Question

A least squares regression line was created to predict the Exam 3 score of STA 2023 students based on their Exam 1 score. The study found that the value of R-squared was 28.8% and the least squares regression line was yhat=50.57+0.4845x. What is the correlation coefficient, r?a. 0.54b. -0.54c. 5.37d. -5.37e. 0.08f. -0.08

Answer 1

a) 0.54

Explanation:

The correlation coefficient can be found by taking square root of R-squared value and the sign of correlation coefficient can be assessed by considering the sign of slope value. So,

r²=28.8%=28.8/100=0.288

r=
`\sqrt{r^(2) }`=
`√(0.288)`=0.5367

By rounding to two decimal places the correlation coefficient

r=0.54

We can see that slope=0.4845 has positive sign so, the correlation coefficient contains the positive sign.

Hence the correlation coefficient r=0.54.