Suppose that the fit to the simple linear regression of Y on X from 6 observations produces the following residuals: -3.3, 2.1, -4.0, -1.5, 5.1, 1.6.

a) What is the estimate of sigma squared?
b) What is the estimate of sigma?
c) What are the degrees of freedom?

Sigma = standard deviation
Sigma^2 = variance
(Standard deviation is the square root of the variance.)

Square the residuals, total the squared values, then divide by n-1 (n = sample size). This will be the variance. Then take the square root of the variance for the standard deviation.

I hope this will help.

To calculate the estimates of sigma squared and sigma, you can follow these steps:

a) To estimate sigma squared:

1. Square each of the residuals: (-3.3)^2, (2.1)^2, (-4.0)^2, (-1.5)^2, (5.1)^2, (1.6)^2.
2. Add up all the squared values: (-3.3)^2 + (2.1)^2 + (-4.0)^2 + (-1.5)^2 + (5.1)^2 + (1.6)^2.
3. Divide the sum from the previous step by (n-1), where n is the number of observations in the dataset. In this case, since there are 6 observations, divide the sum by 5.
4. The result is the estimate of sigma squared.

b) To estimate sigma:

1. Take the square root of the estimate of sigma squared from step (a).
2. The result is the estimate of sigma.

c) The degrees of freedom:

The degrees of freedom, denoted as df, is equal to (n - 1), where n is the number of observations in the dataset. In this case, since there are 6 observations, the degrees of freedom would be 6 - 1 = 5.

By following these steps, you should be able to find the estimates of sigma squared and sigma, as well as the degrees of freedom.