Data Analysis: The Sun Coast Remediation Data Set ✓ Solved

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Data Analysis: The Sun Coast Remediation Data Set

Data Analysis: Hypothesis Testing In this project, we are going to use the data set: Sun Coast Remediation in Microsoft Excel using the Data Analysis Toolpack to explore the correlation of variables and conduct regression analysis. The results of the analysis will be displayed here directly from Microsoft Excel and the resulting predictive regression equations will be discussed.

Correlation: Hypothesis Testing

Hypotheses: i. Microns versus mean annual sick days per employee Ho1: There is no significant linear relationship/correlation between microns and mean annual sick days per employee. Ha1: There is a significant linear relationship/correlation between microns and mean annual sick days per employee. The Pearson correlation coefficient is r = -0.71598 when rounded to 4 decimal places, indicating a strong negative correlation between the two variables. The value of the coefficient of determination, r² is 0.5126. This means that about 51.26% of the variation between microns and mean annual sick days per employee is explained by the relationship. The p-value is 1.89E-17, which is less than the alpha level of significance (0.05), leading us to reject the null hypothesis.

Simple Regression: Hypothesis Testing

Hypotheses: Ho2: β1 = 0 (The regression is not significant) Ha2: β1 ≠ 0 (The regression is significant) The regression model indicates that Y = 1753.15739*X2, meaning for every additional hour in lost time hours, the safety training expenditure decreases by 6.15739 units. With multiple R of 0.939559 and R square of 0.882772, the model explains 88.2772% of the data variation. The ANOVA F-value is significant with 7.6586E-105, thus rejecting the null hypothesis and affirming the predictive power of the regression analysis.

Multiple Regression: Hypothesis Testing

Hypotheses: Ho3: β1 = β2 = β3 = β4 = β5 = 0 (The regression fit is not significant) Ha3: At least one is different from zero (The regression fit is significant). The model explains only 34.07% of the variability of the response data. The ANOVA significant F-value is 1.2E-132, which suggests a strong rejection of the null hypothesis, indicating significant predictors of frequency from the angles, velocity, displacement, and decibel measurements.

Paper For Above Instructions

The Sun Coast Remediation data analysis project delves into the correlation between various metrics represented in the dataset, specifically focusing on sick days and other factors such as microns, safety training expenditures, lost time, and frequency in relation to different predictors. By employing Excel’s Data Analysis Toolpack, both correlation and regression analyses were conducted to identify significant relationships between the variables.

Correlation Analysis Results

Correlation analysis primarily investigates the relationship between microns and mean annual sick days per employee. The first hypothesis states that there is no significant linear relationship (Ho1), while the alternative posits a significant relationship (Ha1). The coefficient, known as Pearson's r, revealed a value of -0.71598, indicating a substantial negative correlation between the two variables. The associated r² value was found to be 0.5126, meaning that approximately 51.26% of the variations in mean annual sick days can be attributed to fluctuations in microns.

The statistical significance of these findings emphasizes a p-value of 1.89E-17, confirming that the null hypothesis can be discarded. With an alpha level set at 0.05, the evidence strongly upholds the alternative hypothesis, concluding the presence of a significant relationship.

Simple Regression Analysis Results

For the simple regression analysis, the second hypothesis explores the significance of the regression model concerning lost time hours and safety training expenditure. The hypotheses include Ho2: β1 = 0 (the regression is not significant) and Ha2: β1 ≠ 0 (the regression is significant). In this analysis, the regression outputs included a multiple R of 0.939559, suggesting a strong positive correlation between safety training expenditures and lost time hours.

The calculated R squared value of 0.882772 highlights that the regression model effectively accounts for 88.27% of the variability in the data. ANOVA results revealed a significance F value of 7.6586E-105, which is substantially less than the alpha level of 0.05, thereby altogether rejecting the null hypothesis. The alternative hypothesis is accepted, thus affirming the predictive capability of the model. Moreover, the coefficients indicated a direct linear relationship where an increase in lost time hours decreases safety training expenditures.

Multiple Regression Analysis Results

In assessing the multiple regression hypothesis (Ho3: β1 = β2 = β3 = β4 = β5 = 0), it is critical that at least one predictor significantly influences the dependent variable. The regression model’s output showed a moderate relationship with a multiple R value of approximately 0. However, it indicated an R² value of just 34.07%, suggesting only a modest explanation of data variability. Nevertheless, the ANOVA F-value was notably small at 1.2E-132, pointing toward the model's relevancy.

This supports the notion of rejecting Ho3, thus concluding that at least one predictor among Angle in Degrees, Velocity, Displacement, and Decibel has a significant impact. Each of these predictors holds relevance as significant predictors of frequency, while Chord Length was the only variable found insignificant.

Conclusion

The overall findings from the Sun Coast Remediation data set analysis emphasize the intricate connections between the various metrics examined. The rejection of the null hypotheses across correlation and regression analyses delineates statistically significant relationships that are pivotal for organizational decision-making and policy development aimed at enhancing workforce productivity and optimizing safety training expenditures. These analyses not only reveal key metrics about employee productivity related to environmental factors, but they also underscore the importance of strategic data-driven decision-making in remediation initiatives.

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