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Statistical Analysis of Academic Performance: Correlation, Prediction, and Data Comparison

Analyzes statistical correlations and predictions in academic performance.

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    Statistical Analysis of Academic Performance: Correlation, Prediction, and Data Comparison 1. Correlation, Scatterplots, and Prediction a) Which relationship is stronger, the relationship between GPA and AGE or the relationship between GPA and SAT score? Be sure to include all appropriate measures and explain and defend your answer. Is this result what you would expect, why or why not? Correlation between GPA and AGE 0.233751 Correlation between GPA and SAT score 0.320311 Looking at the co rrelation values we see that the correlation between GPA and SAT is more than GPA and AGE. Hence the relationship between GPA and SAT score is stronger than the relationship between GPA and AGE. The result is as expected as GPA and SAT both being related to scores are more co r related to each other than AGE. b) Create and paste in a scatterplot that compares Final Exam Score and Project Score. What is the correlation (r - value)? How would you describe the correlation (positive, negative, strong, weak, medium, none)? Include the “trendline” and “equation of the trendine” as part of your scatterplot. The correlation (r - value) = sqrt(. 1429 ) = .378 y = 0.2836x + 54.747 R² = 0.1429 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Project score Final exam score

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    The correlation is positive hence project score and final score both have similar behavior, that is both of them increases or decreases together. But the strength of the relationship bet ween the two is week as t he r - value is close to 0 than 1. c) Using the equation from your above scatterplot trendline, predict (estimate) the Project score for a person who gets a final exam score of 82. Show all of your work. y = 0.2836x + 54.747 So, the project score of a person whose final exam score 82 is y = 0.2836*82 + 54.747 = 78.002 2. Comparing and Describing Data For the Final Exam Score and then for the Project Score, calculate the mean, median, mode, range, standard deviation, and variance. (Hint: remember to use the sample std dev and sample variance). Final exam score Project score Mean 71.23529412 74.94823529 median 74.5 75.855 mode 89 68 range 62 55.66 standard deviation 17.71672523 13.29268572 variance 313.8823529 176.6954938 a) Which two numerical measures offer you the best information for comparing performance between these two assignments? Use these two numerical measures to describe and compare student performance between the final exam and the Project . Mean and standard deviation provides best information for comparing performance between these two assignments. Mean of the two assignments shows that on an average the students have more project scores than final exam scores. Also the variability in scores among different students is more in the final exam scores as compared to the project scores. b) Which variable, Final Exam Score or Project Score has greater variation of data? Which two numerical measures are best to offer this information? Choose the two numerical

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