A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 29.73 and that the y-values are 11, 14, 19, 22, 26, 27,
Find $$R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } } \text {. }$$
A) $0.844$
B) $0.144$
C) $0.88$
D) $0.856$

Question

Quizplus · Accepted Answer

The coefficient of determination $R^2$ is a measure of how well a regression model fits a set of data. It is calculated as the square of the correlation coefficient between the observed and predicted values of the dependent variable. In this case, the sum of squares of residuals is 29.73 and the y-values are 11, 14, 19, 22, 26, 27. The mean of the y-values is 19.83. The total sum of squares is the sum of the squared deviations of the y-values from their mean, which is 116.67. Therefore, the coefficient of determination is:$$R^2 = 1 - \frac{29.73}{116.67} = 0.856$$

A Quadratic Regression Model Is Fit to a Set of Sample