What term is used for the best regression line?

What term is used for the best regression line?

• A. The sum of square errors (SSE)
• B. The residual sum of squares (RSS)
• C. The coefficient of determination (R^2)
• D. The standard error line

Answer: (A)

The best-fitting regression line is determined by the least squares criterion: it minimizes the total squared differences between observed values and the values predicted by the line. This total is called the sum of squared errors (SSE). By squaring the residuals (the differences between observed and predicted) we ensure all deviations contribute positively and larger errors weigh more, so the line that yields the smallest SSE is the one that fits the data most tightly in a least-squares sense. In this sense, SSE is the quantity that defines and identifies the best line. Understandably, other terms describe related ideas: the residual sum of squares (SSE) is the same concept in different terminology, the portion of total variation explained by the model is often called the regression sum of squares (SSR) and together they add up to the total sum of squares (TSS), while R^2 reflects the proportion of variance explained. But the key point for the best-fit line is that its determination comes from minimizing SSE, yielding the least squares regression line.

The best-fitting regression line is determined by the least squares criterion: it minimizes the total squared differences between observed values and the values predicted by the line. This total is called the sum of squared errors (SSE). By squaring the residuals (the differences between observed and predicted) we ensure all deviations contribute positively and larger errors weigh more, so the line that yields the smallest SSE is the one that fits the data most tightly in a least-squares sense. In this sense, SSE is the quantity that defines and identifies the best line.

Understandably, other terms describe related ideas: the residual sum of squares (SSE) is the same concept in different terminology, the portion of total variation explained by the model is often called the regression sum of squares (SSR) and together they add up to the total sum of squares (TSS), while R^2 reflects the proportion of variance explained. But the key point for the best-fit line is that its determination comes from minimizing SSE, yielding the least squares regression line.