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Assumptions 1. 2.^ PastQuantified^ into^ form of data Error measurements
Trends 3. continued pattern
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- simple -1 flexible Future (^) I = (^) a tbt ' frnecdnatem a variance (^) adjusted ① NAIVE -^ baseline^ Etty = At L^ projected value < (^) actual (^) present be Eta - lEt)(E# (^) x stationary ⑦ simple^ iaiiiiiiiiaiiiiaiaiiaiiiiiiiim (^) ". Eat. " sis.int?a..:..::::i:i÷:÷:÷÷÷÷:÷÷:: Moving AV^ " → responsive, (^) , i :O (^) a = A- - BE (^) ÷i. Seasonal Ty - a. of cycle annual) 'factor^ '
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lags a^ trend^ Ifn ( Trio^ :^ A ), )^ SmoothingAM X stable^ constant inn trend'^ nib^ for^ PRESENT^ period^0
at ✓^ Stable^ Si^ '^ -^ 121=0.28^9 :^40 .tt#teigeeasrg;gn ⑤ Adjusted ✓^ trend^ expo^ smoothed trend factor predict51.9 season n in (^) ft :S ) Exponential +^ seasonality^ Aff -^ -^ Ft-11^ +^ Ttt,^ Forecasty :^ 40.7^ -14.4Gt^ -^ -^ 40.7+4.46157= SMOOTHING t^ t^ for^ period^ season^ 1 :^ Snfs =^ 0.281631 i^ 17. darth-^ d)^ Fe / Bette,^ -^ ft^ )^ -111^ - B) Tt ① Ho benttereminden.fm stable ) ②^ Hq^ Hypothesissteps} ① Goodness^ of^ fit^ tests^ 1)^ observed^ ③ Test stats
- Check distribution 2)^ Expected( find )^ ④ critical (^) region pi is^ given :^ Multinomial^ /^ Emstaiieiffff^ ⑤^ conclusion^ inborn observed
/ k outcomes - Normal VS Homogeneity tests
Ii:! (^) !! (^) ;e'as:' :p! !"pi (^).^ .fi?9iii9iydf=K-rU-XnOfindprobpoow:iPooanoior.uao=^ ' to : (^) indiscrete ru Binomial^ Geo^ -^ metric^ Bernoulli^ 't^ (Xi) = Mpi (^) ③ find E (^) y category W (^) j category
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Pi 's are functions iunieopmflinosmi.fi?yphergeoiinr.^ L, arraign^ ' em. R i^ ①^ ioii^ column^ noii^ columns Enn Aliunde^ Formula Pex :# a- et nigra rrwoiosvr.mn#-1 (^) pig !! Caution hp; 75 if not (^) , (^) you column^ ①^ Ho^ :^ pm^ =^ Pmi^ Pr^ ,^ =^ pay^ for^ each^ j^ -^ -^ 1943, Distribution is^ continuous^ ⑦ Ha^ :^ Ho^ is^ not^ true Kw : K2^ p^ n^ Nog^ = normal Eiinpio^ area"^ !'^ estimate^14 i^ 0. ftp.r. ,^ =^ E^ ( (^) Observed - E) ' ③ Test Statistics Distribution (^) Ex. 8 intervals aniioo , E^ ' 100 ×18=125 Eas - D (^). # XZ = (^10) df : 3
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- = (^) E ( hi - hp;) ' 0.07 Cp - value C^ 0. ⑦ contingency Idf qnorosiwjwprob.li# :^ re^ -^ no^ -^ i^ )^ i^ :^ '^ Tpi ④critical^ Region
- (^) Homogeneity Ho^ : Pij : Rj =^.^.^.^ -^ - Pij X!.gg (^) , ,^ =^ 9.384-^ Voy^ >^ E' o.osasn.ndgpyq.mgow @ (^) going"g for^ each^ jink.^.^ .aJ^ : (^). Reject at (^) 95% Confidence ( (^) I fixed iiioaume^ mainly "^ population^ divided^ into^ j^ categories^ E^ :^ - row^ total^ x^ Col^ totalf mann^.^ routed^ a^ j^ column^ totals^ are^ random^ IUVO^ @^ Nosed^ )^ n Independence (^) find relationship of factors ftp.iiiimgni^ )
2 factors^ in
- nails (^) independent TWIN (^) Ho : Pij =p^ ,^ -^ * pj for^ i.^ Ig^.^.^ .gI
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space :{^ Salalah) (^) y' : (^) 13111.83't.... PIKA :e° :^ 0.368^ 22. 0!
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i. Rejection^ Xhosa 4 - o - i pay -^ -^ e "'^ '^ 0.184^ : (^) as , PIX Prx -^ -? 3) 3) - e-} '^ -^ 0.061^ : Do (^) not Reject Ho i black Amarna up 25 Ho : Pij =^ Pit (^) Pj for i^ :... - I j=^ ... ]
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( factor →^ ①^ finders 2 X^ Replicate^ ②^ SSAASSBGSSIAB^ ) Factor I^ 2.^ NoteHoa^ Ha^ all^3 ① completely^ Randomized^ Design^ lone^
- WAY ANOVA ! neawariedsrv^ Reff'sfate③ 3.^ ③^ iii.gig " 2 Factor^ =^ IDV Independent sample^ t-^ test^ lever. fan. ④ Randomized Block (^) Design Total SS =^ SST^ + nk-xeatnent.am#oroivomreaanndVoh2oio^ SSE^ main^ N'- response → var (^) measure k treatments each Of b blocks (^) a no. Of observations n - - bk by experimenter f-NYVA → (^) upper tail always! oh^ Farid^ And ate^ block-^ to^ -^ block^ variability .^ F^ Test^ ritical^ Region^ :^ Faadfiadfi^ Total SS^ SST^ t^ SSB t^ SSE F Test ① Ho^ :^ Mr^ =μz=μz=.^.^.^ '^ Mk ④ axb^ Factorial^ Experiment^ ① Ha :^ at least onedimffanenis a levels^ of^ factor^ A y investigate interaction^ ③ Test^ statistic^ :^ F^ '^ -^ Mst b levels^ of^ factor^ B^ between^ A^ and^ B^ Ho^ :^ +^ interact^ MSE replicated r^ times^ test for Interaction! (^) Ha : vintner (^) ④ rejection Region : (^) Fob > (^) Fagdf Total SS^ =^ SS^ At^ SSB^ 1- (^) SS IAB) 1-^ SSE ② ② ① I. (^) Best of estimate 62 ③ Inference^ f.Penne.^ raging^2 Population^ variances ⑦ serious^ test^ gigs, n^ brien^ F^ critical ① (^) Test +^ CI for difference (^) between (^2) population means Large sample^ r^ >^301 x, ax, independent (^) egg df (^) , adf, = 1-baton^ equal a^ UNEQUAL ( (^2) Sample 2- test t (^) CI /
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