# Scatterplots with regression lines allow a visual picture of correlation where a dot or circle shows a specific point for two variables

## Scatterplots with regression lines allow a visual picture of correlation where a dot or circle shows a specific point for two variables

D6.8.1 Scatterplots and Regression Lines

Scatterplots with regression lines allow a visual picture of correlation where a dot or circle shows a specific point for two variables, with one on the X axis and one on the Y axis. The plot also allows other points to be shown easily for comparison of information along with seeing bivariate outliers, or those points that are further away from the regression line. Although it may be an outlier, if there are several that are away from the majority, it may be that a better fitting line as a curve instead of straight which would violate a linear relationship assumption and instead of Pearson, Spearman or Kendall’s tau-b might be better suited tests (Morgan et al., 2020).

D6.8.2 Correlation

D6.8.2.a Correlation Coefficients

The correlation coefficients help explain statistical significance, but even more valuable the output prints the exact significance level of p which is more specific than simply saying statistically significant or not (Morgan et al., 2020).

To date EEG brain signals, or electroencephalography, which are neurons that connect all human thinking have not been analyzed using Pearson correlation coefficient, PCC, even though it is one of the most widely used and accepted measure of relationships between random variables and relationships between signals (Šverko et al., 2022). When utilizing PCC side by side with other measures being used, it turned out that PCC was the same or more accurate in measuring the data being studied and scatterplots made it even more real and useful for researchers (Šverko et al., 2022).

D6.8.2.b r2 for Pearson correlation and Meaning

The suggests about 10 percent of the “variance in math achievement test scores can be predicted from mother’s education (Morgan et al., 2020).

D6.8.2.c Compare Pearson and Spearman

The Pearson correlation is r(73) = .34, p = .003, although the number of participants is 75 the degrees of freedom is applied which is N – 2. The Spearman correlation is (73) = .32, p = .006. Many times, Pearson and Spearman have a similar significance level as they do in the book for this case (Morgan et al., 2020).

D6.8.2.d When to Use a Specific Type

With the example provided both Pearson’s and Spearman’s should not be reported, selecting one with assumptions that best fit the data is imperative and would be Spearman because the mother’s education was very skewed (Morgan et al., 2020).

The medical research industry uses correlations as a standard and that is no different in the ophthalmology field, however, often results are reported incorrectly or use of the incorrect correlation is used (Alsaqr, 2021). Between Pearson’s and Spearman’s researchers concluded that “the most crucial factors affecting thechoice of an appropriate test include data type, linearity ofrelationship, presence of outliers and violation of parametricassumptions” (Alsaqr, 2021).

D6.8.5 Standardized Regression Weights and/orCoefficients

Standardized coefficients allow comparison of the amount that each variable contributes to predicting a dependent variable when all variables are used as predictors. Standardizing the coefficient puts all predictors on the same scale, so they can be compared. When predictors significantly combine together, they can predict the dependent variable. It is also valuable to note that unstandardized coefficients are better to use for predicting the dependent variable from the predictor scores (Morgan et al., 2022).

References

Alsaqr, A. M. (2021). Remarks on the use of Pearson’s and Spearman’s correlation coefficients in assessing relationships in ophthalmic data. African Vision and Eye Health, 80(1), 1-10. https://doi.org/10.4102/aveh.v80i1.612

Morgan, L., Leech, N., Gloeckner, G., & Barrett, K. (2020). IBM SPSS for introductory statistics. Routledge.

Šverko, Z., Vrankić, M., Vlahinić, S., & Rogelj, P. (2022). Complex pearson correlation coefficient for EEG connectivity analysis. Sensors, 22(4), 1-19. https://doi.org/10.3390/s22041477

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