CH12 - 12.3:1 Plots can he done either by hand or by...

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Unformatted text preview: 12.3 :1. Plots can he done either by hand or by computer. with such a small data set (and such convenient mitt-hers}. Plot ofu' versus 1' q.l'|- - . ., 3.5 - 3.I1 - I u .. I. .15 .'-'.I'I - I II II- |.fi - I.I'I - I II + L.“ [5 F" 3‘ E- ?III I. Plot oft: versus .1: t5.- .. 5' ' + 1 . b- .E' a 2-. . + Lil'l 1's in is so I. Plot oft: versus w it - 5 .- 1 .. I‘ 3 - I I. |_ n. I IJZI l 5 P‘JII 3.5 1D 3 5 II] 'H h. The plot of w versus 3: indicates zero correlation. There is no treni upward or downward, in this plot. In fact. the values are pe-n‘fectlyr balanced. The plot of v versus 1' shows a very clear increasing relation and therefore positive correlation. The plot of 1: versus w shows only a very slight positive correlation. so slight that it"s not obvious at first glance. 12.4 a. For the model with only 1' as an independent variable, shown first in the output, we can read the regression equation fl'om the I.Coefcolumn. The equation is t=ri5+tux The residual standard desiation is shown as 3 = 3.33151 life can read the results for the model with all three predictors similarly. The least squares prediction equation is i-=1Etfl+5flr+lflw+lflr The residual standard desiation is shown as 3 = 2.54574. b. The multiple R: in the three-predictor model is shown as 39.3%, which is larger than the r2 for the one-predictor model, 33.3%. 1r"es, the residual standard deviation in the larger model (2.545) is smaller than the residual standard deviation ofthe one-predictor model (3.331). 12.11] a. Thel-I'Stflegiessionj is 159.63. The M3[Residual:| is 3.30. b. The value of the F statistic is F = lfififil-‘TJII-[II = 22.31. c. They-value is shown in the Analysis of's-‘ariance table as .1103. As a partial check, in Appendix Table IS with 3 and 3 degrees offleedom, the largest entijr' is 15.33 [or = .III-Ell}. .F' =12.3l F 15-33 sop-value ii .331. cl. Because the pI-value for the F test is extremely small, we would emphaticallv reject the null hvpothesis, HE, : 131 = '31 = '83 = '34 = t] in favor ofthe alternative hypothesis, Ha : at least one ,3} 9% ID . That is, we have strong evidence that the independent variables, I, w, and v, collectively, have at least some predictive value in predicting the dependent variable, y. e. The output shows a coefficient ofr equal to 13-30, and a standard error [in the SE I.Coefcolurun} equal to 5.395. The onl}r additional information we need is the appropriate ttable value. For 9531: confidence, we want a onetail area equal to .112 i: the dfwe want is the error dfi shown as 3 in the output. From Appendix Table 4-, the value we want is 2.335. Therefore, the 95% confidence interval for the true coefficient ofr is 5.1134] — 2-3116(6395} £ ,31 5' Sflflfll + 2-3116(6395} —lC|-EHIIC| E- 331 £23934] This is a very wide interval. It includes G, indicating that we don't have evidence that the a variable adds predictive value to the others. 111-1 :1. The R: value for the ueduced model {the second model in the output) is labeled R—Sq and has a value of 213.5%. In. The complete model is the that model shown in the output. with all three predictors used It shows an R1 value off-fifth. c. The F statistic based on the incremental R: can be calculated fl'om the given output. F = dim-fr — shim n...-ts — a II] — RAWW.” lift” — Eli + III) where = as? = cos l: = #- variables for complete model = 3- g = # variables for reduced model = l .u — [.t' —1} = df' for ciroi' in the complete model = l? Thenefore, F = (397" — -2051.-'I{3 — l) = 24-3 (1 — .TEIT}_.-'1T The null hypothesis tested is HI] : .BEusAccta = fiCompedno-n = D that is__ the independent variables Busifliccts and Competition have no pnedictive value once Income is included as a predictor. The computed value of'F is much larger than an}: ofthe values in the .F' table for l and 17" di‘. Therefone, u-‘e neject the null hypothesis mid conclude instead that at least one ofBusAccts and Competition adds predictive value, over and above that of Income. ...
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CH12 - 12.3:1 Plots can he done either by hand or by...

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