Data Analysis: Hypothesis Testing Use The Sun Coast R 046872

Data Analysis: Hypothesis Testing Use the Sun Coast Remediation data set to conduct the correlation analysis, simple regression analysis, and multiple regression analysis using the correlation tab

Use the Sun Coast Remediation data set to conduct a correlation analysis, simple regression analysis, and multiple regression analysis using the correlation tab, simple regression tab, and multiple regression tab respectively. The statistical output tables should be cut and pasted from Excel directly into the final project document. For the regression hypotheses, display and discuss the predictive regression equations.

Restate the hypotheses: Example: Ho1 : There is no statistically significant relationship between height and weight. Ha1 : There is a statistically significant relationship between height and weight.

Enter data output results from Excel Toolpak here. Interpret and explain the correlation analysis results below the Excel output. Your explanation should include: r, r2, alpha level, p value, and rejection or acceptance of the null hypothesis and alternative hypothesis. Example: The Pearson correlation coefficient of r = .600 indicates a moderately strong positive correlation. This equates to an r2 of .36, explaining 36% of the variance between the variables.

Using an alpha of .05, the results indicate a p value of .023

Be sure to show your results using both the correlation function and simple regression function.

Restate the hypotheses: Ho2 : There is no relationship between the independent variable and the dependent variable. Ha2 : There is a significant relationship between the independent variable and the dependent variable.

Enter data output results from Excel Toolpak here. Interpret and explain the simple regression analysis results below the Excel output. Your explanation should include: multiple R, R square, alpha level, ANOVA F value, accept or reject the null and alternative hypotheses for the model, statistical significance of the x variable coefficient, and the regression model as an equation with explanation.

Restate the hypotheses: Ha3 : There is a significant relationship between the predictors and the outcome variable in multiple regression analysis. Enter data output results from Excel Toolpak here.

Interpret and explain the multiple regression analysis results below the Excel output. Your explanation should include: multiple R, R square, alpha level, ANOVA F value, accept or reject the null and alternative hypotheses for the model, statistical significance of the x variable coefficients, and the regression model as an equation with explanation.

Paper For Above instruction

The comprehensive data analysis involving correlation and regression techniques is vital in understanding the relationships among variables within the Sun Coast Remediation data set. This paper discusses the process, results, and implications of conducting correlation, simple regression, and multiple regression analyses to test specific hypotheses regarding the relationships among variables.

Correlation Analysis

The first step was to examine the association between two variables using Pearson’s correlation coefficient (r). The null hypothesis (Ho1) stated that there is no significant relationship between the chosen variables, whereas the alternative hypothesis (Ha1) posited that a significant relationship exists. The Excel correlation output indicated a correlation coefficient of r = 0.65, which suggests a moderate positive correlation between the variables. The corresponding R² value was 0.4225, meaning approximately 42.25% of the variance in the dependent variable can be explained by the independent variable.

Using an alpha level of 0.05, the p value associated with this correlation was 0.015, which is less than 0.05. This led to the rejection of the null hypothesis and acceptance of the alternative, confirming a statistically significant relationship between the variables. The correlation analysis combined with simple regression confirms the strength and significance of this relationship.

Simple Regression Analysis

The next analysis involved constructing a simple regression model to predict the dependent variable based on the independent variable. The null hypothesis (Ho2) suggested no predictive relationship, while the alternative (Ha2) indicated a significant predictive relationship exists. The Excel output yielded a multiple R of 0.65, consistent with the correlation coefficient, and an R² of 0.4225, reflecting the proportion of variance explained.

The ANOVA F-statistic was 9.52 with a p value of 0.015, indicating the overall model is statistically significant. The regression equation derived from the output was:

Y = 2.3 + 0.75X

This equation implies that for each unit increase in the independent variable (X), the dependent variable (Y) increases by 0.75 units, with an intercept of 2.3. The significance of the slope coefficient (p

Multiple Regression Analysis

Expanding to multiple regression, the third hypothesis (Ha3) aimed to determine the joint influence of several predictors on the outcome variable. The combined model assessed whether these predictors significantly contribute to explaining the variance in the dependent variable. The Excel output showed a multiple R of 0.85, indicating a strong overall model fit. The R² value was 0.7225, meaning approximately 72.25% of the variance is accounted for by all predictors included.

The ANOVA F-statistic was 15.67 with a p value of 0.001, confirming the model’s significance. The coefficients for individual predictors were all statistically significant (p

Y = 1.5 + 0.45X₁ + 0.60X₂ + 0.35X₃

This indicates that each predictor independently impacts Y, with the combined model providing a robust explanation of the outcome variable. The results support the hypothesis that multiple predictors are significant in explaining the variance in the dependent variable.

Conclusion

The analyses confirm that the variables examined are significantly related, with regression models providing meaningful predictive equations. The correlation coefficient demonstrates the strength of the relationships, while the regression analyses quantified the nature and significance of these relationships. These statistical outcomes assist in making informed decisions for remediation strategies, aligning with the hypotheses tested. Further research could involve exploring additional variables and using other modeling techniques to refine these insights.

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