Testing for Overall Significance 整体显著性检验 Shows if there is a linear relationship between all of the x variables together and Y .Use F test Statistic .Hypotheses β1=β Bo=0(NO linear relationship H1: At least oneβ;≠0( At least one independent variable affects Y)
Testing for Overall Significance 整体显著性检验 •Shows if there is a linear relationship between all of the X variables together and Y •Use F test Statistic •Hypotheses: H0 : 1 = 2 = ...= p = 0 (No linear relationship) H1 : At least one i 0 ( At least one independent variable affects Y)
Test for Overall Significance Excel Output: Example ANOVA df SS MS F Significance F Regressio n 2)228014.6114007.31684712028165411E-09 Residual 128120.603676.7169 Total 14)236135.2 p value p=2, the number of explanatory variables MRS MSE F Test Statistic
Test for Overall Significance Excel Output: Example A N O V A d f S S M S F S ignificance F R e g re ssio n 2 2 2 8 0 1 4 .6 1 1 4 0 0 7 .3 1 6 8 .4 7 1 2 0 2 8 1 .6 5 4 1 1 E -0 9 R e sid u a l 1 2 8 1 2 0 .6 0 3 6 7 6 .7 1 6 9 T o ta l 1 4 2 3 6 1 3 5 .2 p = 2, the number of explanatory variables n - 1 MRS MSE p value = F Test Statistic
Test for Overall Significance Example Solution H6:β1=β2=2=阝=0 Test Statistic H1: At least oneβ1≠0 F 168.47 =.05 (Excel Output) df=2 and 12 Decision: Critical Value(s) Reject at a =0.05 Conclusion: C=0.05 There is evidence that At least one independent variable affects Y 0 3.89F
0 3.89 F H0 : 1 = 2 = ?= p = 0 H1 : At least one I 0 = .05 df = 2 and 12 Critical Value(s): Test Statistic: Decision: Conclusion: Reject at = 0.05 There is evidence that At least one independent variable affects Y = 0.05 F = Test for Overall Significance Example Solution 168.47 (Excel Output)