Which term is another name for the sum of squares?

Which term is another name for the sum of squares?

• A. Sum of squared errors
• B. Sum of squares
• C. Sum of squares and cross-products matrix
• D. Tertium quid

Answer: (A)

In regression analysis, the part of the total variability that comes from the model’s mistakes is captured by the sum of squared errors. This is computed by taking each observed value, subtracting the model’s predicted value for that observation, squaring the result, and then summing those squared differences: SSE = Σ(y_i − ŷ_i)². This quantity represents the unexplained variation left after fitting the model. The term “sum of squares” is a broad label for these squared deviations. When we’re talking specifically about the portion due to random error or unexplained variation in a regression context, that sum of squares is called the sum of squared errors. So this phrase is the conventional synonym for the sum of squares in that setting. Other options refer to different concepts: a sum of squares and cross-products matrix is a data-structure used in calculations, not the residual variability, and tertium quid is just a Latin phrase with no statistical meaning here.

In regression analysis, the part of the total variability that comes from the model’s mistakes is captured by the sum of squared errors. This is computed by taking each observed value, subtracting the model’s predicted value for that observation, squaring the result, and then summing those squared differences: SSE = Σ(y_i − ŷ_i)². This quantity represents the unexplained variation left after fitting the model.

The term “sum of squares” is a broad label for these squared deviations. When we’re talking specifically about the portion due to random error or unexplained variation in a regression context, that sum of squares is called the sum of squared errors. So this phrase is the conventional synonym for the sum of squares in that setting.

Other options refer to different concepts: a sum of squares and cross-products matrix is a data-structure used in calculations, not the residual variability, and tertium quid is just a Latin phrase with no statistical meaning here.