PowerPoint Presentation
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Unit V Scholarly Activity
Michell Muldrow
Columbia Southern University
Research Methods
Dr. Senft
November 2, 2021
Data Analysis: Hypothesis Testing
Correlation: Hypothesis Testing
Ho1: There is no statistically significant relationship between particulate matter size and employee sick days.
Ha1: There is a statistically significant relationship between particulate matter size and employee sick days.
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|
microns |
mean annual sick days per employee |
|
microns |
1 |
|
|
mean annual sick days per employee |
-0.715984185 |
1 |
|
Regression Statistics |
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Multiple R |
0.715984185 |
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R Square |
0.512633354 |
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Adjusted R Square |
0.507807941 |
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Standard Error |
1.327783455 |
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Observations |
103 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
187.2953239 |
187.2953 |
106.2361758 |
1.89059E-17 |
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Residual |
101 |
178.0638994 |
1.763009 |
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Total |
102 |
365.3592233 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
|
Intercept |
10.08144483 |
0.315156969 |
31.98865 |
1.16929E-54 |
9.456258184 |
|
microns |
-0.522376554 |
0.050681267 |
-10.3071 |
1.89059E-17 |
-0.622914554 |
The Pearson correlation coefficient of r = -0.71 indicates a moderately negative correlation. This equates to an r2 of 0.5126, explaining 50% of the variance between the variables.
Using an alpha of .05, the results indicate a p value of 1.89 < .05. Therefore, the null hypothesis is rejected, and the alternative hypothesis is accepted that there is a statistically significant relationship between (PM) and annual sick days(employee health).
Simple Regression: Hypothesis Testing
Ho2: There is no statistically significant relationship between safety training expenditure and lost-time hours..
Ha2: There is a statistically significant relationship between safety training expenditure and lost-time hours.
|
Regression Statistics |
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|
Multiple R |
0.939559324 |
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R Square |
0.882771723 |
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Adjusted R Square |
0.882241279 |
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Standard Error |
24.61328875 |
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Observations |
223 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
|
Regression |
1 |
1008202.105 |
1008202 |
1664.210687 |
7.6586E-105 |
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Residual |
221 |
133884.8903 |
605.814 |
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Total |
222 |
1142086.996 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
|
Intercept |
273.449419 |
2.665261963 |
102.5976 |
2.1412E-188 |
268.1968373 |
|
safety training expenditure |
-0.143367741 |
0.003514368 |
-40.7947 |
7.6586E-105 |
-0.150293705 |
The multiple R is 0.93 which shows there is a strong positive relationship between to 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 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. 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.
Y= 273.44(intercept) +-(0.1433)(safety training)(X)
Multiple Regression: Hypothesis Testing
Ho3; There is no significant relationship between frequency, angle in degrees, chord length, velocity, and displacement and decibel level.
Ha3: There is a statistically significant relationship between frequency, angle in degrees, chord length, velocity, and displacement and decibel level.
|
Regression Statistics |
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Multiple R |
0.601841822 |
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R Square |
0.362213579 |
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Adjusted R Square |
0.360083364 |
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Standard Error |
5.51856585 |
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Observations |
1503 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
5 |
25891.89 |
5178.378 |
170.0361 |
2.1289E-143 |
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Residual |
1497 |
45590.49 |
30.45457 |
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Total |
1502 |
71482.38 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
|
Intercept |
126.8224555 |
0.62382 |
203.2997 |
0 |
125.5988009 |
|
Frequency (Hz) |
-0.0011169 |
4.76E-05 |
-23.4885 |
4.1E-104 |
-0.001210174 |
|
Angle in Degrees |
0.047342353 |
0.037308 |
1.268957 |
0.204654 |
-0.025839288 |
|
Chord Length |
-5.495318335 |
2.927962 |
-1.87684 |
0.060734 |
-11.23866234 |
|
Velocity (Meters per Second) |
0.083239634 |
0.0093 |
8.950317 |
1.02E-18 |
0.064996851 |
|
Displacement |
-240.5059086 |
16.51903 |
-14.5593 |
5.21E-45 |
-272.9088041 |
The multiple R value is 0.60 indicating a positive correlation between the regression model and the dependent variable. The R square value is 0.36622. This means that 36% of the variables in DB can be explained by the entire set of the independent variables(frequency, angle, chord length, velocity and displacement).
The ANOVA F value of 2.1289. This is way lesser than the alpha level of 0.05, meaning that there is a statistically significant relationship between frequency, angle in degrees, chord length, velocity, and displacement and decibel level. As such, we reject the null hypothesis and accept the alternative hypothesis that dB levels have a statistically significant relationship with frequency, angle, chord length, velocity, and displacement.
The regression model as an equation is as represented below:
Y = a0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5
y = 126.822 – (-0.001)(X1) + (0.047)(X2) -5.495(X3) + 0.083(X4) - 240.506(X5)
Where: X1 = frequency (Hz)
X2 = Angle in degrees
X3 = Chord Length
X4 = Velocity (m/s)
X5 = Displacement
Y = Decibels
References
Porterfield, T. (2017, May 18). Excel 2016 Correlation Analysis [Video file]. Retrieved from
https://www.youtube.com/watch?v=kr64tfZmiGA
Seber, G. A., & Lee, A. J. (2012). Linear regression analysis (Vol. 329). John Wiley & Sons.