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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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