Introductory Biostatistics

serves as an estimate of the constant variances^2 as stipulated by the

regressionmodel.

2. The breakdowns of the total sum of squares and its associated degree
   of freedom aredisplayedin the form of ananalysis-of-variance(ANOVA)
   table(Table 8.3). The test statisticFfor the analysis-of-variance approach
   above compares MSR and MSE. A value near 1 supports the null hy-
   pothesis of independence. In fact, we have

F¼t^2

wheretis the test statistic for testing whether or notb 1 ¼0; theFtest is

equivalent to the two-sidedttest when refered to theFtable in Appendix

E withð 1 ;n
 2 Þdegrees of freedom.

Example 8.5 For the birth-weight problem of Examples 8.1 and 8.3, we have
the analysis of variance shown in Table 8.4.

Example 8.6 For the blood pressure problem of Examples 8.2 and 8.4, we
have the analysis of variance shown in Table 8.5.

TABLE 8.3

Source of
Variation SS df MS FStatistic pValue

Regression SSR 1 MSR¼SSR= 1 F¼MSR=MSE p
Error SSE n
2 MSE¼SSE=ðn
2 Þ

Total SST n
1

TABLE 8.4

Source of Variation SS df MS FStatistic pValue

Regression 6508.43 1 6508.43 85.657 0.0001
Error 759.82 10 75.98

Total 7268.25 11

TABLE 8.5

Source of Variation SS df MS FStatistic pValue

Regression 1691.20 1 1691.20 6.071 0.0285
Error 3621.20 13 278.55

Total 5312.40 14

SIMPLE REGRESSION ANALYSIS 293