Answer:
B. The coefficient of determination is 54.76%. Therefore, 54.76% of the variation in weight can be explained by the regression line.
Step-by-step explanation:
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.
The coefficient of determination is a measure to quantify how a model explains an dependent variable.
The formula for the correlation coeffcient is given by:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
The formula for the coefficient of determination is ![r^2](https://tex.z-dn.net/?f=r%5E2%20)
In our case the correlation coefficient obtained was 0.74
And the determination coefficient is
, and if we convert this into % we got 54.76%
Assume that height is the predictor (X) and weight is the response (Y)
And the best answer for this case is:
B. The coefficient of determination is 54.76%. Therefore, 54.76% of the variation in weight can be explained by the regression line.