Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The li

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Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The li

near 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.

Mathematics

1 answer:

HACTEHA [7] · Answer 1 · 2022-09-01T13:22:58+03:00

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.