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SSE Calculator

Enter the independent and dependent variables in the tool, and the calculator will compute the SSE value.

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SSE Calculator

The SSE calculator is a statistical tool used to estimate the variability of data values around a regression line. It calculates how much the dependent variable deviates from predicted values in regression analysis.

What Is SSE in Statistics?

The Sum of Squared Errors (SSE) or Residual Sum of Squares (RSS) measures the difference between observed and predicted values. It shows the spread of dataset values and is an alternative measure to standard deviation or absolute deviation.

Practical Example:

Consider the following dataset:

Independent variables (X): 6, 7, 7, 8, 12, 14, 15, 16, 16, 19
Dependent variables (Y): 14, 15, 15, 17, 18, 18, 16, 14, 11, 8

We want to find the Sum of Squared Residuals (SSE) for this data.

Solution Steps:

Predict the dependent values using regression.
Compute residuals: observed - predicted.
Square each residual.
Sum all squared residuals to get SSE.

Data Table:

Obs.	X	Y
1	6	14
2	7	15
3	7	15
4	8	17
5	12	18
6	14	18
7	15	16
8	16	14
9	16	11
10	19	8

Step 1: Compute Sum of Squares

For X:

SS_XX = ΣX_i² - (ΣX_i)² / n = 1636 - (120)² / 10 = 196

For Y:

SS_YY = ΣY_i² - (ΣY_i)² / n = 2220 - (146)² / 10 = 88.4

For XY:

SS_XY = Σ(X_i·Y_i) - (ΣX_i·ΣY_i) / n = 1690 - (120·146)/10 = -62

Step 2: Calculate Regression Coefficients

Slope (β̂₁): β̂₁ = SS_XY / SS_XX = -62 / 196 = -0.31633

Intercept (β̂₀): β̂₀ = Ȳ - β̂₁·X̄ = 14.6 - (-0.31633 × 12) = 18.396

Regression Equation: Ŷ = 18.396 - 0.31633X

Step 3: Compute Total, Regression, and Error Sum of Squares

Total Sum of Squares: SS_Total = SS_YY = 88.4

Regression Sum of Squares: SS_R = β̂₁·SS_XY = -0.31633 × -62 = 19.612

Error Sum of Squares (SSE): SS_E = SS_Total - SS_R = 88.4 - 19.612 = 68.788

FAQs

What is SSE in correlation?

SSE explains how closely the independent variable relates to the dependent variable.

What does a high SSE mean?

A high SSE indicates greater deviation from predicted values, implying a less accurate model fit.

Is SSE the same as standard deviation?

No. SD measures overall variability, while SSE measures squared deviations from predicted values.

Can SSE be negative?

No. SSE is always positive because it is computed by squaring residuals.

References

365 Data Science: Sum of Squares
Six Sigma Study Guide: SSE

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