Answer:
A) The adjusted R² = 0.923
Step-by-step explanation:
Given data
sum of squares of regression (SSR) = 210.9
Sum of squares of residuals = 15.6
Total sum of squares(SST) = 226.5
Degrees of freedom of Regression = 2
Degrees of freedom of Residuals = 17
Total number of degrees of freedom = 19
The R² is determined by
[tex]R^{2} = \frac{Regression SS}{Total SS}[/tex]
[tex]R^{2} = \frac{210.9}{226.5} = 0.9311[/tex]
Adjusted R² is determined by
R⁻² [tex]= 1-(1-R^{2})(\frac{n-1}{n-k-1)})[/tex]
The degrees of freedom of residuals
n -k-1 = 17
given data k= 2 (degrees of freedom of regression = 2)
n - 2 -1 =17
n = 17 +3 =20
The Adjusted R²
[tex]= 1-(1-R^{2})(\frac{n-1}{n-k-1)})[/tex]
[tex]= 1-(1-0.9311)(\frac{20-1}{17})[/tex]
on calculation, we get
R⁻² = 0.923
Final answer:-
The adjusted R² = 0.923