PaulKuneshAssignmentChapter8.docx

Chapter 8 Quantitative Analysis: Correlation and Regression

Paul Kunesh

School of Business, Liberty University

BUSI820: Quantitative Research Methods (D04)

Dr. David Danley

November 30, 2025

Author Note

Paul Kunesh

I have no known conflict of interest to disclose.

8.2 Correlational Analysis...............................................................................................................4

8.3 Correlation Matrix.....................................................................................................................6

8.4 Gender at Birth and Same Sex Parent’s Height.........................................................................8

References......................................................................................................................................11

As indicated by Figure 1 the same sex parent’s mean height was 66.78 with a standard

deviation of 5.10. Additionally, the student’s mean height was 67.3 with a standard deviation of

3.94. The Pearson correlation between student height and parent height was r = .842 as listed in

Figure 2. This indicates a strong positive relationship, meaning that higher parent height is

associated with higher student height. Given the sample size N = 50, an r of .842 is statistically

significant at p < .001. This shows that the likelihood of observing such a strong correlation by

chance is extremely low. For effect size, Morgan et al. (2020) classify correlations around .10 as

small, .30 as moderate, and .50 or higher as large. Therefore, r = .842 represents a large effect

size, demonstrating a substantial and meaningful association between the two variables.

The scatterplot shown in Figure 4 shows a clear upward linear pattern, indicating that as

parent height increases, student height also tends to increase. The points are relatively tight and

closely clustered around an implied straight line, which visually reflects a strong linear

relationship consistent with the calculated correlation of r = .842. There are no major outliers that

break the pattern. While there is some natural variability in the data that parents around 65 inches

are producing children between roughly 62–70 inches, the overall trend remains highly

consistent. The data points spread more vertically in the midrange heights, but the relationship

remains linear and strong across the entire scale. The scatterplot does not show any curvature or

across different parent height levels which is a condition Morgan et al. (2020) note as important

when interpreting correlations. The results of the scatterplot provide strong visual evidence that

Is there a relationship between the number of hours students work per week and their current

GPA?

Both variables listed above in the question, weekly work hours and GPA, are scale

variables and approximately normal, making them appropriate for correlational analysis. To

answer the proposed question a Pearson correlation was computed using data from 49 students.

The descriptive statistics show that students work an average of 26.12 hours per week, with a

standard deviation of 14.86, and have an average GPA of 3.18 with a standard deviation of .39.

The correlation between hours worked and GPA was r = .303, with a significance level of p

there is a genuine relationship between the two variables rather than a random fluctuation. The

correlation of .303 indicates a small-to-moderate effect, meaning that students who work more

hours tend to have slightly higher GPAs. Although the effect is not large, it is still meaningful.

As Morgan et al. (2020) explain, correlations of this size reflect a real but modest association,

reminding us that many other factors also play a role in shaping GPA. Spearman’s RHO was

included but not needed since this analysis aligns with the assumptions for Pearson’s r, making

Pearson’s the preferred and most informative statistic for these variables.

Q. 8.3 Make a correlation matrix using at least four appropriate variables. Identify, using the

< .001 and the negative relationship between TV watched and hours studied r = –.358, p = .011.

These results indicate that students who watch more TV tend to work more hours and study

fewer hours, patterns that Morgan et al. (2020) note are typical of moderate correlations that

represent meaningful, systematic associations. In contrast, the weakest correlations were between

hours studied and GPA r = .114, p = .436 and between hours studied and hours worked r = .219,

p = .131, both of which were small and nonsignificant. As Morgan et al. (2020) explain, such

low r values reflect trivial linear relationships, suggesting that these variables do not

meaningfully predict one another. The matrix clearly shows that only the correlations involving

TV viewing were strong enough to be considered meaningful, while the others showed minimal

amount of variance in student height. The model fit indices R = .815, R square = .664, adjusted

Rsquare = .650 show that about 66% of the variability in student height is accounted for by

gender at birth and the height of the same-sex parent, which Morgan et al. (2020) describe as a

strong predictive relationship. Both Betas -.425 and predictors, same-sex parent height B =

–.042, p = .009 and gender at birth p < .001 were individually significant and each contributed

meaningfully to the model. The findings clearly indicate that gender at birth and same-sex parent

height together form a statistically significant and meaningful predictor set for student height,

consistent with the regression interpretation guidelines outlined by Morgan et al. (2020).