Final answer:
The expression sum( Y - Y')² is the SSE (Sum of Squared Errors), representing the total error of prediction in a regression model. It is the sum of the squares of the residuals, and it is used to calculate the standard deviation of the residuals. The correct option is c.
Step-by-step explanation:
The expression sum( Y - Y')² refers to the sum of the squares of the differences between the observed values (Y) and the predicted values (Y'). This expression is commonly used in statistics to measure the total prediction error in a regression model, representing the SSE (Sum of Squared Errors).
The term (Y - Y') is also known as the residual or error, with the square of the residual summing up to the SSE. The variance within samples, on the other hand, represents a different concept: the average of the sample variances or the unexplained variation within the data.
To calculate the standard deviation of the residuals, which measures the typical size of the residuals or prediction errors, you would take the square root of the average of these squared residuals (variance).
s = √( SSE / (n - 2) )
Here, s is the standard deviation of the residuals, and n represents the total number of data points. To answer the student's question, sum( Y - Y')2 most closely corresponds to the total error of prediction. Hence, c is the correct option.