Total sum of squares measures which of the following?

• A. A measure of the total variability within a set of observations; it is the total squared deviance between each observation and the overall mean of all observations.
• B. The sum of squared residuals in a regression
• C. The mean of squared deviations
• D. The product of the sample size and the variance

Answer: (A)

Total sum of squares reflects how much the data vary overall by summing the squared differences of each observation from the grand mean. In formula terms, it’s the sum of (Yi − Ȳ)² across all observations. This quantity captures the total variability present before considering any model or predictions. In regression ANOVA, SST is the total variability that gets partitioned into the part explained by the model (SSR) and the part left as error (SSE). It isn’t the sum of squared residuals (that would be SSE), nor the mean of squared deviations (that’s the variance when you average the squared deviations), and it isn’t simply the product of sample size and variance under the usual sample-variance definition. So the description that matches the concept is the measure of total variability given by the sum of squared deviations from the grand mean.