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?
1.0.54
2.-0.54
3.5.37
4.-5.37
5.0.08
6.-0.08

Answer 1

Answer: Option (1) is the correct answer.

Explanation:

Formula to calculate correlation coefficient is as follows.

           Correlation coefficient = $\sqrt{R^{2}}$

As the slope for given equation is positive so, it means that the correlation will also be positive in nature.

Therefore, we will calculate the value of correlation coefficient as follows.

         Correlation coefficient = $\sqrt{R^{2}}$

                                               = $\sqrt{(0.288)^{2}}$  

                                               = 0.54

Thus, we can conclude that the correlation coefficient, r is 0.54.