Charles University FSV UK STAKAN III Institute of Economic Studies Faculty of Social Sciences Institute of Economic Studies Faculty of Social Sciences Jan Ámos Víšek Jan Ámos Víšek Econometrics Econometrics Tuesday, 14.00 – 15.20 Charles University Second Lecture
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Charles University FSV UK STAKAN III Institute of Economic Studies Faculty of Social Sciences Institute of Economic Studies Faculty of Social Sciences.
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Charles University
FSV UK
STAKAN III
Institute of Economic Studies
Faculty of Social Sciences Institute of Economic Studies
Faculty of Social Sciences
Jan Ámos VíšekJan Ámos Víšek
Econometrics Econometrics
Tuesday, 14.00 – 15.20
Charles University
Second Lecture
Schedule of today talk
A brief repetition of the “results” of the first lecture.
The Ordinary Least Squares
What it is, does it exist at all, formula and properties ( in the form of a theorem).
An alternative method
Galton, F. (1886): Regression towards mediocrity in hereditary stature. (Návrat k průměru ve zděděné postavě.)
Journal of the Anthropological Institute vol.~15, pp. 246-263.
0XY
How to estimate from data?0
REGRESSION MODEL
At the end of previous lecture we arrived at:
Response
variable
Explanatory variable
Tiii
p XY)(rR
1
tan2
iX
iY )(r)(Sn
1i
2i
Find minimum of over all !!)(S pR
-th residual i
The method is called : The ( ordinary ) least squares
Adrien Marie Legendre (1805) Carl Friedriech Gauss (1809)
n,,2,1i,XYp
1ji
0jiji
2n
1ij
p
1jijiR
)n,OLS( XYminargˆp
2n
1i
TiiR
XYminarg p
The Ordinary Least Squares Odhad metodou nejmenší čtverců
)n,OLS(̂
2n
1i
TiiR
XYminarg p
The Ordinary Least Squares Odhad metodou nejmenší čtverců