Question

You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N=51 observations. (a) The estimated error variance ^σ2=2.04672. What is the sum of the squared least squares residual?

Answer 1

The sum of squared residuals (SSE) can be found by multiplying the estimated error variance (2.04672) by the degrees of freedom (49) for a simple linear regression with 51 observations, resulting in an SSE of 100.28928.

Step-by-step explanation:

The question is asking about the sum of squared residuals, often represented as SSE (Sum of Squared Errors), in the context of a simple linear regression analysis with total of N=51 observations. Given the estimated error variance σ²=2.04672, and knowing that there are N observations, we can find the SSE by multiplying the estimated error variance by the degrees of freedom, which in a simple linear regression is N-2 since we estimate two parameters (the slope and intercept).

The formula to calculate the SSE is:

1. Identify the estimated error variance (σ²).
2. Multiply it by the degrees of freedom (N-2), which in this case is 51 - 2 = 49.
3. So, SSE = σ² * (N-2) = 2.04672 * 49.
4. Calculate the value to find the SSE.

Performing the calculation:

SSE = 2.04672 * 49 = 100.28928.

Therefore, the SSE for the given linear regression with 51 observations and an estimated error variance of 2.04672 is 100.28928.