Correlation and Regression Analysis

Data analysis: Correlation and Regression
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Course
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Data Analysis: Hypothesis Testing
Hypothesis testing is a type of inferential statistics that helps a researcher make conclusions about a population using sample data. This technique tests a claim about a population parameter based on representative sample data (Emmert-Streib & Dehmer, 2019). This project used the Sun Coast Remediation dataset to carry out correlation, simple regression, and multiple regression hypothesis testing to test relationships between variables. The analysis was carried out using the data analysis Toolpak in Excel.
Correlation: Hypothesis Testing
Correlation is used to test associations between two variables. This project conducted correlation analysis to establish the relationship between employees’ health and particulate matter size. The data used was from one hundred and three job sites. The hypotheses were formulated as follows:
H01: There is no statistically significant relationship between mean sick days among the employees and the number of microns
Ha1: There is a statistically significant relationship between mean sick days among the employees and the number of microns
The table below shows the results of the analysis from Excel
 

Microns

Mean Annual sick days

Microns

1


Mean Annual sick days

-0.715984185

1

Table SEQ Table \* ARABIC 1: Correlation Table
SUMMARY OUTPUT








Regression Statistics






Multiple R

0.71598






R Square

0.51263






Adjusted R Square

0.50781






Standard Error

1.32778






Observations

103













ANOVA







 

df

SS

MS

F

Significance F


Regression

1

187.29532

187.29532

106.23618

1.891E-17


Residual

101

178.06390

1.76301




Total

102

365.35922

 

 

 









 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

10.0814

0.31516

31.98865

1.169E-54

9.45626

10.70663

microns

-0.5224

0.05068

-10.30709

1.891E-17

-0.62291

-0.42184

Table SEQ Table \* ARABIC 2: Regression Table
Table 1 above shows a Pearson correlation coefficient of r = -0.7160. This indicates a strong negative correlation between the two variables: a decrease in the size of the microns of particulate matter increases the mean sick days. This equates to an r2 of 0.5126, explaining 51.26% of the variance between the two variables. The results indicate a p-value of 1.169 x 10-54, which is less than the alpha level of 0.05. Therefore, the null hypothesis is rejected, and the alternative hypothesis that there is a statistically significant relationship between mean annual sick days and the size of microns of particulate matter.
Simple Regression: Hypothesis Testing
A simple regression model uses a straight line to describe the relationship between two continuous variables. This analysis aims to predict a single dependent variable based on one independent variable (Darlington & Hayes, 2017). This project conducted a simple regression analysis to establish the relationship between safety training expenses and lost time hours. The data used was from two hundred and twenty-three contracts. The hypotheses were formulated as follows:
H02: There is no statistically significant relationship to predict lost time hours from safety training expenses.
Ha2: There is a statistically significant relationship to predict lost time hours from safety training expenses.
The table below shows the results of the analysis from Excel
SUMMARY OUTPUT













Regression Statistics






Multiple R

0.93956






R Square

0.88277






Adjusted R Square

0.88224






Standard Error

24.61329






Observations

223













ANOVA







 

df

SS

MS

F

Significance F


Regression

1

1008202.11

1008202

1664.211

7.7E-105

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