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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
mitthers}. 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 pen‘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 threepredictor model is shown as 39.3%, which is larger than the r2 for the
onepredictor model, 33.3%. 1r"es, the residual standard deviation in the larger model (2.545) is smaller than the residual standard deviation
ofthe onepredictor model (3.331). 12.11] a. ThelI'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. Theyvalue 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 = .IIIEll}. .F' =12.3l F 1533 sopvalue ii .331. cl. Because the pIvalue 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 1330, 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] — 23116(6395} £ ,31 5' Sﬂﬂﬂl + 23116(6395}
—lCEHIIC 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. 1111 :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 offﬁfth. c. The F statistic based on the incremental R: can be calculated ﬂ'om the given output. F = dimfr — 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) = 243
(1 — .TEIT}_.'1T
The null hypothesis tested is HI] : .BEusAccta = ﬁCompednon = 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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This note was uploaded on 01/11/2012 for the course STATS 1305 taught by Professor Shahmai during the Spring '11 term at NYU.
 Spring '11
 shahmai

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