Understanding Correlation and Regression: A Comprehensive Guide

1 Discussion replies: Correlation and Regression Student’s Name Institutional Affiliation Date

2 1. Laura As stated by Gillan (2020) scatterplots play various roles. To begin with, they are useful in the visualization of relationships between two variables. It therefore makes it easy for the analysist to identify patterns, and trends. One can also easily identify outliers. Scatterplots also makes it easy to identify whether the relationship is positive, negative, or whether there is no correlation. On the other hand, the regression lines, offers a mathematical summary of the relationship between variables by offering the central trend. moreover, the regression line makes it easy to have a quantifiable measure of the change of a specific variable due to the change of the other unit. I therefore agree with your sentiments that regression lines make it easy to identify the y and x values. According to Schober et al. (2018), correlation coefficients evaluate the linear relationship, strength, and direction, between two variables. If the correlation coefficient is near +1, then the relationship is strong and positive. Where the correlation coefficient is near -1, then the relationship is strong but negative. Where the coefficient is near zero, then the relationship is weak or nonexistent. I also agree with you that the r2 for the Pearson correlation indicates that there exists a linear relationship between the variables. Where the mother has a high education level, then their math’s score is higher. Standardized regression weights are also called standardized beta coefficients (Van Ginkel, 2020). The standardized regression weights enable the evaluation of the predictive power of the independent variable on the outcomes of the dependent variable. Reference

3 Gillan, D. J. (2020). Fitting regression lines to scatterplots: The role of Perceptual Heuristics. Proceedings of the Human Factors and Ergonomics Society Annual Meeting , 64 (1), 1650–1654. https://doi.org/10.1177/1071181320641401 Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation Coefficients: appropriate use and interpretation. Anesthesia & Analgesia , 126 (5), 1763–1768. https://doi.org/10.1213/ane.0000000000002864 Van Ginkel, J. R. (2020). Standardized regression coefficients and newly proposed estimators for $${R}^{{2}}$$ in multiply imputed data. Psychometrika , 85 (1), 185–205. https://doi.org/10.1007/s11336-020-09696-4 2. Robert Scatterplots perform a number of functions. To begin with, they enable the visualization of the data being presented. One can thus identify the patterns and trends easily. Scatterplots also makes it very easy to identify the outliers (Gillan, 2020). Moreover, due to the visualization, one can easily identify the nature of the relationship between variables in a scatterplot. It is easy to tell whether the relationship positive, negative, or whether there exists a relationship at all. I agree with you that one can determine the correlation between variables by using the regression line. I would also like to add that it also makes it possible to determine the change of specific variables due to the change of the other variables. The spearman’s rho is defined as “a rank correlation coefficient that measures the correlation between two variables based on their corresponding ranks” (Yu & Hutson, 2022). I agree with you that the null hypothesis should be rejected due to the Pearson correlation coefficient of 0.34 and a sig of 0.003 which is smaller than the p-value of 0.05. The spearman’s rho indicates that there exists a positive correlation between the variables. I also agree with your

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

4 conclusion that the r2 score predicts an 11% variance in the prediction of the two variables. Finally, as stated by Van Ginkel (2020), standard regression weights, also known as standard beta coefficients, are used in the evaluation of the predictive power of independent variables regarding the outcome of the dependent variables. They are also useful in comparing different predictors within models and even across different studies. Reference Gillan, D. J. (2020). Fitting regression lines to scatterplots: The role of Perceptual Heuristics. Proceedings of the Human Factors and Ergonomics Society Annual Meeting , 64 (1), 1650–1654. https://doi.org/10.1177/1071181320641401 Van Ginkel, J. R. (2020). Standardized regression coefficients and newly proposed estimators for $${R}^{{2}}$$ in multiply imputed data. Psychometrika , 85 (1), 185–205. https://doi.org/10.1007/s11336-020-09696-4 Yu, H., & Hutson, A. D. (2022). A robust Spearman correlation coefficient permutation test. Communications in Statistics - Theory and Methods , 1–13. https://doi.org/10.1080/03610926.2022.2121144 3. Yanitza While I agree with you that the scatterplot is useful in visualizing the association between two variables, I disagree with your statement that it “allows us to see is a Pearson correlation would be the better option”. As opined by Gillan (2020), the scatterplot is used to visualize relationships between variables, identify the type of relationships, enable the identification of outliers, and can also be used for group comparison if different variables can be colored using different colors. In such cases, scatterplots can be used to visualize the difference between variables across different groups. However, since they are mainly used for visualization, they

5 may not offer accurate quantifiable measurements. Regression lines on the other hand, can be used for trend estimation, predictive analysis and even quantifying relationships. I agree with your deductions that the significance is 0.003 from the Pearson correlation coefficient of 0.34. since the p-value is 0.05, and hence the significance value is lower, then the null hypothesis is rejected. The r2, is also known as the coefficient of determination as it evaluates the degree of variation in the dependent variable caused by the independent variable as indicated in a linear regression model. The r2 in this case indicates an 11% variance between the two variables. It also shows that there is a linear relationship between the variables. I would also like to add that The standardized regression weights enable the evaluation of the predictive power of the independent variable on the outcomes of the dependent variable (Van Ginkel, 2020). Reference Gillan, D. J. (2020). Fitting regression lines to scatterplots: The role of Perceptual Heuristics. Proceedings of the Human Factors and Ergonomics Society Annual Meeting , 64 (1), 1650–1654. https://doi.org/10.1177/1071181320641401 Van Ginkel, J. R. (2020). Standardized regression coefficients and newly proposed estimators for $${R}^{{2}}$$ in multiply imputed data. Psychometrika , 85 (1), 185–205. https://doi.org/10.1007/s11336-020-09696-4

6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

answer_1 (2)

Related Documents