Final answer:
The variance of the residuals (s^2) is calculated as 87,386.27670, and the standard deviation (s) is approximately 295.6112 for the regression based on 12 observations with SSE of 873,862.7670.
Step-by-step explanation:
When a least squares line is fit to the 12 observations in the labor cost data, and we obtain SSE = 873,862.7670, the calculation of s2 (the variance of the residuals) and s (the standard deviation of the residuals) can be done using the formulas derived from the principles of linear regression. In this case, since we have 12 observations, the degrees of freedom for the model will be 12 - 2 (for the two parameters estimated, which are the slope and the intercept), leaving us with 10 degrees of freedom.
To calculate the variance s2, we use the formula:
s2 = SSE / (n - 2),
where SSE is the sum of squared errors, and n is the total number of observations.
Substituting the given values,
s2 = 873,862.7670 / (12 - 2) = 873,862.7670 / 10 = 87,386.27670.
Next, to find the standard deviation s, we take the square root of the variance:
s = √s2 = √87,386.27670 ≈ 295.6112.
Thus, the variance of the residuals s2 is 87,386.27670, and the standard deviation of the residuals s is approximately 295.6112.