Question

question 6 (1 point)
based on the coefficient of determination (r²) value given for graph a, which is the best possibility of the coefficient of determination (r²) for graph b?
graph a
r² = 0.9073
graph b
r² = 0.95
r² = -0.6
r² = 1.5
r² = 0.6

Explanation:

Step1: Recall the properties of \(R^{2}\)

The coefficient of determination \(R^{2}\) has a range \(0\leq R^{2}\leq1\). So, \(R^{2}=- 0.6\) (negative value) and \(R^{2}=1.5\) (greater than 1) are invalid.

Step2: Analyze the scatter of data points

In Graph A, data points are relatively close to the regression line (\(R^{2}=0.9073\)). In Graph B, data points are more scattered from the regression line. A more scattered data set has a lower \(R^{2}\) value. Since \(0.6<0.9073<0.95\) and considering the scatter, \(R^{2} = 0.6\) is more appropriate.

Answer:

\(R^{2}=0.6\)