Question

Assume that you have paired values consisting of heights​ (in inches) and weights​ (in lb) from 40 randomly selected men. The linear correlation coefficient r is 0.4450.445. Find the value of the coefficient of determination. What practical information does the coefficient of determination​ provide? Choose the correct answer below. A. The coefficient of determination is 0.8020.802. 19.819.8​% of the variation is explained by the linear​ correlation, and 80.280.2​% is explained by other factors. B. The coefficient of determination is 0.1980.198. 19.819.8​% of the variation is explained by the linear​ correlation, and 80.280.2​% is explained by other factors. C. The coefficient of determination is 0.8020.802. 80.280.2​% of the variation is explained by the linear​ correlation, and 19.819.8​% is explained by other factors. D. The coefficient of determination is 0.1980.198. 80.280.2​% of the variation is explained by the linear​ correlation, and 19.819.8​% is explained by other factors.

Answer 1

Answer:

$R^2 = r^2 = 0.445^2= 0.198$

B. The coefficient of determination is 0.1980, 19.8​% of the variation is explained by the linear​ correlation, and 80.2​% is explained by other factors.

Step-by-step explanation:

Previous concepts

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.  

Solution to the problem

In order to calculate the correlation coefficient we can use this formula:  

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$  

On this case we got that r =0.445

The determinaton coefficient is just:

$R^2 = r^2 = 0.445^2= 0.198$

And we can put it on % and we got 19.8%. And represent the variation explained by a linear model. The best option on this case would be:

B. The coefficient of determination is 0.1980, 19.8​% of the variation is explained by the linear​ correlation, and 80.2​% is explained by other factors.

Since the explained variation is 19.8% and the remain 100-19.8= 80.2% is explained by other factors.