multivariate linear regression Flashcards
To obtain Beta (estimate), we need to do the following minimization procedure
Minimize RSS with respect to the vector Beta
Loss function in a multivariate model
L = ˆu′ * ˆu
with ˆu = (y-XˆB)
SE in a multivariate case is calculated by:
adding the square roots of the diagonal elements of the variance-covariance matrix of ^B, which equals s²(X’X)^-1
Purpose of the F test
testing more than one coefficiemt simultaneously
F test estimates two regressions. Name them and explain how they differ
unrestricted regression: the coefficients are freely determined by the data
restricted regression: coefficients are restricted and usually imposed on some or all Betas
Think-pair-share vector derivatives
computing derivatives of functions with respect to vectors
conformable matrices
when multiplying, the number of columns of one matrix must equal the number of rows of another matrix
ina multivariate OLS case, the residual sum of squares is displayed as:
a column matrix Tx1
^u′u is the RSS, show the multiplication in detail
row vector x column vector = sum of ^u²
OLS in a multivariate case
L function aufschreiben;
nach beta ableiten und gleich null setzen;
nach beta umstellen;
XB+u statt y einsetzen;
in die varianz einsetzen
variance of errors in a univariate case
s²= (sum ^u²) / (T-2)
F-test tests the following:
two regressions and their coefficients simultaneously
test stat for F test
RRSS-URSS / RRSS * T-n/m
what tests test the stability of parameters overtime?
chow test
predictive failure test
F test table
F(m, T-n)
