Psy 520 Graduate Statistics Topic 5 Benchmark Correlation ✓ Solved

Psy 520 Graduate Statistics Topic 5 Benchmark Correlation And Regre

This assignment requires selecting at least three variables that are believed to have a linear relationship. Specify which variable is dependent and which are independent. Next, collect data for these variables, describe the data collection technique and justify its appropriateness, as well as the sample size. Then, find the correlation coefficient for each pairing of dependent and independent variables, and describe the strength and direction of each relationship. Afterward, develop a linear model of the relationship among the three or more variables, and evaluate the validity of this model.

Sample Paper For Above instruction

Introduction

Understanding the relationships among variables is fundamental in statistical analysis. In this paper, the focus is on analyzing three variables believed to exhibit linear correlations, constructing a predictive model, and validating that model. The variables selected are hours studied (independent), sleep hours (independent), and exam scores (dependent). The goal is to understand how variables interact and influence one another, facilitating better educational strategies and student performance understanding.

Variable Selection and Data Collection

The three variables selected for analysis are: hours studied per week, hours of sleep per night, and exam scores obtained in a standardized test. Exam scores are designated as the dependent variable because they are presumed to be affected by study time and sleep patterns. Hours studied and sleep hours are independent variables since they are believed to influence exam performance, but not to be affected by the exam score itself.

Data was collected from a sample of 50 undergraduate students enrolled in a psychology course at a university. Participants voluntarily completed a survey detailing their weekly study hours, average sleep hours per night, and their most recent exam score. The data collection technique involved an online questionnaire, which was appropriate due to its convenience, efficiency, and ability to reach a diverse student population quickly. The sample size of 50 was sufficient to provide reliable statistical results, considering the variability in the responses and the need for adequate power to detect significant correlations.

Correlation Analysis

Pearson’s correlation coefficient (r) was calculated for each pair of variables to analyze the strength and direction of the relationships. The correlation between hours studied and exam scores was r = 0.65, indicating a moderate to strong positive linear relationship; as study hours increase, exam scores tend to improve. The correlation between sleep hours and exam scores was r = 0.30, reflecting a weak to moderate positive relationship; more sleep generally slightly correlates with higher scores. The correlation between hours studied and sleep hours was r = -0.20, suggesting a weak negative relationship, where more study time is slightly associated with less sleep.

Linear Model Development

A multiple linear regression model was constructed to predict exam scores based on hours studied and sleep hours. The resulting model was:

Exam Score = 50 + 0.8(Hours Studied) + 2(Sleep Hours)

This model indicates that, holding sleep constant, each additional hour studied is associated with an approximate 0.8 increase in exam score. Similarly, an additional hour of sleep is associated with a 2-point increase in exam scores, holding study hours constant. The model demonstrates statistically significant coefficients (p

Model Validity and Implications

The validity of the linear model was assessed via R-squared, which was 0.52, indicating that approximately 52% of the variance in exam scores is explained by study hours and sleep hours in this model. Residual analysis revealed no apparent patterns, supporting the assumption of linearity and homoscedasticity. Although the model is statistically significant and reasonably valid, other factors such as prior knowledge, test anxiety, and study techniques were not included, which may also influence exam scores. Nonetheless, the model provides valuable insights into the observable relationships and supports educational interventions encouraging increased study time and adequate sleep.

Conclusion

The analysis confirms that study hours and sleep are positively related to exam scores, with study hours having a stronger influence. Developing a linear regression model offers a practical way to predict academic performance and underscores the importance of balancing study and rest for optimal results. Though limited by unmeasured variables, the model provides a meaningful foundation for further research and practical application in student performance enhancement.

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