Question

Suppose you fit a least squares line to 26 data points and the calculated value of SSE is 8.02 . a. Find 5 2 , the estimator of 0

2
(the variance of the random error term 8 ). b. What is the largest deviation that you might expect between any one of the 26 points and the least squares lin a. Find s 2 , the estimator of o 2
(the variance of the random error term e ). 5 2
=( (Round to four decimal places as needed.)

Answer 1

To find 5 2, the estimator of 0 2, divide SSE by (n-2). The largest deviation between any point and the least squares line is determined using the standard deviation of the residuals.

Step-by-step explanation:

To find 5 2, the estimator of 0 2, we can use the formula:

5 2 = SSE / (n-2)

Substituting the given values, we get:

5 2 = 8.02 / (26-2) = 0.3208 (rounded to four decimal places)

Therefore, the estimator of 0 2 is 0.3208.

For part b, the largest deviation that you might expect between any one of the 26 points and the least squares line can be determined using the standard deviation of the residuals (s).

Since the standard deviation of the residuals is not provided in the question, we cannot calculate the exact largest deviation.

However, if we have the standard deviation of the residuals, we can use the formula:

Largest Deviation = 2s

Where s is the standard deviation of the residuals.