Question

5. Calculating the Pearson correlation and the 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 80 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 \(\mathrm{X}\) and the average grades \(Y\). Then, you add up your data values \((\Sigma X\) and \(\Sigma Y)\), add up the squares of your data values \(\left(\Sigma X^{2}\right.\) and \(\left.\Sigma Y^{2}\right)\), and add up the products of your data values ( \(2 \mathrm{XY}\) ). The following table summarizes your results:

Sigma X	380
Sigma Y	5,820
SigmaX^(2)	2,708
Sigma Y2	440,838
Sigma xy	26,709

The sum of squares for average grades is \(\mathrm{SS}_{y}=\)

The sum of products for the total number of absences and average grades is \(\mathrm{SP}=\)

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 \(r^{2}=\) , 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 correlation between the total number of days students attended school and average grades to be

Answer 1