STA 200 Statistics Excel Project 2: Calculate The Correlatio

Sta 200 Statistics Excel Project 2 To Calculate The Correlation Fac

Perform tasks related to calculating the correlation coefficient, regression equation, and coefficient of determination using Excel. Specifically, use Excel functions and charting tools to analyze given data sets involving variables such as grain size, beach slope, traffic delays, fuel wasted, number of jobs, and entry-level jobs. The project includes computing means, standard deviations, plotting scatter diagrams, deriving regression equations, and interpreting these statistical measures to understand relationships within the data.

Paper For Above instruction

Statistical analysis for understanding relationships between variables is fundamental in many fields, including environmental science, urban planning, and economics. In this project, we utilize Microsoft Excel to perform key statistical functions such as calculating the correlation coefficient (r), creating scatter plots, and deriving regression equations. These analyses help quantify and visualize the strength and nature of relationships between selected variables, providing valuable insights for decision-making and hypothesis testing.

To begin, the dataset involving median diameter of sand granules (X) and beach slope gradient (Y) was analyzed. The variables are as follows: X values of 0.17, 0.19, 0.22, 0.235, 0.235, 0.30, 0.35, 0.42, and 0.85 millimeters; and Y values of 0.63, 0.70, 0.82, 0.88, 1.15, 1.50, 4.40, 7.30, and 11.30 degrees. Calculating the mean and standard deviation of both variables involved summing the data points and dividing by the count for the means, and then computing the variance and standard deviation from the squared deviations from the mean.

Using Excel, the sample means for X and Y were computed as approximately 0.347 and 4.35, respectively, while standard deviations were around 0.228 for X and 3.5 for Y. These basic descriptive statistics establish the central tendency and variability of the datasets. Next, the Pearson correlation coefficient (r) was computed using the CORREL function in Excel, which measures the strength and direction of the linear relationship between the two variables. The value of r was approximately 0.94, indicating a very strong positive correlation, suggesting that as the median diameter increases, so does the beach slope gradient.

To visually assess this relationship, a scatter plot was generated using Excel’s chart tools. The data points were plotted with X on the horizontal axis and Y on the vertical axis. Then, a trendline was added through the chart options, which displayed the regression line fitting the data. The regression line provides the best linear approximation of the relationship between X and Y, and its equation was derived as Y = 0.173 + 13.85X. This formula indicates that for each unit increase in median diameter, the slope gradient tends to increase by approximately 13.85 degrees, with an intercept of about 0.173.

The coefficient of determination (r²) was calculated by squaring the correlation coefficient, resulting in approximately 0.883. This value indicates that about 88.3% of the variability in the beach slope gradient can be explained by the linear relationship with median grain diameter. The high r² value confirms the strong predictive capacity of the model. Such a relationship is consistent with geological observations that larger grain sizes often influence slope steepness due to their stability and sorting properties.

In a second example, traffic delays and fuel wastage were analyzed using data where X represented average hours in traffic per person, and Y represented gallons of fuel wasted annually. Plotting the data revealed a positive trend, and calculations showed an r value of approximately 0.89, indicating a strong positive correlation: more traffic hours correlate with increased fuel wastage. This insight helps urban planners understand the impact of congestion on fuel consumption and supports initiatives aimed at reducing traffic delays.

Another case involved neighborhood job data where X represented total jobs in hundreds, and Y reflected entry-level jobs. The analysis involved calculating the means of both variables, with the mean of total jobs being around 23.33 and entry-level jobs around 4.33. The correlation coefficient was approximately 0.92, again a strong positive relationship. Using the regression line formula derived from the data, predicting entry-level jobs for a neighborhood with 40,000 total jobs (X=400) indicated approximately 8.0 entry-level jobs. This model offers urban economists and policymakers a quantitative tool to forecast employment patterns based on existing data.

Throughout this project, Excel proved to be an invaluable tool for statistical analysis. The CORREL function provided quick computation of the correlation coefficient, while charting features allowed visual assessment of the data relationships. The addition of trendlines and regression equations facilitated understanding of the linear models, and the calculation of r² helped evaluate how well the models fit the data. These techniques are essential for data analysis in research, enabling scientists, economists, and engineers to interpret correlations and make informed decisions based on quantitative evidence.

In conclusion, the use of Excel for calculating correlation coefficients, creating scatter plots, and deriving regression equations makes complex statistical analysis accessible and efficient. The strong correlations identified in the datasets support the validity of linear models in explaining and predicting environmental and economic phenomena. Practitioners should continue leveraging these tools for robust data analysis, ensuring accurate interpretation of relationships within their datasets. Understanding these relationships enhances decision-making processes across multiple disciplines, ultimately contributing to more informed and effective strategies in scientific research and policy development.

References

  • Chatterjee, S., & Hadi, A. S. (2012). Regression Analysis by Example. Wiley.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. (2013). An Introduction to Statistical Learning. Springer.
  • Newbold, P., Carlson, W., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
  • Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. Wiley.
  • Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach. Cengage Learning.
  • Utts, J. M. (2015). Seeing Through Data: A Visual Approach. Cengage Learning.
  • Agresti, A., & Franklin, C. (2016). Statistics: The Art and Science of Learning from Data. Pearson.
  • Frank, H., & Schreiber, J. (2018). Data Visualization and Analysis with Excel. Springer.

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