Discussion Replies: Correlation and Regression

Discussion Thread: Correlation and Regression

Brian

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D6.8.1 Why would we graph scatterplots and regression lines?

Using regression lines, also known as best-fit lines, on scatterplots helps to reveal the dominant patterns in data, such as the correlation between two variables which can be modeled through linear regression. Scatterplots effectively show the relationship between two variables, making it easier for researchers to quickly spot any patterns like waves or curves in the data. If the data aligns well with quadratic or cubic curves, the regression line will reflect this shape (Morgan et al., 2020). Scatterplots might be challenging and overwhelming for those not familiar with these types of visualizations. However, when these plots include a regression line, outliers become more apparent as they are far from the average (Ciccione & Dehaene, 2021).

D6.8.2 In Output 8.2, (a) What do the correlation coefficients tell us? (b) What is r2 for the Pearson correlation? What does it mean? (c) Compare the Pearson and Spearman correlations on both correlation size and significance level; (d) When should you use which type in this case?

In the section on Correlation Coefficients Explanation from Output 8.2 (a), the Pearson correlation coefficient is described as a commonly used statistical measure to assess the strength and direction of a linear relationship between two variables. A coefficient of -1 signifies a strong negative relationship, while a coefficient of 1 indicates a strong positive relationship. A coefficient near zero suggests a weak or nonexistent linear relationship. Correlation coefficients less than 0.8, whether positive or negative, are generally not considered statistically significant (Schober et al., 2018).

Even though both interpretations are significant, +1 and -1 are not equivalent. For instance, students with high aptitudes often have low grades, while those with good grades frequently exhibit lower aptitudes, as evidenced by a significant negative correlation between these factors. Establishing dependable connections without a correlation is challenging. For instance, a student with higher-than-average intelligence might display below-average academic performance. In this scenario, the variables of math achievement and the mother's level of education are being examined, with Output 8.2 providing detailed information about both. The primary focus is on the tables titled "Correlations" (Morgan et al., 2020).

D6.8.5 In Output 8.5, what do the standardized regression weights or coefficients tell you about the ability of the predictors to predict the dependent variable?

            Estimates of the relationship between two variables, after normalizing the data so that the variances of both dependent and independent variables are equal to 1, are referred to as standardized (regression) coefficients, also known as "beta coefficients" or "beta weights" (Benitez et al., 2020). The researcher can utilize these standardized regression weights or coefficients to assess the significance of each predictor in determining the outcome (in this instance, math achievement in Output 8.5) when all predictors are considered. To more easily determine which predictors have the strongest and weakest connections with the dependent variable, it is advisable to standardize them so they are all measured on the same scale (Morgan et al., 2020).

References

Benitez, J., Henseler, J., Castillo, A., & Schuberth, F. (2020). How to perform and report an

impactful analysis using partial least squares: Guidelines for confirmatory and explanatory IS research. Information & Management ,57 (2), 103168.

Ciccione, L., & Dehaene, S. (2021). Can humans perform mental regression on a graph? Accuracy and bias in the perception of scatterplots. Cognitive Psychology, 128, 101406–01406.

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics Use and Interpretation (6th ed.). New York, NY, USA: Routledge.

Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia and Analgesia, 126 (5), 1763-1768.