Research Methods, Final Project?

Data Analysis: Hypothesis Testing

Sun Coast Remediation data set was used to conduct a correlation analysis, simple regression analysis, and multiple regression analysis.

Correlation: Hypothesis Testing

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

Analysis showed that the Pearson correlation r = -.716 implying a strong negative relationship between the variables. The R2 = .51 indicates that 51% variation in microns is explained by the mean annual sick days per employee.

An alpha level of .05 was used in this case and the p value according to the results was < .01 which implies we reject the null hypothesis and conclude that there is a statistically significant relationship between microns and mean annual sick days per employee.

Simple Regression: Hypothesis Testing

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

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

Analysis showed that multiple r = .94 which implies a very strong relationship between lost time hours and safety training expenditure. The R2= .88 which indicates that 88% variation in safety training expenditure was explained by lost time.

Alpha level was set at .05. Analysis showed that F (1, 221) = 1664.21, p< 0.01 which indicates we reject the null hypothesis and conclude that there was a significant relationship between lost time hours and safety training expenditure. The coefficient of lost time was statistically significant since b = -6.157, t (221) = -40.79, p< .001 (Warner, 2020). The regression equation will be given as;

Safety training expenditure = 1753.60 – 6.157 * lost time hours

This implies that there was a constant expenditure of 1753.60 when holding other factors constant. An increase in lost time by an hour, decreases safety training expenditure by $6.157 holding other factors constant.

Multiple Regression: Hypothesis Testing

Ho3:There is no significant relationship between angle in degrees, chord length, velocity, displacement, decibels and frequency.

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

The results showed that r = .584 indicating a moderate strong positive relationship between the variables. The R2 = .34 implying that only 34% variation in frequency was explained by the explanatory variables.

Analysis showed that the model was statistically significant at .05 level of significance since F (5, 1497) = 154.73, p< 0.01 indicating we reject the null hypothesis and conclude that there is a significant relationship between angle in degrees, chord length, velocity, displacement, decibels and frequency. All independent variables’ coefficients were statistically significant except for chord length (b = -741.556, t (1497) = -0.545, p = .59). The coefficients were as given; angle in degrees (b = -86.46, t (1497) = -5.03, p< .01), velocity (b = 42.06, t (1497) = 9.78, p< .01), displacement (b = -65093.4, t (1497) = -8.11, p< .01) and decibel (b = -241.11, t (1497) = -23.49, p< .01).

The multiple regression equation becomes;

Frequency = 32243.94 – 86.46*Angle in degrees – 741.556*chord length + 42.06*Velocity – 65093.4*Displacement – 241.11*Decibel

This implies there was a constant frequency of 32243.94 holding other factors constant. An increase in angle by a degree decreases frequency by 86.46 Hz holding other factors constant. An increase in chord length decreases frequency by 741.556 Hz holding other factors constant. An increase in velocity by 1 m/s increases frequency by 42.06 Hz holding other factors constant. Increasing displacement by a unit decreases frequency by 65093.4 HZ while other factors are held constant. An increase in decibel by a unit, decreases frequency by 241.11 Hz holding other factors constant.

References

Warner, R. M. (2020). Applied statistics I: Basic bivariate techniques. Sage Publications.