51 also evident in the regression analysis output This explains 51 of the

51 also evident in the regression analysis output

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of 0.51 (also evident in the regression analysis output). This explains 51% of the variance between the variables. As is evident from the regression analysis output, the p-value is 1.89099E-17. This is way lower than the alpha of 0.05, thus allowing us to reject the null hypothesis. The alternative hypothesis is accepted that there is a statistically significant relationship between employee health and PM size. This relationship is strongly negative as evidenced by the r-value. Simple Regression: Hypothesis Testing
BUSINESS RESEARCH METHODS 35 Hypothesis: Ho 2 : There is no statistically significant relationship between safety training expenditure and lost time hours Ha 2 : There is a statistically significant relationship between safety training expenditure and lost time hours Simple Regression Output: Regression Statistics Multiple R 0.93955932 4 R Square 0.88277172 3 Adjusted R Square 0.88224127 9 Standard Error 24.6132887 5 Observation s 223 ANOVA df SS MS F Significance F Regression 1 1008202.10 5 1008202.10 5 1664.21068 7 7.6586E- 105 Residual 221 133884.890 3 605.813983 1 Total 222 1142086.99 6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 273.449419 2.66526196 3 102.597576 8 2.1412E- 188 268.196837 3 278.702000 7 268.196837 3 278.702000 7 safety training expenditure - 0.14336774 1 0.00351436 8 - 40.7947384 8 7.6586E- 105 - 0.15029370 5 - 0.13644177 8 - 0.15029370 5 - 0.13644178
BUSINESS RESEARCH METHODS 36 Since there are only two variables, the Multiple R is identical to the Pearson’s r. As such the Multiple R-value of 0.93956 means that there is a strong positive relationship between the two variables. The R square value of 0.8828 means that the regression model explains 88.28% of the variation between safety training expenditure and lost time hours. The considerably high R square value shows that the model has a reliable predictive power. The ANOVA significance (F) value is 7.6586E-105. This is way lesser than the alpha level of 0.05, meaning that there is a statistically significant relationship between the two variables (Seber & Lee, 2012). As such, we reject the null hypothesis and accept the alternative hypothesis that there is a statistically significant relationship between safety training expenditure and lost time hours. The regression model as an equation is as represented below: y = 273.45 - 0.14X Where y is lost time hours and X is the safety training expenditure. Multiple Regression: Hypothesis Testing Hypotheses: Ha 3 : Noise levels do not have a statistically significant relationship with frequency, angle, chord length, velocity, and displacement. Ha 3 : Noise levels have a statistically significant relationship with frequency, angle, chord length, velocity, and displacement. Multiple Regression Analysis Output: Regression Statistics Multiple R 0.601841822 R Square 0.362213579 Adjusted R Square 0.360083364
BUSINESS RESEARCH METHODS 37 Standard Error 5.51856585 Observations 1503 ANOVA df SS MS F Significance F Regression 5 25891.88784 5178.37 8 170.0361467 2.1289E-143 Residual 1497 45590.48986 30.4545 7 Total 1502 71482.3777 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 126.8224555 0.623820253 203.299 7 0 125.5988009 128.0461101 125.5988 128.0461 Frequency (Hz) -0.0011169 4.7551E-05 -23.4885 4.0652E-104 - 0.001210174 - 0.001023627 -0.00121 -0.00102 Angle in Degrees 0.047342353 0.037308069 1.26895 7 0.204653501 - 0.025839288 0.120523993 -0.02584 0.120524 Chord Length - 5.495318335 2.927962181 -1.87684 0.060734309 - 11.23866234 0.248025671 -11.2387 0.248026 Velocity (Meters per Second) 0.083239634 0.009300188 8.95031 7 1.02398E-18 0.064996851 0.101482417 0.064997 0.101482 Displacement - 240.5059086 16.51902666 -14.5593 5.20583E-45 - 272.9088041 -208.103013 -272.909 -208.103 The positive multiple R-value in this case is indicative of a positive relationship.