Question

The mean square error (mse) is a. the sse divided by the number of observations. b. denoted by s. c. the sse divided by the degrees of freedom (n-k-1). d. denoted by k?

1) the sse divided by the number of observations
2) denoted by s
3) the sse divided by the degrees of freedom (n-k-1)
4) denoted by k

Answer 1

The mean square error (MSE) is calculated by taking the sum of squared errors (SSE) and dividing it by the degrees of freedom for the error term (n - k), hence that the correct answer is c. 'the SSE divided by the degrees of freedom (n-k-1)'.the correct answer is option c)

Step-by-step explanation:

The mean square error (MSE) is often used in regression analysis and ANOVA to measure the average squared differences between estimated and observed values. The correct definition of MSE is that it is the sum of squared errors (SSE) divided by the degrees of freedom (df). In the context of ANOVA, this can be referred to as MS within or the mean square due to error. This can be calculated by taking the SSE and dividing it by the degrees of freedom associated with the error term, which is typically (n - k), where 'n' is the total number of observations and 'k' is the number of groups. Therefore, option c. 'the SSE divided by the degrees of freedom (n-k-1)' is correct.

To illustrate this with an example, if there are 120 total observations and 4 groups, the degrees of freedom for the error would be 120 - 4 = 116. Consequently, the mean square error would be calculated by dividing the SSE by 116.