1. Set up and test the hypothesis that GPA does not contribute to prediction of SCORE for students who are homogeneous on NHS and NHR.
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1 1 1. Set up nd test the hypothesis tht GPA does not contriute to prediction of SCOE for students who re homogeneous on NHS nd NH. First Approch test of specific hypothesis: t test Y NH NHS GPA 1 3 H0 : 3 0 H : 0 A 3 t S t, 1.05, pc nk t Fil to eect We cnnot conclude tht GPA contriutes to prediction of SCOE when NHS nd NH re controlled. Approch 1 is the most efficient pproch nd is the esiest to use if pproprite informtion on nd S is ville. Approprite mens tht model hs een estimted tht contins only the vrile of interest (here GPA) nd the control vriles (here NHS nd NH). Second Approch suset pproch, with suset of one Full Model Y NH NHS GPA 1 3 educed Model Y NH NHS 1 H0 : 3 0 H : 0 A 3
2 1 FM M nk1 F kg FM F , kg, nk1 F.05,3, F Fil to eect We cnnot conclude tht GPA contriutes to prediction of SCOE when NHS nd NH re controlled. Approch is the more complicted to use thn is the first pproch. It requires for two models. The full model contins the vrile interest (here GPA) nd the control vriles (here NHS nd NH). The reduced model contins only the control vriles (here NHS nd NH) Third test of specific hypothesis: control-preceding-vriles F test inc up to 1 1 up to F nk, F inc up to F F.05,1, Fil to eect,1, n k up to 1 We cnnot conclude tht GPA contriutes to prediction of SCOE when NHS nd NH re controlled. Approch 3 is equivlent to pproch. It requires for two models. The full model contins the vrile interest (here GPA) nd the control vriles (here NHS nd NH). The reduced model contins only the control vriles (here NHS nd NH). Approch 3 is more complicted thn the second pproch ecuse it require you to recognize tht FM. cn e computed FM M inc nd tht up to is
3 3. Wht proportion of the totl vrition of SCOE is ssocited with GPA nd GE when NHS nd NH re controlled? Full Model Y NH NHS GPA GE educed Model Y NH NHS 1 FM M, inc GPA GE , inc GPA GE.14 (14%) of the totl vrition of SCOE is ssocited with GPA nd GE when NHS nd NH re controlled 3. Set up nd test single null hypothesis relevnt to the question of whether GE nd/or GPA re relted to score when NH nd NHS re controlled. Full Model Y NH NHS GPA GE educed Model Y NH NHS 1 H : FM M nk1 F kg FM F F 3.6 F, kg, nk1 F.05,4, Fil to eect
4 4 We cnnot conclude tht GE nd/or GPA re relted to score when NH nd NHS re controlled. 4. Wht is the slope of the regression line for homework section? Yˆ dz Yˆ Z Yˆ Slope of the regression line for homework section is Set up nd test hypotheses relevnt to the question of whether there is difference etween the two groups on the finl exmintion score when the pretest is controlled. H : 0 0 H : 0 A t d S d t t, 1.05, pc nk t Fil to eect We cnnot conclude tht there is difference etween the two groups on the finl exmintion score when the pretest is controlled. 6. Wht is the dusted men of the finl score for the quiz section? Yˆ dz Z 0 Yˆ Z
5 5 n n n n Yˆ ˆ Y 7. In order to interpret d (the estimte of ) s vlid estimte of the tretment effect, wht must the instructor e prepred to rgue with regrd to cuses of the finl exmintion score other thn the pretest? The resercher must e prepred to rgue either tht A. With nd Z controlled, no other vrile will predict Y. If this rgument is vlid then dding nother predictor will not chnge the regression coefficients nd so d from the eqution ctully used will e vlid estimte of the tretments effect. Therefore there is no need to control other vriles. B. With controlled no other vrile will e relted to Z. If this rgument is vlid then the groups do not differ on other vriles tht might e dded to the model nd therefore there is no need to control other vriles. 8. Wht is the numeric vlue of ry Z? r Y Z t t nk ry Z Interpret ry Z? ry Z.80 is the estimte of the correltion etween pretest scores nd finl exmintion scores within either tretment group.
