Question

Coefficient of Determination Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.394. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?

Short answer

The value of the coefficient of determination is 0.155.

It means that 15.5% variation in the weight of males is explained by the linear association between height and weight. Other factors, as well as random variation, account for the remaining 84.5%.

Step-by-step solution

Given information

The linear correlation coefficient between height and weight is 0.394.

Coefficient of determination

The coefficient of determination is the square of the linear correlation coefficient between the response variable and the predictor variable.

Here, the linear correlation coefficient (r) between height and weight is 0.394.

Thus,

\(\begin{array}{c}{\rm{Coefficient}}\;{\rm{of}}\;{\rm{Determination}} = {r^2}\\ = {0.394^2}\\ = 0.155\end{array}\)

Therefore, the coefficient of determination is 0.155.

Practical interpretation of the coefficient of determination

The actual interpretation of this value is that approximately 15.5% variation in the response variable “weights of males” is explained by the linear relationship between weight and height.

The remaining variation in y is \(100\% - 15.5\% = 84.5\% \). It can be explained by other variables/factors or random variation.