MALIK_BUSI820_Assignment6

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Southern New Hampshire University *

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Feb 20, 2024

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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 What is the correlation between student’s height and parent’s height? Also produce a scatterplot. Interpret the results, including statistical significance, direction, and effect size. Figure 1 Descriptive Statistics Mean Std. Deviation N student height in inches 67.3000 3.93959 50 same sex parent's height 66.7800 5.10418 50 Correlations student height in inches same sex parent's height student height in inches Pearson Correlation 1 .842 ** Sig. (2-tailed) <.001 N 50 50 same sex parent's height Pearson Correlation .842 ** 1 Sig. (2-tailed) <.001 N 50 50 **. Correlation is significant at the 0.01 level (2-tailed). Figure 2 3
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
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