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

          The assumption that correlation and regression statistics are linear is incorrect and must be checked for breaches in its conditions. The display of the scatterplot gives researchers a

visual to see if there are any curves and waves in the data points. The regression line forms a line where its quadratic or cubic bends capture the data precisely (Morgan, et al., 2020). To

readers who are unfamiliar with both forms of display, the scatterplot is noisy andoverwhelming. But the regression line makes outliers most apparent since they fall far outside of most data.

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?

          The correlation coefficients seek out to show if there is a relationship between variables. The table duplicates its findings in a matrix format and anything below the diagonal line of the

correlations table is not to be considered when making conclusions (Morgan et al., 2020). The Pearson correlation for the mothers education is listed as r(73) = .34 with a significance of

p=0.003. The degrees of freedom are placed in parentheses for the Pearson correlation and found by subtracting two from the n-value of 75.

          The spearman rho correlation is stated as r = 0.32 with a significance level of p = 0.006. The rho correlation is found with ranking the scores instead of the raw scores. When

The parameters of the Pearson correlation are disobeyed, it can be said that the scores are ordinal and the data may be skewed (Morgan, et al., 2020). In the output, the mothers

education variable was labeled as skewed making the Spearman rho the best fit.

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?

          The coefficients table in the output displays the contribution of each variable toward anticipating the math achievement variable. Each variable is placed on identical scales for comparison, and all are

considered to make a prediction for the dependent variable. The tables allow researchers to clearly identify which variable serves as the strongest indicator for the dependent variable.

References

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics. New York, NY: Routledge.