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
$R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } }$
A) 0.844
B) 0.144
C) 0.88
D) 0.856

Question

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
$R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } }$
A)  0.844 
B)  0.144 
C)  0.88 
D)  0.856

Quizplus · Accepted Answer

The total sum of squares (SST) is calculated as the sum of the squared differences between each y-value and the mean of y-values. The sum of squares of residuals (SSE) is given as 29.73. R² is calculated as 1 - (SSE/SST). After calculating SST and substituting the values, R² is approximately 0.856.

A Quadratic Regression Model Is Fit to a Set of Sample