Answer:
[tex] R^2 = r^2 = 0.445^2= 0.198[/tex]
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:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
On this case we got that r =0.445
The determinaton coefficient is just:
[tex] R^2 = r^2 = 0.445^2= 0.198[/tex]
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.
The Coefficient of determination is the squared Value of the correlation Coefficient. Hence, the coefficient of determination is 0.198. The practical information given by the R² value is "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.
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