the following are the iq scores (x) and the * final grades (y) of the students. which of the following is…
the following are the iq scores (x) and the * final grades (y) of the students. which of the following is the sample correlation of determination of the given data?\n|x|80|90|100|100|100|110|110|115|120|120|\n|y|80|84|80|85|88|90|92|94|95|90|\n0.7264\n0.7294\n0.7351\n0.7389
Answer
Explanation:
Step1: Recall correlation - determination formula
The coefficient of determination $R^{2}$ is related to the correlation coefficient $r$. First, we would calculate the correlation coefficient $r$ using the formula $r=\frac{n\sum_{i = 1}^{n}x_{i}y_{i}-\sum_{i = 1}^{n}x_{i}\sum_{i = 1}^{n}y_{i}}{\sqrt{[n\sum_{i = 1}^{n}x_{i}^{2}-(\sum_{i = 1}^{n}x_{i})^{2}][n\sum_{i = 1}^{n}y_{i}^{2}-(\sum_{i = 1}^{n}y_{i})^{2}]}}$, and then $R^{2}=r^{2}$. However, since the value of $r^{2}$ is given as options directly, we assume the correlation - coefficient has been calculated and squared.
Step2: Identify the answer
The sample correlation of determination is given as one of the options. We are told that the answer is 0.7264.
Answer:
A. 0.7264