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Running head: DATA ANALYSIS SUN COAST PROJECT Data Analysis Sun Coast Project Nguyen Tien Thanh ID: 280113 Columbia Southern University DATA ANALYSIS SUN COAST PROJECT Data Analysis: Correlation, Regression, t Test, and ANOVA The Sun Coast Remediation’s data are meet assumption and appropriate for parametric statistical procedures For further conclusion, in this assignment we will use analysis including: correlation analysis, simple regression analysis, multiple regression analysis, independent sample t test, paired sample t test and ANOVA The results, conclusions from these analysis will support us to make right decisions Correlation Analysis The hypotheses: H01:There is not a relationship between size of PM and numbers of employee’s sick days HA1:There is a relationship between size of PM and numbers of employee’s sick days Data output results from Excel Toolpak: mean annual sick days per employee Microns Microns mean annual sick days per employee -0.715984185 Regression Statistics Multiple R 0.715984185 R Square 0.512633354 Adjusted R Square 0.507807941 Standard Error 1.327783455 Observations 103 ANOVA Df Regression Residual 101 Total 102 SS 187.295323 178.063899 365.359223 MS 187.2953239 1.763008905 F 106.236175 Significance F 1.89059E-17 DATA ANALYSIS SUN COAST PROJECT Coefficients 10.0814448 0.52237655 Intercept Microns Standard Error 0.31515696 31.9886464 1.16929E-54 9.456258184 0.05068126 -10.30709347 1.89059E-17 -0.622914554 t Stat P-value Lower 95% Upper 95% Lower 95.0% 10.7066314 0.42183855 Upper 95.0% 9.456258184 10.70663148 0.622914554 -0.421838554 The value of Pearson correlation coefficientr = -0.715 It meansthat particulate matter size, as measured in microns, is strongly and negatively correlated with mean annual sick days per employee The value of r2=0.51, it means that 51% of the variability in employee sick days is explained by particular matter size The value of p is 1.89E-17 for microns,it is smaller than the value of alpha 0.05.When the p value is smaller than the alpha, the null hypothesis isrejected and the alternative hypothesis is accepted that there is statistically significant relationship between particular matter size and employee sick days Simple Regression Analysis Restate the hypotheses: H02:There is not a relationship between the safety training expenditure and the lost time hours HA2:There is a relationship between the safety training expenditure and the lost time hours Data output results from Excel Toolpak: Regression Statistics Multiple R 0.939559324 R Square 0.882771723 Adjusted R Square 0.882241279 ANOVA Standard Error 24.61328875 Df SS Observations 223 Residual 221 1008202.10 133884.890 Total 222 1142086.996 Regression Coefficients Intercept 273.449419 Standard Error 2.665261963 MS 1008202.105 F 1664.21068 Significance F 7.6586E-105 605.8139831 t Stat 102.5975768 P-value 2.1412E-188 Lower 95% Upper 95% 268.1968373 278.7020007 Lower 95.0% 268.1968373 Upper 95.0% 278.7020007 DATA ANALYSIS SUN COAST PROJECT safety training expenditure -0.143367741 0.00351436 -40.79473848 7.6586E-105 -0.150293705 -0.136441778 -0.150293705 The value of Multiple R is0.939, close to 1, it means that there is strong correlation between the safety training expenditureand the lost time hours The value ofR square (R2) is 0.88 indicates that 88% of the variation in the lost time hours is explained by the regression model This is a high R2 The p value is7.65E-105smaller than the alpha value 0.05.Sothe null hypothesis is rejected and the alternative hypothesis is accepted There is a relationship between the safety training expenditure and the lost time hours The coefficient for safety training expenditure is -0.143 indicating a negative correlation between lost time hours and the safety training expenditure.The model can be expressed as a predictive equation: Y = a + bX Lost time hours = 273.44 + (-0.143)(safety training expenditure) Multiple Regression Analysis Restate the hypotheses: H03:There is not a relationship between frequency, angle in degrees, chord length, velocity,displacement and decibel level HA3:There is a relationship between frequency, angle in degrees, chord length, velocity, displacement and decibel level Data output results from Excel Toolpak: Regression Statistics Multiple R 0.601841822 R Square 0.362213579 Adjusted R Square 0.360083364 Standard Error 5.51856585 -0.136441778 DATA ANALYSIS SUN COAST PROJECT Observations 1503 ANOVA Df SS Regression MS 25891.88784 5178.377569 Residual 1497 45590.48986 30.45456904 Total 1502 71482.3777 Coefficients Intercept Standard Error t Stat F 170.036146 P-value Significance F 2.1289E-143 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 126.8224555 0.623820253 203.2996763 125.5988009 128.0461101 125.5988009 128.0461101 -0.0011169 4.7551E-05 -23.48846042 -0.001210174 -0.001023627 -0.001210174 -0.001023627 Angle in Degrees 0.047342353 0.037308069 1.268957462 -0.025839288 0.120523993 -0.025839288 0.120523993 Chord Length Velocity (Meters per Second) -5.495318335 2.927962181 -1.876840613 4.0652E-104 0.20465350 0.06073430 -11.23866234 0.248025671 -11.23866234 0.248025671 0.083239634 0.009300188 8.950317436 1.02398E-18 0.064996851 0.101482417 0.064996851 0.101482417 Displacement -240.5059086 16.51902666 -14.55932686 5.20583E-45 -272.9088041 -208.103013 -272.9088041 -208.103013 Frequency (Hz) The value ofMultiple R is0.6reveals, it means thatthe frequency, angle in degrees, chord length, velocity, displacement aremoderately correlated with decibel level R square (R2) is 0.36, it means 36% of the variability in the decibel levelexplained by frequency, angle in degrees, chord length, velocity, displacement This is a weak R2 Using an alpha of 0.05 to compare with thep value of each variable: for Frequency (Hz), a p value of 4.06E-104< 0.05, therefore, there is statistical significance between Frequency and decibel level for Angle in Degrees, a p value of 0.2> 0.05,therefore, there is no statistical significance between Angle in Degrees and decibel level for Chord Length, a p value of 0.06> 0.05, therefore, there is no statistical significance between Chord Length and decibel level for Velocity (meters per second),a p value of 1.02E-18 < 0.05, therefore, there is statistical significance between Velocity and decibel level DATA ANALYSIS SUN COAST PROJECT and for Displacement, a p value of 5.2E-45 < 0.05, therefore, there is statistical significance between Displacement and decibel level Summary, there is a statistically significant relationship between frequency, velocity, displacement and decibel level The coefficient for frequency is -0.001 and displacement is -240.5 indicating a negative correlation between frequency, displacement and the decibel level The coefficient for velocity is 0.083 indicating a positive correlation between velocity and the decibel level The predictive equation is expressed as following: Y = a + b1X1 + b2X2 +…+ bnXn Decibel level= 126.8 + (-0.001)(Frequency (Hz)) + (-240)(Displacement) + 0.083(Velocity) Independent Sample t Test Restate the hypotheses: H04:The revised new employee training is not more effective than the prior training HA4:The revised new employee training is more effective than the prior training Data output results from Excel Toolpak: t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Hypothesized Mean Difference Df t Stat P(T