44549738 Biometrika i Planiranje Istrazivanja 2010

Download 44549738 Biometrika i Planiranje Istrazivanja 2010

Post on 10-Jul-2015

817 views

Category:

Documents

3 download

Embed Size (px)

TRANSCRIPT

Biometrika i planiranje istraivanja na ivotinjama Miroslav Kap tel: 239-3949 e-mail: mkaps@agr.hr 1 UVOD............................................................................................................................................................................. 1 1.1 PODACI I VARIJABLE.................................................................................................................................................. 1 1.2 PRIKAZ PODATAKA.................................................................................................................................................... 3 1.2.1 Grafiki prikazi ................................................................................................................................................. 3 1.2.2 Numerike metode za opis kvantitativnih podataka.......................................................................................... 3 1.2.3 Simboli .............................................................................................................................................................. 3 1.2.4 Aritmetika srednja vrijednost:......................................................................................................................... 4 1.2.5 Varijanca uzorka: ............................................................................................................................................. 4 1.2.6 Standardna devijacija uzorka ........................................................................................................................... 5 1.2.7 Uvodni SAS primjer .......................................................................................................................................... 5 1.3 ZAKLJUCI O POPULACIJAMA NA TEMELJU UZORAKA................................................................................................ 6 1.4 SLUAJNE VARIJABLE I NJIHOVE RASPODJELE ........................................................................................................... 6 1.4.1 Raspodjele vjerojatnosti za diskretne sluajne varijable.................................................................................. 7 1.4.2 Raspodjele vjerojatnosti za kontinuirane sluajne varijable............................................................................ 8 1.5 FUNKCIJE SLUAJNE VARIJABLE.............................................................................................................................. 14 1.5.1 Neke statistike i njihove raspodjele................................................................................................................. 15 1.5.2 Stupnjevi slobode ............................................................................................................................................ 16 1.6 ZAKLJUIVANJE O POPULACIJI NA TEMELJU UZORAKA............................................................................................ 16 1.7 PROCJENA PARAMETARA......................................................................................................................................... 16 1.7.1 Procjena srednje vrijednosti populacije ......................................................................................................... 17 1.7.2 Procjena varijance u normalnoj populaciji .................................................................................................... 17 1.8 PROVJERA HIPOTEZA............................................................................................................................................... 17 1.8.1 P-vrijednost..................................................................................................................................................... 18 1.8.2 Statistika i praktina znaajnost ................................................................................................................... 19 1.8.3 Mogue greke kod statistikog zakljuivanja i snaga provjere..................................................................... 19 2 JEDNOSTAVNA LINEARNA REGRESIJA........................................................................................................... 21 2.1 UVOD...................................................................................................................................................................... 21 2.2 PROCJENA PARAMETARA 0 I 1............................................................................................................................... 23 2.3 OSTATAK I SVOJSTVA OSTATKA............................................................................................................................... 24 2.4 PROSJECI I VARIJANCE PROCJENITELJA.................................................................................................................... 24 2.5 STUDENTOVA T-PROVJERA I INTERVAL POUZDANOSTI PROCJENE PARAMETARA...................................................... 25 2.6 INTERVAL POUZDANOSTI ZA 1................................................................................................................................ 26 2.7 INTERVALI POUZDANOSTI ZAVISNE VARIJABLE ....................................................................................................... 26 2.8 RALANJENJE UKUPNE VARIJABILNOSTI ................................................................................................................ 28 2.8.1 Veza izmeu suma kvadrata............................................................................................................................ 29 2.9 PROVJERA HIPOTEZA - F- PROVJERA........................................................................................................................ 30 2.10 KOEFICIJENT DETERMINACIJE (R2) ........................................................................................................................ 31 2.11 SAS PRIMJER ZA JEDNOSTAVNU LINEARNU REGRESIJU.......................................................................................... 32 3 KOEFICIJENT KORELACIJE................................................................................................................................ 34 3.1 PROCJENA KOEFICIJENTA KORELACIJE..................................................................................................................... 35 4 VEKTORI I MATRICE ............................................................................................................................................. 36 4.1 TIPOVI I SVOJSTVA MATRICA................................................................................................................................... 36 4.1.1 Operacije s matricama i vektorima: ............................................................................................................... 37 5 JEDNOSTAVNA REGRESIJA U MATRINOM PRIKAZU............................................................................... 40 6 MULTIPLA REGRESIJA.......................................................................................................................................... 43 6.1 DVIJE NEZAVISNE VARIJABLE.................................................................................................................................. 43 6.1.1 Ralanjenje ukupne varijabilnosti i provjera hipoteza ................................................................................. 45 6.2 PARCIJALNE I STUPNJEVITE EKSTRA SUME KVADRATA ............................................................................................ 46 6.3 SAS PRIMJER ZA MULTIPLU REGRESIJU ................................................................................................................... 47 6.4 KRIVOLINIJSKA REGRESIJA DRUGOG STUPNJA ......................................................................................................... 48 6.4.1 SAS primjer za kvadratnu regresiju................................................................................................................ 49 6.5 MOGUE POTEKOE KOD UPOTREBE REGRESIJE .................................................................................................... 50 6.5.1 Analiza ostataka i naruenost pretpostavki modela........................................................................................ 51 6.5.2 Loa opaanja................................................................................................................................................. 52 6.5.3 Multikolinearnost............................................................................................................................................ 52 6.6 IZGRADNJA MODELA I KRITERIJI ZA IZBOR MODELA................................................................................................. 53 7 JEDNOSTRUKA ANALIZA VARIJANCE............................................................................................................. 54 7.1 MODEL JEDNOSTRUKE ANALIZE VARIJANCE S FIKSNIM UTJECAJIMA........................................................................ 55 7.1.1 Ralanjenje ukupne varijabilnosti na izvore varijabilnosti: ......................................................................... 56 7.1.2 Postavljanje hipoteza i F-provjera ................................................................................................................. 57 7.2 USPOREDBA SREDNJIH VRIJEDNOSTI POJEDINIH GRUPA ........................................................................................... 59 7.2.1 Najmanja znaajna razlika (LSD) .................................................................................................................. 59 7.2.2 Tukey provjera (HSD)..................................................................................................................................... 59 7.3 SAS PRIMJER JEDNOSTRUKE ANALIZE VARIJANCE S FIKSNIM UTJEC