Question

A study among first-year students at a state university showed that in general students who skipped more classes earned lower grades. Number of classes skipped explained 36% of the variation in grade index among the students. What is the numerical value of the correlation between number of classes skipped and grade index?

Answer 1

The numerical value of the correlation between number of classes skipped and grade index is 0.60.

Explanation:

In statistics R² is a measure that is used to determine the proportion of variation in the dependent variable that can be explained by the independent variable. The value of R² is compute by squaring the correlation coefficient (r) between the dependent and independent variable.

`R^(2)=(r)^(2)`

In this case the dependent variable is the grades and the independent variable is the number of classes skipped.

The R² between the grades and the number of classes skipped is 36% or 0.36.

Compute the value of r as follows:

`R^(2)=(r)^(2)\\r=\sqrt{R^(2)}\\ =√(0.36) \\=\pm0.60`

Thus, the correlation between number of classes skipped and grade index is ±0.60.