MALIK_BUSI820_Assignment6

School of Business, Liberty University Faizan Malik Quantitative Analysis- Correlation and Regression Assignment Author Note: Faizan Malik I have no known conflict of interest to disclose. Correspondence concerning this article should be addressed to Faizan Malik: Fmalik@Liberty.edu

BUSI820 Assignment 6 Table of Contents Quantitative Analysis- Correlation and Regression 3 Pearson Correlation Coefficient (r) and Coefficient of Determination (r 2 ) 3 Spearman’s correlation (p) 5 Correlation Matrix 7 F-Value and Standardized Coefficients8 References 10 2

BUSI820 Assignment 6 8.1.a. As explained by Sedgwick (2012), the Pearson correlation coefficient or r value is a measure of the strength of the linear relationship between two variables, with a value of - 1 indicating a perfect negative correlation, a value of 0 indicating no correlation, and a value of 1 indicating a perfect positive correlation (Sedgwick, 2012). As demonstrated in Figure 1, the study of student height and same-sex parent's height yielded a r value, or Pearson coefficient of 0.842, for both combinations of variables, based on a sample size of 50 students and their respective parents. When coupled with a p-value for the correlation is less than 0.001 (p < 0.001), this indicates a strong positive correlation between student height and the height of their same-sex parent. In essence, taller parents tend to have taller children and vice versa, something that is not likely to occur by chance alone. In the study, an R-squared value of 0.708 was obtained. R-squared, also known as the coefficient of determination, is a statistical measure that represents the proportion of the variance in the dependent variable (student height in this case) that is predictable from the independent variable (same-sex parent's height) (Kasuya, 2019). It is a measure of how well the independent variable explains the variability in the dependent variable. Figure 2 demonstrates an R-squared value of 0.708. This indicates that approximately 70.8% of the variance in student height can be explained by their same-sex parent's height but variables, such as genetics, nutrition, and environmental factors, may also play a role in determining a student's height. 4

BUSI820 Assignment 6 8.2 Write a question that can be answered via correlational analysis with two approximately normal or scale variables. Run the appropriate statistics to answer the question. Interpret the results. Figure 3 Correlations age group student's current gpa age group Pearson Correlation 1 .605 ** Sig. (2-tailed) <.001 N 50 50 student's current gpa Pearson Correlation .605 ** 1 Sig. (2-tailed) <.001 N 50 50 Figure 4 Correlations age group student's current gpa Spearman's rho age group Correlation Coefficient 1.000 .617 ** Sig. (2-tailed) . <.001 N 50 50 student's current gpa Correlation Coefficient .617 ** 1.000 Sig. (2-tailed) <.001 . N 50 50 **. Correlation is significant at the 0.01 level (2-tailed). Figure 5 5

BUSI820 Assignment 6 8.3 Make a correlation matrix using at least four appropriate variables. Identify, using the variable names, the two strongest and two weakest correlations. What were the r and p values for each correlation? Figure 6 age group student's current gpa student height in inches same sex parent's height age group Pearson Correlation 1 .605 ** -.157 -.111 Sig. (2-tailed) <.001 .277 .442 N 50 50 50 50 student's current gpa Pearson Correlation .605 ** 1 -.212 -.134 Sig. (2-tailed) <.001 .140 .353 N 50 50 50 50 student height in inches Pearson Correlation -.157 -.212 1 .842 ** Sig. (2-tailed) .277 .140 <.001 N 50 50 50 50 same sex parent's height Pearson Correlation -.111 -.134 .842 ** 1 Sig. (2-tailed) .442 .353 <.001 N 50 50 50 50 **. Correlation is significant at the 0.01 level (2-tailed). 8.3.1.a. Based on the results in Figure 4, the strongest correlations are between a student’s height in inches and their respect same-sex parent's height (r = 0. 842 and a p-value = <0.001), and a student’s current GPA and their respective age group (r = 0.605 and a p- value = <0.001). The weakest correlations are carried by a student's height in inches (r = - 0.157 and a p-value = 0.277), a student's current GPA, and their same-sex parent's height (r = -0.134 and a p-value = 0.353). 7

BUSI820 Assignment 6 8.4 Is there a combination of gender at birth and same-sex parent’s height that significantly predicts student’s height? Figure 7 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .865 a .748 .737 2.01962 a. Predictors: (Constant), sex at birth, same sex parent's height Figure 8 ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 568.794 2 284.397 69.725 <.001 b Residual 191.706 47 4.079 Total 760.500 49 a. Dependent Variable: student height in inches b. Predictors: (Constant), sex at birth, same sex parent's height Figure 9 Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 40.466 7.176 5.639 <.001 same sex parent's height .457 .091 .592 5.038 <.001 sex at birth -2.491 .917 -.319 -2.715 .009 a. Dependent Variable: student height in inches 8

BUSI820 Assignment 6 References Bring, J. (1994). How to standardize regression coefficients.  The American Statistician ,  48 (3), 209-213. Hauke, J., & Kossowski, T. (2011). Comparison of values of Pearson's and Spearman's correlation coefficients on the same sets of data.  Quaestiones geographicae ,  30 (2), 87-93. Herzog, M. H., Francis, G., Clarke, A., Herzog, M. H., Francis, G., & Clarke, A. (2019). Anova.  Understanding Statistics and Experimental Design: How to Not Lie with Statistics , 67-82. Kasuya, E. (2019).  On the use of r and r squared in correlation and regression (Vol. 34, No. 1, pp. 235-236). Hoboken, USA: John Wiley & Sons, Inc. Sedgwick, P. (2012). Pearson’s correlation coefficient.  Bmj ,  345 . 10