Answer:
SSE = 507.75
R² = 0.924
Ra² = 0.812
Step-by-step explanation:
The estimated regression equation is given by
y = 29.1270 + 0.5906x₁ + 0.4980x₂
Find SSE
The total sum of squares is given by
SST = SSR + SSE
Where SSR is the sum of squares due to regression and SSE is sum of squares due to error
SSE = SST - SSR
SSE = 6724.125 - 6216.375
SSE = 507.75
Compute R²
The Coefficient of determination is given by
R² = SSR/SST
R² = 6216.375/6724.125
R² = 0.924
Compute Ra²
The adjusted coefficient of determination is given by
Ra² = 1 - ((1 - R²)(N - 1)/(N - P - 1))
Where N is the total number of samples and P is the number of predictors
Ra² = 1 - ((1 - 0.924²)(10 - 1)/(10 - 2 - 1))
Ra² = 0.812
How good is the fit provided by the estimated regression equation?
The coefficient of determination can provide a good insight about the fitness of estimated regression equation.
A higher value of R² indicates a good fit on the other hand a lower value of Ra² also indicates a good fit. Since we have got a high value of R² and low value of Ra², we can conclude that that it is a good fit.
