The exercise involving data in this and subsequent sections were designed to be solved using Excel. Consider the following estimated regression equation, based on 10 observations. y^ = 29.1270 + .5906x1 + .4980x2 The values of SST and SSR are 6724.125 and 6216.375, respectively. Find SSE (to 2 decimals). Compute R2 (to 3 decimals). Compute Ra2 (to 3 decimals). How good is the fit provided by the estimated regression equation?

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.

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step-by-step explanation: