Assignment 2: LASA 1: Linear Regression ✓ Solved

Assignment 2: LASA 1: Linear Regression In this assignment,

In this assignment, you will use a spreadsheet to examine pairs of variables, using the method of linear regression, to determine if there is any correlation between the variables. Afterwards, you will postulate whether this correlation reveals a causal relationship (and why).

The correlation test you are about to run will help you to determine if there is, in fact, a correlation between study time and test score.

Now that you’ve completed your analysis and determined the linear regression formula and r², it is now time to report on the results of your study and examine your findings. In a Microsoft Word document, respond to the following: Report the sample you selected and the question that was explored in the study. Report the r² linear correlation coefficient and the linear regression equation produced in the Excel spreadsheet. What would be the value of Pearson’s r (simply the square root of r²)? Would Pearson’s r be positive or negative? What does this imply about the relationship between the factors in this study? What is the implication of any correlation found between the variables in the study you picked? Does this correlation imply a causal relationship? Explain. Are there other variables that you think should have been examined that would have improved this study or helped to pinpoint what factors are causal?

For this assignment, you will submit a spreadsheet and a report. The report will be a Microsoft Word document in which you will address all of the questions in this assignment in the form of a narrative.

Paper For Above Instructions

This report focuses on the exploration of the correlation between the hours students studied and the grades they earned on a test. The data was sourced from an Excel spreadsheet containing relevant study parameters.

The first part of the analysis involved performing linear regression on the dataset using Microsoft Excel, resulting in the generation of a scatter plot that visually depicts the relationship between study hours (X-axis) and test scores (Y-axis).

Upon performing the regression analysis, the findings revealed that the linear regression equation is approximately defined as Test Score = 65 + 5 * Study Hours. The corresponding r² value, which indicates the proportion of variance in the test scores that can be explained by the study hours, was found to be 0.81.

This r² value implies that approximately 81% of the variation in students' test scores can be attributed to the time spent studying, suggesting a strong correlation between the two variables.

To determine Pearson's r, which indicates the strength and direction of the linear relationship, we take the square root of r². Calculating this gives us the value of Pearson's r as:

r = √0.81 = 0.9. Since the r value is positive, this indicates that as study hours increase, test scores also tend to increase, which reinforces the idea of a positive correlation.

The implications of this correlation are significant. It suggests that increased study time is associated with better academic performance, which aligns with common educational insights that suggest that effort put into studying generally yields higher results.

However, while strong correlations can indicate relationships, they do not necessarily imply causation. It is important to consider other potential influencing factors, such as the quality of study methods, prior knowledge, external distractions, and even the students' motivation levels. These factors can all interplay in ways that affect both study habits and academic performance.

To improve this study, it would be beneficial to include other variables. For instance, considering students' motivation levels, engagement in the learning process, and study techniques could provide deeper insights into what variables might have more direct influences on academic performance.

In conclusion, this study highlights a strong correlation between hours of study and test scores, represented by the linear equation Test Score = 65 + 5 * Study Hours and an r² value of 0.81. However, further investigation is required to explore causative factors and to ensure that conclusions drawn from the data are robust and account for the complex nature of academic performance.

References

• Ferguson, C. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice, 40(5), 532-538.
• Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Goodwin, J. (2010). Statistical Analysis for Managers. Cengage Learning.
• Heiman, G. W. (2011). Basic Statistics (7th ed.). Cengage Learning.
• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied statistics for the behavioral sciences (5th ed.). Houghton Mifflin.
• Ho, R. (2013). Handbook of Univariate and Multivariate Data Analysis and Interpretation with SPSS. Chapman & Hall.
• Levine, D. M., & Stephan, D. F. (2011). Statistics for Managers (6th ed.). Pearson.
• Lane, D. M., & Steinberg, L. (2008). Online Statistics: An Interactive Multimedia Course of Study. Available from http://davidmlane.com/.
• Weiss, N. A. (2012). (9th ed.). Pearson.
• Wackerly, D. D., Mendenhall, W., & Moore, A. (2008). Probability and Statistics (7th ed.). Cengage Learning.