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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5. Calculating the Pearson correlation and coefficient of determination

Suppose you are interested in seeing whether the total number of days students are absent from high school correlates with their grades. You obtain school records that list the total absences and average grades (on a percentage scale) for 100 graduating seniors.

You decide to use the computational formula to calculate the Pearson correlation between the total number of absences and average grades. To do so, you call the total number of absences X and the average grades Y. Then, you add up your data values (ΣX and ΣY), add up the squares of your data values (ΣX² and ΣY²), and add up the products of your data values (ΣXY). The following table summarizes your results:

ΣX	460
ΣY	8,060
ΣX²	3,446
ΣY²	659,226
ΣXY	36,477

The sum of squares for the total number of absences is SSxx = .

The sum of squares for average grades is SSyy = .

The sum of products for the total number of absences and average grades is SP = .

The Pearson correlation coefficient is r = .

Suppose you want to predict average grades from the total number of absences among students. The coefficient of determination is r² = , indicating that of the variability in the average grades can be explained by the relationship between the average grades and the total number of absences.

When doing your analysis, suppose that, in addition to having data for the total number of absences for these students, you have data for the total number of days students attended school. You’d expect the correlation between the total number of days students attended school and the total number of absences to be and the correlation between the total number of days students attended school and average grades to be ..

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