1) In performing a regression, ANOVA, or ANCOVA, what four assumptions must be satisfied?

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1 Statistics 56 - Sping - Final Exam (modifid fo Sping Pactic) Pat I: Answ th two following qustions Fiv points ach ) In pfoming a gssion, ANOVA, o ANCOVA, what fou assumptions must b satisfid? ) Dfin what is mant by th p-valu (o mpiical significanc lvl) of a tst Pat II: Answ fiftn of th following sixtn qustions Six points ach Qustions -4 f to th attachd sults fo pfoming a multipl gssion using th data st Spd Not that som pats of th output hav bn whitd out ) Cafully stat what null and altnat hypothss th bold facd p-valu is tsting, idntifying any modl paamts you us Do w accpt o jct this null hypothsis at α=5? ) Find th SSE, MSE, and thi cosponding df ) Which of th citis would caus th modl to b changd th most if it was movd? Which statistic did you us to tll this? Would th chang in th modl b vy lag? 4) What st of ths vaiabls foms th bst gssion modl fo pdicting th dath at fom hat attacks? What did you us to tll this? Qustions 5-8 f to th attachd sults fo pfoming an ANOVA on th data st ating 5) Complt th modl quation fo this ANOVA, idntifying th paamts usd [NOT th stimatd modl quation!] y ijk = µ bas + y ijk = th k th obsvation in spcialty i and city j µ bas = th baslin man 6) What hypothsis is bing tstd by Contast? 7) Say that th Holm pocdu was usd to s which spcialtis w significantly diffnt fom th oth spcialtis Why can w assum that ths diffncs btwn th spcialtis a th sam gadlss of th city? 8) Suppos you could not tll whth th vaiancs of th siduals w qual fom th plots What is th nam of th tst w usd fo this hypothsis?

2 Qustions 9- f to th attachd sults fo pfoming an ANCOVA on th data st Faculty Us α=5 if ndd 9) Assum th assumption of qual slops is mt Is th a significant diffnc in th tolanc shown by pofssos of th sam ag but diffnt anks? If so, what is th avag diffnc in th tolanc of an assistant and a full pofsso of th sam ag? ) Assum th assumption of qual slops is mt Is th a significant ffct of Ag on Tolanc fo pofssos of a givn ank? If so, what is th avag chang in Tolanc fo ach additional ya of Ag? ) Assum th assumption of qual slops is mt What pcnt of th vaiation in Tolanc is xplaind by this modl using ank and Ag? ) Is th assumption of qual slops mt fo this modl? (How could you tll?) Qustions -6 f to th attachd sults fo pfoming a logistic gssion on th data st Bumpus ) Dos a logistic gssion sm to fit this data at α=5? (What tst did you us to tll this?) 4) Assuming that th logistic gssion dos fit this data, is th lngth of th spaow latd to thi chanc of suviving at an α=5 lvl? (What tst did you us to tll this?) 5) What is th pdictd chanc of suviving fo a spaow of lngth? 6) Why can t you tust th answ you gav in pat c?

3 Th data st Spd is fom a 99 aticl in Amican Scintist Th th indpndnt vaiabls a latd to th pac of lif in ach of th 6 citis in th study: bank th avag tim it taks a bank clk to mak chang fo two $ bills walk th avag walking spd of pdstians ov 6ft on a cla summ businss day downtown talk th talking spd of postal clks xplaining th diffnc btwn gula, ctifid, and insud mail Th dpndnt vaiabl is th ag-adjustd dath at fom ischmic hat disas All fou vaiabls hav bn put on a standad scal so that units do not play a ol in th analysis DATA Spd; INPUT bank walk talk hat city $; CADS; 8 Boston 9 Buffalo 9 8 NwYok 8 8 SaltLak 7 Columbus Wocst 7 Povidnc 8 9 Spingfild 8 ochst KansasCity StLouis Houston 4 Patson 9 8 Baksfild Atlanta 4 Dtoit 7 Youngstown Indianapolis Chicago 9 8 Philadlphia Louisvill Canton 7 Knoxvill 9 8 SanFancisco Chattanooga 8 Dallas Oxnad 9 Nashvill 9 8 SanDigo EastLansing Fsno Mmphis SanJos Shvpot 6 8 Sacamnto 6 LosAngls ; POC INSIGHT; OPEN Spd; FIT hat = bank walk talk; UN; POC EG DATA=Spd; MODEL hat = bank walk talk / SELECTION = SQUAE ADJSQ CP; UN;

4 ou hat = bank walk talk spons Distibution: Nomal Link Function: Idntity Modl Equation hat = bank walk talk Summay of Fit Man of spons 9856 oot MSE 485 Modl Eo C Total bank walk talk bank walk talk Vaiabl cpt bank walk talk h a t Squa Adj -Sq 59 Analysis of Vaianc Sum of Squas Sum of Squas Sum of Squas Estimat Phat h a t Typ I Tsts Typ III Tsts - Man Squa 794 Man Squa Man Squa Paamt Estimats Std Eo t Stat Nhat P > F 46 P > F P > F P > t Tolanc Va Inflation

