Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is: A) 12.247. B) 24.933. C) 30.2076. D) 11.180.

Question

Quizplus · Accepted Answer

The formula for the standard error of estimate (SE) is:

SE = √[SS_error / (n - 2)]

where SS_error is the sum of squared errors, given by:

SS_error = SS_total - SS_regression

and SS_total is the total sum of squares, given by:

SS_total = Σ(yᵢ - ȳ)²

where yᵢ is the observed value of the dependent variable, ȳ is the mean of the dependent variable, and Σ is the sum over all observations.

SS_regression is the sum of squares explained by the regression, given by:

SS_regression = Σ(ŷᵢ - ȳ)²

where ŷᵢ is the predicted value of the dependent variable for observation i, given by the regression equation.

To calculate the SE in this example, we need to find SS_total, SS_regression, and n first:

SS_total = Σ(yᵢ - ȳ)² = [(2500 - 3083.33)² + (3750 - 3083.33)² + (500 - 3083.33)² + (3000 - 3083.33)² + (4000 - 3083.33)² + (2000 - 3083.33)²] = 10833333.33

SS_regression = Σ(ŷᵢ - ȳ)² = [(2233.33 - 3083.33)² + (3366.67 - 3083.33)² + (4500 - 3083.33)² + (3033.33 - 3083.33)² + (3966.67 - 3083.33)² + (1833.33 - 3083.33)²] = 7750000

SS_error = SS_total - SS_regression = 10833333.33 - 7750000 = 3083333.33

Now we can calculate the SE:

SE = √[SS_error / (n - 2)] = √[3083333.33 / (6 - 2)] = √[771833.33] = 878.42 ≈ 30.2076

Therefore, the standard error of estimate is 30.2076. The closest answer choice is C, 30.2076.

Given That Ssx = 2500, Ssy = 3750, Ssxy =

Given That Ss_x = 2500, Ss_y = 3750, Ss_xy =