Using the number of deaths in each day as our dependent variable, Table
8.11 is the resulting ANOVA table. The result of the overallFtestðp¼ 0 : 0001 Þ
indicates that taken collectively, the two independent variables contribute sig-
nificantly to the prediction of the dependent variable. In addition, we have the
results shown in Table 8.12. The e¤ects of both factors, the mean atmospheric
smoke and the mean atmospheric sulfur dioxide content, are significant even at
the 1% level (bothp< 0 :001).
Contribution of a Group of Variables This testing procedure addresses the
more general problem of assessing the additional contribution of two or more
factors to prediction of the response over and above that made by other vari-
ables already in the regression model. In other words, the null hypothesis is of
the form
H 0 :b 1 ¼b 2 ¼¼bm¼ 0To test such a null hypothesis, one can fit two regression models, one with all
X’s included to obtain the regression sum of squares (SSR 1 ) and one with all
TABLE 8.10
Number of Deaths Smoke Sulfur Dioxide
112 0.30 0.09
140 0.49 0.16
143 0.61 0.22
120 0.49 0.14
196 2.64 0.75
294 3.45 0.86
513 4.46 1.34
518 4.46 1.34
430 1.22 0.47
274 1.22 0.47
255 0.32 0.22
236 0.29 0.23
256 0.50 0.26
222 0.32 0.16
213 0.32 0.16
TABLE 8.11
Source of Variation SS df MS FStatistic pValue
Regression 205,097.52 2 102,548.76 36.566 0.0001
Error 33,654.20 12 2,804.52
Total 238,751.73 14
MULTIPLE REGRESSION ANALYSIS 301