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

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Statistical Analysis of Academic Performance: Correlation, Prediction, and DataComparison1.Correlation, Scatterplots, and Predictiona)Which relationship is stronger, the relationship between GPA and AGE or therelationship between GPA and SAT score? Be sure to include all appropriate measuresand explain and defend your answer. Is this result what you would expect, why or whynot?Correlation between GPA and AGE0.233751Correlation between GPA and SATscore0.320311Looking at the correlation values we see that the correlation between GPA and SAT is more thanGPA and AGE. Hencethe relationship between GPA and SAT score is stronger than therelationship between GPA and AGE.The result is as expected as GPA and SAT both being relatedto scores are more correlated to eachother 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 thetrendine” as part of your scatterplot.The correlation (r-value) = sqrt(.1429) = .378y = 0.2836x + 54.747R² = 0.1429020406080100120020406080100120Project scoreFinal exam score

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The correlation is positive hence project score and final score both have similarbehavior, that is both of them increases or decreases together. But the strength of therelationship between the two isweek as the r-value is close to 0 than 1.c)Using the equation from your above scatterplot trendline, predict (estimate) theProjectscore for a person who gets a final exam score of 82. Show all of your work.y = 0.2836x + 54.747So, the project score of a person whose final exam score 82 isy = 0.2836*82+ 54.747= 78.0022.Comparing and Describing DataFor 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 devand sample variance).Final examscoreProjectscoreMean71.2352941274.94823529median74.575.855mode8968range6255.66standarddeviation17.7167252313.29268572variance313.8823529176.6954938a)Which two numerical measuresofferyou the best information for comparingperformance between these two assignments? Use these two numerical measures todescribe and compare student performance between the final exam and theProject.Mean and standard deviation provides best information for comparing performance betweenthese two assignments. Mean of the two assignments shows that on an average the studentshave more project scores than final exam scores. Also the variability in scores among differentstudents is more inthe final exam scores as compared to the project scores.b)Which variable, Final Exam Score or Project Score has greater variation of data? Whichtwo numerical measures are best to offer this information? Choose the two numerical

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