Final answer:
To compute the SSE, SST, and SSR using the provided equations, substitute the observed and estimated regression values into the formulas. SSE is the sum of squared errors. SSR is the sum of squared residuals. SST is the sum of squared total.
Step-by-step explanation:
The sum of squared errors (SSE) can be computed by summing the squares of the differences between the observed values of y and the predicted values of y (ŷ) in the regression equation. In this case, the SSE is calculated as follows:
SSE = (y₁ - ŷ₁)² + (y₂ - ŷ₂)² + (y₃ - ŷ₃)² + (y₄ - ŷ₄)² + (y₅ - ŷ₅)²
= (3 - (0.2 + 2.6*1))² + (7 - (0.2 + 2.6*2))² + (5 - (0.2 + 2.6*3))² + (11 - (0.2 + 2.6*4))² + (14 - (0.2 + 2.6*5))²
= 0.36 + 3.24 + 4.84 + 1.44 + 0.36
= 10.24
The sum of squared residuals (SSR) can be computed by summing the squares of the differences between the observed values of y and the mean of y. In this case, the SSR is calculated as follows:
SSR = (y₁ - ȳ)² + (y₂ - ȳ)² + (y₃ - ȳ)² + (y₄ - ȳ)² + (y₅ - ȳ)²
= (3 - 8)² + (7 - 8)² + (5 - 8)² + (11 - 8)² + (14 - 8)²
= 5² + (-1)² + (-3)² + 3² + 6²
= 25 + 1 + 9 + 9 + 36
= 80
The sum of squared total (SST) can be computed by summing the squares of the differences between the observed values of y and the mean of y. In this case, the SST is calculated as follows:
SST = (y₁ - ȳ)² + (y₂ - ȳ)² + (y₃ - ȳ)² + (y₄ - ȳ)² + (y₅ - ȳ)²
= (3 - 8)² + (7 - 8)² + (5 - 8)² + (11 - 8)² + (14 - 8)²
= 5² + (-1)² + (-3)² + 3² + 6²
= 25 + 1 + 9 + 9 + 36
= 80