The testing of the hypotheses was conducted using the Sun Coast Remediation data. The data that was used for this section involved the correlation analysis, the simple regression analysis, and the multiple regression analysis.
Correlation: Hypothesis Testing
Hypothesis:
Ho 1 : There is no statistically significant relationship between particulate matter size and employee annual sick days.
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Ha 1 : There is a statistically significant relationship between particulate matter size and employee annual sick days.
|
microns |
mean annual sick days per employee |
|
| microns |
1 |
|
| mean annual sick days per employee |
-0.715984185 |
1 |
SUMMARY REGRESSION OUTPUT |
||||||||
|
Regression Statistics |
||||||||
| Multiple R |
0.715984185 |
|||||||
| R Square |
0.512633354 |
|||||||
| Adjusted R Square |
0.507807941 |
|||||||
| Standard Error |
1.327783455 |
|||||||
| Observations |
103 |
|||||||
| ANOVA | ||||||||
|
df |
SS |
MS |
F |
Significance F |
||||
| Regression |
1 |
187.2953239 |
187.2953239 |
106.2361758 |
1.89059E-17 |
|||
| Residual |
101 |
178.0638994 |
1.763008905 |
|||||
| Total |
102 |
365.3592233 |
||||||
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
| Intercept |
10.08144483 |
0.315156969 |
31.9886464 |
1.16929E-54 |
9.456258184 |
10.70663148 |
9.456258184 |
10.70663148 |
| microns |
-0.522376554 |
0.050681267 |
-10.30709347 |
1.89059E-17 |
-0.622914554 |
-0.421838554 |
-0.622914554 |
-0.421838554 |
The correlation data revealed Pearson’s correlation coefficient (r) as -0.7158. This was an indicator that the relationship between the annual number of employees’ sick days and particulate matter size was negative. The correlation could also be described as being strongly negative since the value of r is close to -1 (Mu et al., 2018). The value of r 2 was 0.5126 as shown in the regression analysis output. The variance between the given variables was thus given as 51.26%.
The p-value was given as 1.89059E-17 and the alpha level was 0.05. The null hypothesis Ho 1 is thus rejected while the alternative hypothesis Ha 1 is accepted. This indicates that there is a statistically significant relationship between the employees’ annual sick days and the particulate matter size.
Simple Regression: Hypothesis Testing
Ho 2 : There is no statistically significant relationship between the safety training programs, the expenditure, and the lost time hours.
Ha 2 : There is a statistically significant relationship between the safety training programs, the expenditure, and the lost time hours.
SIMPL REGRESSION SUMMARY OUTPUT |
||||||||
|
Regression Statistics |
||||||||
| Multiple R |
0.939559324 |
|||||||
| R Square |
0.882771723 |
|||||||
| Adjusted R Square |
0.882241279 |
|||||||
| Standard Error |
24.61328875 |
|||||||
| Observations |
223 |
|||||||
| ANOVA | ||||||||
|
df |
SS |
MS |
F |
Significance F |
||||
| Regression |
1 |
1008202.105 |
1008202.105 |
1664.210687 |
7.6586E-105 |
|||
| Residual |
221 |
133884.8903 |
605.8139831 |
|||||
| Total |
222 |
1142086.996 |
||||||
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
| Intercept |
273.449419 |
2.665261963 |
102.5975768 |
2.1412E-188 |
268.1968373 |
278.7020007 |
268.1968373 |
278.7020007 |
| safety training expenditure |
-0.143367741 |
0.003514368 |
-40.79473848 |
7.6586E-105 |
-0.150293705 |
-0.136441778 |
-0.150293705 |
-0.136441778 |
There were two variables and the value of R was given as 0.9395 indicating that there is a strong positive relationship between the given variables. The R square value was 0.8828 indicating that there was an 88.28% variation between the lost time hours, safety training, and expenditure. The ANOVA F value was 7.6586E-105. This value was less than the alpha level of 0.05 and it thus indicated a statistically significant relationship between the given variables (Porterfield, 2017). The null hypothesis is thus rejected and the alternative hypothesis is accepted. There is thus a statistically significant relationship between safety training, expenditure, and the lost time hours.
The equation for the regression model was given as y = 273.45 - 0.14X where y indicated the lost time hours and x indicated the safety training expenditure.
Multiple Regression: Hypothesis Testing
Hypothesis
Ha 3 : There is no statistically significant relationship between the primary variables of frequency, angle in degrees, cord length, velocity, and displacement with the variable of the decibel level.
Ha 3 : There is a statistically significant relationship between the primary variables of frequency, angle in degrees, cord length, velocity, and displacement with the variable of the decibel level.
|
SUMMARY OUTPUT |
||||||||
|
Regression Statistics |
||||||||
| Multiple R |
0.601841822 |
|||||||
| R Square |
0.362213579 |
|||||||
| Adjusted R Square |
0.360083364 |
|||||||
| Standard Error |
5.51856585 |
|||||||
| Observations |
1503 |
|||||||
| ANOVA | ||||||||
|
df |
SS |
MS |
F |
Significance F |
||||
| Regression |
5 |
25891.88784 |
5178.377569 |
170.0361467 |
2.1289E-143 |
|||
| Residual |
1497 |
45590.48986 |
30.45456904 |
|||||
| 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 |
203.2996763 |
0 |
125.5988009 |
128.0461101 |
125.5988009 |
128.0461101 |
| Frequency (Hz) |
-0.0011169 |
4.7551E-05 |
-23.48846042 |
4.0652E-104 |
-0.001210174 |
-0.001023627 |
-0.001210174 |
-0.001023627 |
| Angle in Degrees |
0.047342353 |
0.037308069 |
1.268957462 |
0.204653501 |
-0.025839288 |
0.120523993 |
-0.025839288 |
0.120523993 |
| Chord Length |
-5.495318335 |
2.927962181 |
-1.876840613 |
0.060734309 |
-11.23866234 |
0.248025671 |
-11.23866234 |
0.248025671 |
| Velocity (M/s) |
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 |
There was a positive R-value and this indicated that there was a positive relationship among the given variables. The presence of multiple variables meant that the value could not be applied conclusively. The value of R squared for the given case was given as 0.3622 indicating that 36.22% of the variable of decibel could be explained through the entire set of the independent variables. The ANOVA F value was given as 2.1289E-143 and it was less than the alpha level of 0.04. This was an indication that there was a statistically significant relationship between the independent variables and the Noise level. Therefore, the null hypothesis is rejected while the alternative hypothesis is accepted.
Using the coefficients from the regression analysis, provided, it was possible to write an equation that represented the relationship as shown below.
y = 126.822 - 0.001X 1 + 0.047X 2 -5.495X 3 + 0.083X 4 - 240.506X 5
where:
y = Noise levels (Decibels)
X 1 = Frequency (Hz)
X 2 = Angle (degrees)
X 3 = Chord length
X 4 = Velocity (meters/second)
X 5 = Displacement.
References
Mu, Y., Liu, X., & Wang, L. (2018). A Pearson’s correlation coefficient based decision tree and its parallel implementation. Information Sciences , 435 , 40-58.
Porterfield, T. (2017, May 18). Excel 2016 correlation analysis [Video file]. Retrieved from https:/ /www.youtube.com/watch?v=kr64tfZmiGA
Rev. 02.03.2019
