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hw4 solution

# hw4 solution - 4 a The test statistics and p-Values for the...

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Unformatted text preview: 4 a The test statistics and p-Values for the three iraIiahles—added—in—order tests are: . ._. _ 1053.623 _ _ __ﬁ 1 r (Jig—W — 30.762 (119.1,” P a 0.001. 17 .. .. 133.113 - =—= ' =:Z a: '3.l 1%ch Ills) 40128? 7.325 df. 1., 16 0.0]. P 0.0-) 16 iii Fig.3 Xg,Xs}= 33629382 =1.563 df: l, 15 [1.] =12 Pcil 0.25 - 15 X3. artng are significant; .1”; is not. b Ho.',fi'1=ﬁ2 = 0 vs. HA: 3% e U and."orﬁ; = CI in the model Y=ﬂ3 +3151} +3313 +ﬁ513 + E 221.?25 Fﬂl’hX‘. X3) = = 4.577 dfzﬁ, 15 15 0.025 P-=: 0.05 At least one ofthe variables Xi and X2 is significant, given thatin is in the model. C Using the given ADIOVA table, we cannot test Hg: ,8; = ,3; = D in the model Y= ,8; + .3111] + ,3ng + ,83X3. + E, as the variables have not entered the model in the right order to perform this test. The test statistic that would be needed is: [Regression 55(Xl. X3 . X3) - Regression SSﬂijy ., FILE X. - i L' 3' -) ResidualMSthsz.X5} d X: and X; are important variables whereas X; should be excluded from the ﬁnal model. . a The three F—tests are: i H0: ,6". =ﬁ2 = 0 vs. H2: ﬁrst! and-"orﬁ’zeO inthe model l"=,80 +£1.15 +39ng + E. F(.¥1,X2)=26.36 df: 2, 22 P-=: 0.0001 At a = 0.05, we reject Hg and conclude that ,81 .= 0 and-'orﬂg e 0. ii Hg: ,6'; = 0 vs.H_.:,:,81¢ 0 in the model Y=,3;+35’LX1 + E. FlCth=1J4 df: 1,23 P=0.2 At a = 0.05, we do not reject H0 and conclude thatﬁ‘;= 0. iii Hg: ,0" = 0 vs. H_.:,:ﬁg e 0 in the model Y=ﬁ:+x5’1X2 + E. Flngj = 53.96. df: l, 23 P-=: 0.0001 At a = 0.05, we reject Hg and conclude that ,8: .= 0. X3 is the more important predictor of J". In chapter 8, problem 3th), the model containing both predictors was chosen based on R] values. However, based on the partial F—tests above, we would choose the more parsimonious model containing only X2. 12 The two variables-added—in-order tests are: t See 03(0) ii H0: ,8: = U 0‘s. Haj: e U in the model Y=ﬂ3+ﬁle+j93X3 + E. H E, I Y }_ 55601111 _ 85(X;Ji'.‘}—SSEX1} ‘ 3 ‘ 1 Residual 0130112,) Residual 0130212,) 102520.014? 402312202 = 4230 .2253 = “'45 22 df: . 22 P-=: 0.001 At a = 0.05, we reject Hg and conclude thatﬁg e 0 in the model 1"=.3:+.31X1+.3241'2+ 5- c The two variables-added—in-order tests are: i See 6a(iii}. ii Hg: ,8; = 0 0‘s. H_:.: ,8; .= 0 in the model }'=ﬁg +IBIX1+ﬁﬁll +E. a . _102570.814T—101932.665? _ _ M 2*(X1 Jig—W432: dil,“ 22 P:= 0.25 At 0: = 0.05, we do not reject Hg and conclude thatﬁ‘; = 0 in the model 3—: .3: +3154??st + E- d Source df 83 MS F X1 X2 1 638.149 638.149 0.328 X2 X1 1 92339.089 92339.089 42.45? Residual 22 42806225 1945.238 Total 24 145372.040 e No differences are discernahle; all approaches indicate that A] does not signiﬁcantly aid in the prediction of 1’. either alone or in addition to X2. X3 does signiﬁcantly aid in the prediction of I’. 8' 3 H0319? =33 = 0 “14:11:32 -= 0 Mid-"OWE = U in the model 1930 +135? +£2.15 +193X5+ E. {7010.03+l0.93) Page X.)=—3=32.79 df: 2, 21 2243.23 /21 P c=2 0.001 At ct = 0.05. we reject Ho and conclude that at least one .6,- == 0. b Ho:ﬁI=,33=0vs.HA: atleastoneﬂi e 0 inthe model Y=ﬁo+ﬂ£ﬁ+ﬁsﬁ+£ [13953.04+]I‘010.03 . 7 = 2 = 2 -2 '1': PIER-"A; [l'[l.931+22-°l\$.23}4j 1 6'4 dr— 1“ P c: 0.001 At at = 0.05. we reject hi] and conclude that at least one .63- = 0. c The F test corresponds to comparing the models 1’: ﬁg — E and 11,330 +1911“. +1923} 433350 — E- 13. :1 Ho: .31 =13: = 0 vs. Hi: .6; .= 0 and-"0:131 e 0 in the model I’=.6t1 -,31X1-,3;.ﬁ +E {XL = DWNCOSI. X; = URBAN) FLY]. X2} = 8.52 df: 2. 23 P=0.013" At ct = 0.05. we would reject Hg and conclude that at least oneﬁj = 0. h 1 1:11:31 = 0 vs. Ha: .61 e 0 inthe model 1"=,6’: +19tXl-E. F _ Regression SSﬂXIJ _ 132.6203 _ [SSY - Regression SSﬂle].-" 24 _ [600.96l5— 132.6203] 324 df: 1.24 0.01 criPcri 0.025 At 0. = 0.05. we reject Hg and conclude that '31 .= 0. ii 210:3: = 0 vs. H32 .62 = 0 inthe model 1"='.-5’: +ﬁle— 6313+ E. FQLEl IQ = 8.21 df: 1.23 P=0.0088 At or = 0.05. we reject Hg and conclude that '33 e 0. =6.80 c i Ho: ,3: = 0 vs. Ha: ,8: .= 0 in the model l'=ﬁ: +1395:— E. Regression SSﬂXl, X3) — Regression SS(X._ | X1) [SSY {Regression 8301'; . X: 3— Regression SSQ’ll X: )j] 24 = 255.??85—663318 =1105 [600.9615—{255.2235—66.33l3)]:"24 ' (if: 1. 24 0.001 {P c: 0.005 At a = 0.05, we reject Hg. and conclude thatﬁ'; .= 0. ii Hmﬁl = 0 vs. Hg: .81 .= 0 in the model }’=,6'g —ﬁ1)1'1—ﬁ}2'3+E. F011 '3) =4.42 df: 1, 23 P= 0.046? At a = 0.05. we rejectHc. and conclude that atﬁl e 0. d Source i SS MS F X1|X2 1 66.334 66.334 4.42 Xngg 1 123.153 123.158 8.21 Residual 23 345.133 15.008 Total 25 600. 962 9 Both predictors are neces sarjg. Each variable is significant regardless of the order entered in the model and both should be included. ...
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hw4 solution - 4 a The test statistics and p-Values for the...

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