Answer:
SAT scores account for 4 % of the fluctuation in GPA
Step-by-step 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:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
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 [tex]r^2[/tex]
Solution to the problem
The % of variation is given by the determination coefficient given by [tex]r^2[/tex] and on this case [tex]0.2^2 =0.04[/tex], 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
