Week 4 - Multiple Regression. Flashcards
How good is the fitt of a model?
Goodness of Öt: Key elements
Goodness of Öt: DeÖnition
Goodness of Öt: Properties and cautions
The R2 never decreases. In fact, it usually increases as the number of
independent variables increases in the model. (Why?)
2 You should not use the R2
to just decide on including a new variable
to the model. An increase of R2 does not necessarily imply relevance
of a new variable.
3 As you will see below, the key deciding factor to include/exclude a
variable in your model is its statistical relevance.
GAUSS MARKOV 1
GAUSS MARKOV 2
GAUSS MARKOV 3
GAUSS MARKOV 4
GAUSS MARKOV 5
Blue Estimators
The Classical Linear Model (CLM) assumptions
You know that under the Gauss-Markov conditions, OLS estimators
are BLUE.
The Gauss-Markov assumptions do not, however, specify anything
about the distribution of the OLS estimators.
However, in order to make inferences a further assumption about the
distribution of βˆ
j
is needed.
- NORMALITY: The distribution of the unobserved error, u, is
considered to be normally distributed in the population.
The normality assumption of the error term.
The Classical Linear Model (CLM) assumptions
The t statistic
ConÖdence intervals
The t signiÖcance test (t-Test)
t signiÖcance test procedure for one-sided alternative
SigniÖcance t-Test procedure for two-sided alternatives
Testing linear restrictions: The F statistics
:
SSRr
is the sum of the squared residuals from the restricted model.
SSRur is the sum of the squared residuals from the unrestricted model.
q is the numerator degrees of freedom = dfr dfur .
n-k-1 is the denominator degrees of freedom which equals to df
The F statistic is always positive, since the SSR from the restricted
model (r) is, by construction, always larger than the SSR from the
unrestricted model (u
The R-sq form of the F statistic
