Part 2 - second

Question 1

The F-test involves estimating 2 regressions?

Answer 1

The F-test involves estimating 2 regressions:
1. The unrestricted regression
2. The restricted regression

Question 2

test statistic (F test)

Answer 2

test statistic =
(RRSS − URSS) / URSS ×
(T − k) / m

Question 3

What is K?

Answer 3

number of regressors in unrestricted regression

Question 4

What is m?

Answer 4

m = number of restrictions

Question 5

yt = β1 + β2x2t + β3x3t + β4x4t + ut
Test the restriction that y shows unit sensitivity to x2 and x3.

List 4 outcomes when using the model above

Answer 5

γ2 is significant but γ3 is not
▶ γ3 is significant but γ2 is not
▶ γ2 and γ3 are both statistically significant
▶ Neither γ2 nor γ3 are significant

Question 6

yt = β1 + β2x2t + β3x3t + β4x4t + ut
Test the restriction that y shows unit sensitivity to x2 and x3.

Problems with this approach

Answer 6

▶ Possible high correlation between x2 and x3.

Question 7

What is R^2?

Answer 7

The square of the
correlation coefficient between y and ˆy. Goodness of fit measure.

Question 8

R^2 must always lie between zero and one. Proof

Answer 8

R^2 = ESS/TSS = (TSS − RSS)/TSS = 1 −
(RSS/TSS)

Question 9

Problems with R^2 (2)

Answer 9

2. R2 never falls if more regressors are added. to the regression
   3.R2 quite often takes on values of 0.9 or higher for time series
   regressions. → sometimes sign of spurious regressions

Question 10

What is adjusted R^2 (bar on top) + add formula? - check slides

Answer 10

▶ If we add an extra regressor, k increases. Unless R
2
increases
by a more than offsetting amount, R¯2 will actually fall.

Question 11

Problems with the adjusted R^2 (with bar).

Answer 11

There are still problems with the adjusted R
2
:
1. A “soft” rule (favours big models)
2. No distribution for R¯2 or R
2