses Y values. SSTotal=920.9. = 56.03796876.
SSR= SSTotal-SSE = 920.9-56.03796876 = 864.86203124

R2= 0.9391486928

b) Since 0.349005 > 0.05 we fail to reject the H0 and conclude that burger is not a significant variable for predicting cpi.

c)
H0: R12 = R32
Ha: R32 > R12
Test Statistic:
= = 0.133523337*6 = 0.8011400248