Handout #1. Title: Foundations of Econometrics. POPULATION vs. SAMPLE
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- Ferdinand Hardy
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1 Hadout #1 Ttle: Foudatos of Ecoometrcs Course: Eco 367 Fall/015 Istructor: Dr. I-Mg Chu POPULATION vs. SAMPLE From the Bureau of Labor web ste ( we ca fd the uemploymet rate for each moth the U.S. For example, the uemploymet rate s 5.3% Jue 015. How does the Bureau of Labor measure the uemploymet rate? Table 1 Data from the Bureau of Labor (Source: We would lke to choose a represetatve (.e., avod samplg bas) sample to make ferece about the populato. How do we acheve that? Aswer: radom samplg method should be appled. Statstcal ferece: make a cocluso about the populato usg the collected sample data. Probablty (Data collecto) Populato Statstcal Iferece Sample 1
2 Table Parameters ad the correspodg Statstcs Populato parameter Sample statstc Mea u x Meda ~ u ~ x Varace s Stadard Devato s Proporto p pˆ Correlato r Slope (regresso) b *The square of the stadard devato s called varace ( vs. s ) THE STRUCTURE OF DATA Statstcs: the scece of collectg, descrbg, ad aalyzg data. I. Cases & Varables Case: the subjects/objects that we obta formato about. Varable: a varable s ay character that s recorded for each case (ut). Table 3 Geder Smoke Heght Weght Sblgs Eye Color GPA 1 M No Blue 3.13 F Yes Gree.5 3 M No 7 08 Brow.55 4 M No Brow F No Blue.7 6 F No Hazel 3. 7 F No Blue.77 8 M No Brow F No 61 NA Hazel.8 10 F No Brow 3.7 Cases Varables *Table 3 represets a small data set that s retreved from StudetSuvey.csv fle. Notced that cases are rows ad varables are colums.
3 II. Data Classfcato A. Types of Varables a) Quattatve varables e.g. Heght, weght, stock prces, tradg volumes, etc. b) Categorcal varables (omal vs. ordal) e.g. Sex (male, female), workg status (employed, uemployed), poltcal afflato (Dem, Rep, Id) omal. e.g. cup sze at coffee shops (small, medum, large), grade (F, D, C, B, A) ordal. Whe there are oly two levels a categorcal varable, there s o eed to dfferetate whether t s omal or ordal. B. Types of Varables I the feld ecoometrcs the data ca be categorzes as a) Cross-secto e.g. Studets 1 st exam scores of class FE 367 fall 015. b) Tme seres e.g. Daly Dow Joes Idustral Average Idex. c) Logtudal/Pael e.g. Average household come 50 states betwee 1999 ad 014. C. Types of Varables a) Observatoal e.g. Temperatures NJ, crme rates Camde, etc. b) Expermetal e.g. Clcal Trals How do we utlze data? a) Study a sgle varable b) Study the relatoshp betwee varables;.e., respose vs. explaatory varable. Exercse: What do you wat to kow about a sgle varable such as GPA Table 3? Do those studets who do t smoke have a hgher GPA tha those who do? Are studets heghts (Heght) ad weghts (Weght) related? 3
4 GRAPHICAL PRESENTATION OF DATA A. Stem-ad-Leaf Stem-ad-leaf plot for logevty (Logevty) 0* * * * 3. 4* 0 B. Dotplot Logevty Data Logevty Frequecy C. Hstogram Desty Logevty 4
5 MEASURES OF LOCATION AND VARIABILITY I. Locato Mea ( x ) = 1 x Notce: the symbol of mea s for populato ad x for sample. Meda ( ~ x ): the mddle value e.g. 1,, 5, 7, 9 the meda s 5 ( ~ x = 5) 5 7 e.g. 1, 5, 7, 9 the meda s = 6 ( ~ x = 6) Outlers: extreme values Resstace: If a statstc s ot affected by outlers, t s resstat. Q: Is mea or meda more resstat? Q: For each of the followg varables: a) Fd the mea b) Fd the meda c) Idetfy ay outlers 8, 1, 3, 18, 15 41, 53, 38, 1, 115, 47, 50 15,, 1, 8, 58, 18, 5, , 11, 118, 119, 1, 15, 19, 135, 138, 140 II. Varablty Varace (s ) = 1 ( x x) 1 S xx S xx = ( x x) = x - x 1 1 Stadard devato (s) = 1 ( x x) 1 e.g. Usg data 8, 1, 3, 18, 15 to fd varace. Notce: Notce: the symbol of stadard devato s for populato ad s for sample. 5
6 Other measures Percetle: the P th percetle s the value of a quattatve varable whch s greater tha P percet of the data. Fve Number Summary Fve Number Summary: M Q 1 Q 3 Max 5% 5% 5% 5% Statstcs: Ulockg the Power of Data Lock 5 M: mmum, Max: maxmum Q 1 : 1 st quartle (5 th percetle or lower fourth) x~ : meda (50 th percetle) Q 3 : 3 rd quartle (75 th percetle or upper fourth) Rage = Max M Iterquartle rage (IQR or fourth spread) = Q3 Q1 Defto of outlers: f a sample value s smaller tha Q 1 1.5*IQR or greater tha Q *IQR. Fve-umber summary usg Boxplot Outler Logevty Max excludes the outlers M excludes the outlers Q3 or Upper fourth Q1 or Lower fourth Q: use the MammalLogevty.csv data fle to fd these fve umber summary as well as rage ad IQR. (We wll do ths hadout # oce you kow how to use the commads Stata) 6
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