Lab 10 OLS Regressons II Ths lab wll cover how o perform a smple OLS regresson usng dfferen funconal forms. LAB 10 QUICK VIEW Non-lnear relaonshps beween varables nclude: o Log-Ln: o Ln-Log: o Log-Log: o o Recprocal: Smple Quadrac: o Smple Power:, where A s any power o Square Roo: o Oher Roo:, where A represens he A-h roo. Useful excel formulas o modfy daa o reflec he above relaonshps nclude: o =ln(cell) (o ake he naural log of a varable) o =CELL^2 (o square a varable) o =CELL^A (o rase a varable o he power A) o =sqr(cell) (o ake a square roo of a varable) o =CELL^1/A (o ake he A-h roo of a varable) Proper funconal form can be deermned by plong daa (see scaer graphs and rend lnes n chaper 4) and referrng o exsng economc research and heory. 10.1 2016 Unversy of Albera Wren by Lorne Premaza
A) Dfferen Funconal Forms As nroduced n class, he relaonshp beween wo varables can be expressed n many non-lnear ways. Ofen he relaonshp beween wo varables can be esmaed by plong hose wo varables daa (see scaer graphs and rend lnes n chaper 4) or referrng o exsng research and heory. Log-Ln: ln( Y ) Ln-Log: Y 1 2 X 1 2 X ln( ) Log-Log: ln( Y ) 1 2 ln( X ) Recprocal: Y 2 1 X Smple Quadrac: Y Smple Power: Y Square Roo: Y Oher Roo: Y Plus ohers 2 1 2 X A 1 2 X, where A s any power 1 2 X A 1 2 X, where A represens he A-h roo. B) Adjusng varables Boh he X and Y varables can be modfed o f he above funconal forms usng he followng equaons (Where CELL refers o he excel cell locaon of he daa): =ln(cell) (o ake he naural log of a varable) =CELL^2 (o square a varable) =CELL^A (o rase a varable o he power A) =sqr(cell) (o ake a square roo of a varable) =CELL^1/A (o ake he A-h roo of a varable) C) OLS An OLS esmaon of he non-lnear relaonshp beween wo varables can be run by choosng Daa Analyss as seen n lab 9, hen selecng he new varables creaed usng he formulas under B above. D) Trend Lnes One way o see f a non-lnear funconal form s requred s o plo your daa usng a TREND LINE o do hs, selec your daa o plo usng a Scaer Graph/Char and under Char Tools and Desgn selec Add Char Elemen -> Trendlne - > Lnear. If he lnear rend lne does no f he daa, anoher funconal form may be more approprae (See Pracce Lab for an Example). 10.2 2016 Unversy of Albera Wren by Lorne Premaza
Econ 299 Pracce Lab 10 A) Download (hghly recommended) or copy he followng Daa Ses no excel: 10.3 2016 Unversy of Albera Wren by Lorne Premaza
Learnng B) Inser a Scaer Plo of hese varables, wh Sudy as your explanaory (x) varable. (See lab 4 for a refresher f needed.) Inserng a lnear rend lne, we see ha a lnear esmaon sn he bes esmaon: 25 Sudyng and Learnng 20 15 10 5 0 0 10 20 30 40 50 60 70 80 Sudy C) In column C, calculae he square roo of he Sudy varable, along wh an approprae le. D) In column D, calculae he naural log of he Learnng varable, along wh an approprae le. E) In column E, calculae he nverse of he Sudy varable, along wh an approprae le. F) In column F, calculae he naural log of he Sudy varable, along wh an approprae le. G) Use he Regresson opon under Daa Analyss o esmae he real ln-log funcon L 1 2 ln( S ). Inser an approprae le and repor he OLS esmaon. (For a real lab assgnmen, hs can be wren by hand aferwards.) H) Use he Regresson opon under Daa Analyss o esmae he real log-ln funcon ln( L). Inser an approprae le and repor he OLS esmaon. (For a real 1 2S lab assgnmen, hs can be wren by hand aferwards.) I) Use he Regresson opon under Daa Analyss o esmae he real log-log funcon ln( L) 1 2 ln( S ). Inser an approprae le and repor he OLS esmaon. (For a real lab assgnmen, hs can be wren by hand aferwards.) J) Use he Regresson opon under Daa Analyss o esmae he real recprocal funcon L 2 1 S. Inser an approprae le and repor he OLS esmaon. (For a real lab assgnmen, hs can be wren by hand aferwards.) K) Use he Regresson opon under Daa Analyss o esmae he real square roo funcon L 1 2 S. Inser an approprae le and repor he OLS esmaon. (For a real lab assgnmen, hs can be wren by hand aferwards.) 10.4 2016 Unversy of Albera Wren by Lorne Premaza
Econ 299 Pracce Lab 10 Answers 10.5 2016 Unversy of Albera Wren by Lorne Premaza
(Noe: Imporan pars of he regresson oupu have been hghlghed, and he regresson reporng can be wren n by hand aferwards.) 10.6 2016 Unversy of Albera Wren by Lorne Premaza
10.7 2016 Unversy of Albera Wren by Lorne Premaza
10.8 2016 Unversy of Albera Wren by Lorne Premaza