Question

Many high school students take either the SAT or the ACT. However, some students take both. Data were collected from 60 students who took both college entrance exams. The average SAT score was 912 with a standard deviation of 180. The average ACT score was 21 with a standard deviation of 5. The correlation between the two variables equals 0.817.

What fraction of the variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores?

Answer 1

0.6675

Explanation:

Given that many high school students take either the SAT or the ACT.

However, some students take both.

Data were collected from 60 students who took both college entrance exams.

SAT score ACT score with a of 180.

Average 912 21

standard deviation 180 5

Correlation between the two variables r = 0.817

WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores

So we find square of r

`r^2 =0.817^2\\=0.6675`

i.e. 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores