1. What is Total Sum of Squares?

The Total Sum of Squares (SST) is a measure of the total variation in a dataset. It represents the sum of the squared differences between each observation and the overall mean of the data.

2. How Does the Calculator Work?

The calculator uses the SST formula:

Where:

• \( y_i \) — Individual data points
• \( \bar{y} \) — Mean of all data points
• \( n \) — Number of data points

Explanation: The formula calculates how far each data point is from the mean and squares these differences to eliminate negative values, then sums all these squared differences.

3. Importance of SST Calculation

Details: SST is fundamental in statistical analysis, particularly in ANOVA and regression analysis. It helps partition variance into explained and unexplained components.

4. Using the Calculator

Tips: Enter your data points separated by commas (e.g., 5,7,9,11). The calculator will compute the mean and then the sum of squared deviations from this mean.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SST, SSR, and SSE?
A: SST is total variation, SSR is variation explained by the model, and SSE is unexplained variation (SST = SSR + SSE).

Q2: Can SST be negative?
A: No, because it's a sum of squared values which are always non-negative.

Q3: How does SST relate to variance?
A: Sample variance is SST divided by (n-1) for a sample or by n for a population.

Q4: What does a high SST value indicate?
A: A high SST indicates greater variability in your data points around the mean.

Q5: Is SST affected by outliers?
A: Yes, because squaring the deviations gives more weight to extreme values.