Question

If there is a .20 correlation between SAT scores and high school GPA, SAT scores account for _____ % of the fluctuation in GPA

Answer 1

SAT scores account for 4 % of the fluctuation in GPA

Explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

The determinarion coefficient represent "the proportion of the variance in the dependent variable that is predictable or explained from the independent variable".

And is just defined as
`r^2`

Solution to the problem

The % of variation is given by the determination coefficient given by
`r^2` and on this case
`0.2^2 =0.04`, so then the % of variation explained by the linear model is 4%.

And we can conclude that: SAT scores account for 4 % of the fluctuation in GPA