Research Methods

Ha1: There is a statistically significant relationship between microns and sick days per employee.

The output results of correlation between the two variables is shown in table 1:

Table 1: Correlation analysis

According to the results, the correlation r = -0.72. This implies that there is a strong negative relationship between microns and mean annual sick days per employee. It means that an increase in microns will lead to a decrease in mean annual days per employee. R2 = 0.51 which indicates that 51% of variation in mean annual sick days per employee is explained by microns. Test of coefficients was determined to test the statistical significance of the relationship. Table 2 shows that the relationship is statistically significant where p = 1.8906E-17 which is less than 0.05 implying we reject the null hypothesis and conclude that there is a statistically significant relationship between microns and sick days per employee.

Table 2: Test

Simple Regression: Hypothesis Testing

Simple regression is conducted to determine the relationship between one dependent variable and one independent variable (Pal & Bharati, 2019). In this study, the relations between safety training expenditure and lost time hours is determined.

Ho2: There is no statistical significant relationship between safety training expenditure and lost time hours.

Ha2: There is a statistical significant relationship between safety training expenditure and lost time hours.

The output results is as shown in table 3.

Table 3: Simple regression analysis results

The analysis shows that r = -0.94 implying that there is a strong negative relationship safety training expenditure and lost time hours. The R2 = 0.88 which indicates that 88% of variation in safety training expenditure is explained by lost time hours.

The model was statistically significant where F (1, 221) = 1664.21, p = 7.7E-105 which is less than 0.05, hence we reject the null hypothesis and conclude that there is a statistical significant relationship between safety training expenditure and lost time hours.

The coefficient of the x-variable was tested and it showed significance where b = -6.16, t (221) = -40.79, p = 7.7E-105 which is less than 0.05 implying the coefficient is statistically significant in predicting the safety training expenditure. The linear regression model according to the analysis was given as;

Safety training expenditure = 1753.60 – 6.16*lost time hours

This implies that, holding other factors constant, there is a constant expenditure of $1,753.60. An increase of time lost by an hour will decrease the expenditure by $6.16 while holding other factors constant.

Multiple Regression: Hypothesis Testing

Multiple linear regression helps in determining whether there is a significant relationship between one dependent variable and 2 or more independent variables. In this study, the frequency (Hz) was used as the dependent variable, angle in degrees, chord in length, velocity, displacement and decibel are used as the independent variables.

Ha3: There is no statistical significant relationship between frequency, angle in degrees, chord in length, velocity, displacement and decibel.

Ha3: There is a statistical significant relationship between frequency, angle in degrees, chord in length, velocity, displacement and decibel.

Data was analyzed using Excel Toolpak and the output is as shown in table 4.

Table 4: Multiple regression output

The results shows that r = 0.58 which indicates a relative strong relationship between the given variables of the study. The R2 = 0.3407 which implies that 34.07% of variation in frequency is explained by angle in degrees, chord length, velocity, displacement and decibel.

The model was statistically significant where F (5, 1497) = 154.73, p = 1.16E-132 (Warner, 2020) which was less than 0.05 implying we reject the null hypothesis and conclude that there is a statistical significant relationship between frequency, angle in degrees, chord in length, velocity, displacement and decibel.

Individual coefficients were tested and the results shows that all the x-variables were statistically significant except chord length which had b = -741.56, t (1497) = -.54, p = 0.59 which was greater than 0.05 implying it is not contributing statistically to the dependent variable. For angle in degrees, b = -86.46, t (1497) = -5.03, p = 5.58E-07. For velocity, b = 42.06, t (1497) = 9.78, p = 6.02E-22. For displacement, b = -65093.43, t (1497) = -8.11, p = 1.04E-15 and for decibel b = -241.11, t (1497) = -23.49, p = 4.1E-104.

A linear regression model will be given as;

Frequency (Hz) = 32243.94 – 86.46*angle in degrees + 42.06*velocity – 65093.43*Displacement – 241.11*Decibel

This implies that when all other factors are held constant, we have 32243.94 frequency Hz. An increase in 1 degree of angle in degrees will decrease frequency by 86.46 Hz when other factors are held constant. When velocity is increased by 1m/s, frequency increases by 42.06 Hz. When displacement and decibel are increased by 1 unit each, frequency decreases by 65093.43 Hz and 241.11 Hz respectively when only one variable is used holding others constant.

References

Gogtay, N. J., & Thatte, U. M. (2017). Principles of correlation analysis. Journal of the Association of Physicians of India, 65(3), 78-81.

Pal, M., & Bharati, P. (2019). Introduction to correlation and linear regression analysis. In Applications of Regression Techniques (pp. 1-18). Springer, Singapore.

SUMMARY OUTPUT

Regression Statistics

Multiple R0.583706496

R Square0.340713274

Adjusted R Square0.338511248

Standard Error2564.049485

Observations1503

ANOVA

dfSSMSFSignificance F

Regression550861519141.02E+09154.72711.1645E-132

Residual149798418015966574350

Total150214927953510

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept32243.941721307.24084524.665655.3E-11329679.7235334808.16

Angle in Degrees-86.4596200717.1989247-5.027045.58E-07-120.1961696-52.72307

Chord Length-741.55591911361.861656-0.544520.586167-3412.9155541929.8037

Velocity (Meters per Second)42.060937514.2998938999.7818556.02E-2233.6264809450.495394

Displacement-65093.432458026.089764-8.110231.04E-15-80837.00825-49349.86

Decibel-241.109719210.26502865-23.48854.1E-104-261.2450855-220.9744

microns

mean annual sick

days per employee

microns1

mean annual sick days

per employee

-0.715981

SUMMARY OUTPUT

Regression Statistics

Multiple R0.715984185

R Square0.512633354

Adjusted R Square0.507807941

Standard Error1.327783455

Observations103

ANOVA

dfSSMSFSignificance F

Regression1187.2953239187.2953239106.2361.89059E-17

Residual101178.06389941.763008905

Total102365.3592233

SUMMARY OUTPUT

Regression Statistics

Multiple R0.939559

R Square0.882772

Adjusted R Square0.882241

Standard Error161.303

Observations223

ANOVA

dfSSMSFSignificance F

Regression143300521.43433005211664.2117.6586E-105

Residual2215750122.45126018.65

Total22249050643.88

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept1753.60230.3629622357.754652.6E-1351693.7641351813.4401

lost time hours-6.157390.150935993-40.79477.7E-105-6.45485242-5.859936