5 bank walk talk hat Nom city ochst KansasCi StLouis Houston Patson Baksfi Atlanta Dtoit Youngsto Indianap Chicago Philadl Louisvil Canton Knoxvill SanFanc Chattano Dallas Oxnad Nashvill SanDigo EastLans Fsno Mmphis SanJos Shvpo Sacamn LosAngl hat Phat Hhat That Fhat Th EG Pocdu Dpndnt Vaiabl: hat -Squa Slction Mthod Numb in Adjustd Modl -Squa -Squa C(p) Vaiabls in Modl walk bank talk bank walk walk talk bank talk bank walk talk bank walk talk hat Nom city Boston Buffalo NwYok SaltLak Columbus Wocst Povidn Spingfi ochst KansasCi StLouis Houston Patson Baksfi Atlanta Dtoit Youngsto Indianap Chicago Philadl Louisvil Canton Knoxvill SanFanc Chattano Dallas Oxnad Nashvill SanDigo EastLans hat Phat Hhat That Fhat

6 Th data st ating is fom Klinbaum, Kupp, Mull, and Nizam (998) It concns th ffctivnss of family nus pactions (FNPs) with diffnt spcialtis (Spc) fom hospitals in th citis (City) Th th spcialtis a: Pdiatics (), Obsttics and gyncology (), Diabts and hyptnsion () Th th citis a simply numbd,, and Th dpndnt vaiabl is a pfomanc comptncy sco DATA ating; INPUT Spc $ City $ CADS; ; POC INSIGHT; OPEN ating; FIT Sco = Spc City Spc*City; UN; POC GLM DATA=ating ODE=DATA; CLASS Spc City; MODEL Sco = Spc City Spc*City; CONTAST contast Spc -; ESTIMATE contast Spc -; UN;

7 Nominal Vaiabl Infomation Lvl Spc Paamt City Paamt Infomation Vaiabl Spc cpt Spc City Spc*City City Modl Equation Sco = 88 - P P - P5 + 5 P P8 + 4 P9 + 9 P - P Summay of Fit Man of spons 745 oot MSE 676 Modl Eo C Total Spc City Spc*City Vaiabl cpt Spc City Spc*City Spc -Squa 5 Adj -Sq 9 Analysis of Vaianc Sum of Squas Sum of Squas City Typ III Tsts Man Squa Man Squa Estimat P > F 4 Paamt Estimats Std Eo t Stat P > F < P > t < Tolanc Va Inflation S c o PSco S c o - - NSco

8 Th GLM Pocdu Dpndnt Vaiabl: Sco Sum of Squas Man Squa F Valu P > F Modl Eo Coctd Total Squa Coff Va oot MSE Sco Man Typ I SS Man Squa F Valu P > F Spc < City Spc*City Typ III SS Man Squa F Valu P > F Spc < City Spc*City Contast Contast SS Man Squa F Valu P > F contast < Standad Paamt Estimat Eo t Valu P > t contast <

9 Th data st Faculty is fom Klinbaum, Kupp, Mull, and Nizam (998) It concns th political Tolanc of univsity faculty mmbs (high sco quals mo tolanc) basd on th faculty mmbs Ag (in yas) and ank (Full, Associat, o Assistant Pofsso) DATA Faculty; INPUT ank $ Ag Tolanc; CADS; Full 65 Full 6 7 Full 47 4 Full 5 7 Full Full 45 4 Full 4 7 Full 4 55 Full 4 59 Full 9 46 Assoc 4 46 Assoc 5 Assoc 485 Assoc 5 45 Assoc 49 5 Assoc 447 Assoc 4 45 Assoc Assoc 9 57 Assoc 49 5 Assist 5 Assist 586 Assist Assist 455 Assist 447 Assist 57 Assist Assist 58 Assist 67 Assist 7 59 ;

10 POC INSIGHT; OPEN Faculty; FIT Tolanc = Ag ank; UN; Paamt Infomation Paamt Vaiabl cpt Ag ank 4 5 ank Assist Assoc Full Modl Equation Tolanc = Ag + 98 P + 44 P4 Summay of Fit Man of spons oot MSE 75 Modl Eo C Total Ag ank Vaiabl cpt Ag ank 9 ank Assist Assoc Full Sum of Squas Sum of Squas Squa 49 Adj -Sq 7 Analysis of Vaianc Typ III Tsts Estimat Man Squa Man Squa Paamt Estimats Std Eo t Stat P > F P > F P > t < Tolanc Va Inflation T o l a n - T o l a n PTolanc - NTolanc POC INSIGHT; OPEN Faculty; FIT Tolanc = Ag ank Ag*ank; UN; Ag ank Ag*ank Sum of Squas Typ III Tsts Man Squa P > F

11 Th data st bumpus is an xcpt fom th classic data st by Bumpus (898) It concns th motality of hous spaows basd on sval masumnts In this cas suviv= indicats th spaow suvivd, suviv= indicats it did not Th pdicto vaiabl in this cas is lngth DATA bumpus; INPUT suviv lngth CADS; ; POC INSIGHT; OPEN bumpus; UN; POC LOGISTIC DATA=bumpus DESCENDING; MODEL suviv = lngth / LACKFIT; UN;

12 Modl Equation Logit ( suviv ) = lngth s u v i v lngth Man of spons 59 SCALE Modl Eo C Total lngth Vaiabl cpt lngth Dvianc Typ III (Wald) Tsts ChiSq 86 Summay of Fit Dvianc Dvianc / 947 Scald Dv Analysis of Dvianc Dvianc / P > ChiSq 8 Paamt Estimats Estimat Std Eo Scald Dv ChiSq Pason ChiSq 587 Pason ChiSq / Scald ChiSq 587 P > Scald Dv 6 P > ChiSq 6 8 s u v i v Psuviv s u v i v Nsuviv Tsting Global Null Hypothsis: BETA= Tst Chi-Squa P > ChiSq Liklihood atio 6 6 Sco 4794 Wald 86 8 Hosm and Lmshow Goodnss-of-Fit Tst Chi-Squa P > ChiSq