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of 0.51 (also evidentin 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 waylower 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 METHODS35Hypothesis: Ho2:There is no statistically significant relationship between safety training expenditure and lost time hoursHa2:There is a statistically significant relationship between safety training expenditure and lost time hoursSimple Regression Output:RegressionStatisticsMultiple R0.939559324R Square0.882771723Adjusted R Square0.882241279Standard Error24.61328875Observations223ANOVAdfSSMSFSignificanceFRegression11008202.1051008202.1051664.2106877.6586E-105Residual221133884.8903605.8139831Total2221142086.996CoefficientsStandardErrort StatP-valueLower 95%Upper 95%Lower95.0%Upper95.0%Intercept273.4494192.665261963102.59757682.1412E-188268.1968373278.7020007268.1968373278.7020007safety training expenditure-0.1433677410.003514368-40.794738487.6586E-105-0.150293705-0.136441778-0.150293705-0.13644178
BUSINESS RESEARCH METHODS36Since 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% ofthe 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 - 0.14XWhere y is lost time hours and X is the safety training expenditure. Multiple Regression: Hypothesis TestingHypotheses:Ha3:Noise levels do not have a statistically significant relationship with frequency, angle, chord length, velocity, and displacement. Ha3: Noise levels have a statistically significant relationship with frequency, angle, chord length, velocity, and displacement.Multiple Regression Analysis Output:RegressionStatisticsMultiple R0.601841822R Square0.362213579Adjusted R Square0.360083364
BUSINESS RESEARCH METHODS37Standard Error5.51856585Observations1503ANOVAdfSSMSFSignificanceFRegression525891.887845178.378170.03614672.1289E-143Residual149745590.4898630.45457Total150271482.3777CoefficientsStandardErrort StatP-valueLower 95%Upper 95%Lower95.0%Upper95.0%Intercept126.82245550.623820253203.29970125.5988009128.0461101125.5988128.0461Frequency (Hz)-0.00111694.7551E-05-23.48854.0652E-104-0.001210174-0.001023627-0.00121-0.00102Angle in Degrees0.0473423530.0373080691.2689570.204653501-0.0258392880.120523993-0.025840.120524Chord Length-5.4953183352.927962181-1.876840.060734309-11.238662340.248025671-11.23870.248026Velocity (Metersper Second)0.0832396340.0093001888.9503171.02398E-180.0649968510.1014824170.0649970.101482Displacement-240.505908616.51902666-14.55935.20583E-45-272.9088041-208.103013-272.909-208.103The positive multiple R-value in this case is indicative of a positive relationship.