A simple regression model resulted in a sum of squares of error of 125 (i.e., SSE = 125), and the standard error is 3.95. This model is for ___ pairs of data.
A) 8
B) 9
C) 10
D) 11
E) 12

Question

Quizplus · Accepted Answer

The formula for SSE is SSE = ∑(yi - ŷ)2, where yi is the observed value, and ŷ is the predicted value. The larger the SSE, the worse the model's fit to the data. The standard error is a measure of the variability of the residuals (i.e., the distance between the predicted values and the observed values). Higher standard errors indicate greater variability, which typically means a worse model fit.
The formula for standard error is SE = sqrt(SSE / (n - 2)), where n is the number of data points. Solving for n, we get n = (SSE / SE2) + 2. Substituting in the given values, we get n = (125 / 3.952) + 2, which evaluates to approximately 10. Therefore, the regression model is for 10 pairs of data.

A Simple Regression Model Resulted in a Sum of Squares