6 6 10. Set up nd test hypothesis relevnt to the question of whether verge nursing home costs re different for the three types of nursing homes. Y Z Z 1 1 H : nk1 F k 1 1 SSE SST F F, kn, k1 F.05,, eect We cn conclude tht verge nursing home costs re different for t lest two of the three types of nursing homes 11. Set up nd test hypotheses relevnt to the questions of whether verge nursing home costs re different for () privte prty nd government nursing homes or () nonprofit nd government nursing homes. Control the fmilywise error rte. () privte prty nd government nursing ) nonprofit nd government nursing homes homes H0: 1 0 H0 : 0 H A : 1 0 H A : 0 d t S.106 t t fw C nk t Fil to reect d,, 1.05,, t eect
7 7 We cnnot conclude tht verge nursing home costs differ for privte prty nd government nursing homes, ut we cn conclude tht verge nursing home costs differ for not for profit nd government nursing homes 1. Set up nd test hypotheses relevnt to the question of the degree of the polynomil required to dequtely fit the dt. Control the fmilywise error rte. We wnt to test for the following trends liner qudrtic cuic Size ignoring Size Squred nd Size Cued Size Squred controlling Size nd ignoring nd Size Cued Size Cued controlling Size nd Size Squred To do so with the ville results we must use the control-preceding-vriles pproch: inc, F nkup to 1 1 upto inc, is provided in the SCO1 column. You must clculte up to. To compute up to lso known s cumultive the model to the sum of the inc, which is for vrile, dd for vlues for the preceding vriles. Squred Semi-prtil Corr Type I Cumultive Size Size Squred Size Cued For exmple, for Size Squred up to inc, To control the fmilywise error rte we use the Bonferroni criticl vlue. Thus we will hve to convert the F sttistics to t sttistics. Trend t, C, n k 1 liner F 0 11 t t.05,3, fw eect; we conclude there is liner trend
8 8 qudrtic cuic F F t t.05,3,01 Fil to reect;.655 we cnnot conclude there is qudrtic trend t t.05,3,031 Fil to reect;.673 we cnnot conclude there is cuic trend 13. Drw the regression lines for ech of the groups. Lel ech regression line y group. The informtion provided is tht there is covrite, tretment groups, nd dependent vrile. The following model is otined: Y 3Z e We know tht when there is covrite nd tretment groups, the multiple regression eqution cn e decomposed into two simple regression equtions. You re eing sked to drw these equtions. Becuse there is no product term, the lines must e prllel. Becuse the coefficient for is one, the slope of the regression lines must e positive Becuse group is coded one on the dummy vrile nd d 3, the line for group must e ove the line for group.
9 9 Group Group
10 Suppose. Which will e lrger, the men difference or the dusted men difference? e etween is the grnd covrite men. As weighted men of nd nd., it must If we find the predicted vlue in group corresponding to, it will e equl to Y, the dependent vrile men for group. Similrly if we find the predicted vlue in group corresponding to, it will e equl to Y, the dependent vrile men for group. These dependent vrile mens re represented y in the following grph. The predicted vlues, in groups nd respectively, corresponding to the grnd covrite men re the dusted mens for groups nd, respectively. These dependent vrile mens re represented y in the following grph. Group Group We cn see tht the men difference is lrger thn the dusted men difference.
11 Wht re the purposes of using covrite in n experiment in which suects re rndomly ssigned to tretments? When suects re rndomly ssigned to tretments, there re two purposes for the covrite. The first purpose is to test for covrite tretment interction. The second purpose comes into ply if there is no covrite tretment. The second purpose is to increse the ccurcy of the estimted tretment effect nd to increse the power of the test of the tretment effect. These improvements re reltive to n nlysis tht does not employ the covrite c. 19.
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