Sum Squared Error Calculator

Calculator inputs

Actual values

Use commas, spaces, semicolons, or new lines.

Predicted values

The count must match actual values.

Paired rows

When used, paired rows override both lists.

Optional weights

Leave blank for ordinary SSE.

Residual display

SSE is unchanged by the sign choice.

Model parameter count

Used for residual standard error only.

Decimal places

Choose how results are rounded.

Example data table

Actual	Predicted	Residual	Squared Error
12	11.5	0.5	0.25
15	14	1	1
20	18.5	1.5	2.25
22	23	-1	1
30	28	2	4
SSE			8.5

Formula used

Residual: e_i = y_i - ŷ_i

Sum squared error: SSE = ∑(y_i - ŷ_i)²

Weighted SSE: WSSE = ∑w_i(y_i - ŷ_i)²

Mean squared error: MSE = SSE / n

Root mean squared error: RMSE = √MSE

R squared: R² = 1 - SSE / SST

How to use this calculator

Enter actual values in the first box. Enter predicted values in the second box. Keep both lists in the same order.

Paste paired rows if your data is already arranged as actual and predicted columns. Each row should contain two numbers.

Add weights only when some observations should count more. Enter one weight for each pair.

Set the parameter count if you want residual standard error. Click Calculate to see the result above the form.

Use Download CSV or Download PDF to save the same calculation output.

Understanding Sum Squared Error

Sum squared error measures total squared prediction error. It compares each observed value with its predicted value. The difference is called a residual. Each residual is squared. Then all squared residuals are added. A smaller value usually means better fit. It is widely used in regression, forecasting, and machine learning.

Why SSE Matters

SSE gives strong weight to large mistakes. A residual of four contributes sixteen. A residual of one contributes only one. This makes the measure useful when large errors are costly. It also helps compare models trained on the same data. The lower SSE model fits those observations more closely.

How Residuals Explain Fit

Residuals show where a model misses the target. Positive residuals mean actual values are above predictions. Negative residuals mean predictions are higher than actual values. Squaring removes the sign. The calculator still displays residuals, so you can inspect direction. Patterned residuals may show bias, curvature, or missing variables.

Related Accuracy Measures

SSE is useful by itself, but related metrics add context. MSE divides SSE by the number of pairs. RMSE takes the square root of MSE. MAE averages absolute residuals. R squared compares SSE with total variation in the actual values. Residual standard error adjusts for model parameters when enough data exists.

Best Practices

Use the same data points when comparing models. Do not compare SSE across datasets with different sizes without context. Larger datasets often produce larger SSE values. Review the residual table before trusting one number. Check for outliers. Check units. If values are measured in dollars, squared errors use squared dollars. That unit can be hard to interpret, so RMSE can help.

Data Checks

Before analysis, confirm that paired values match correctly. Remove labels, commas in large numbers, and blank rows. Keep units consistent. If a prediction is missing, remove that whole pair rather than shifting rows. Document every data change.

Using This Calculator

Enter actual values and predicted values in matching order. You can also paste paired rows. Optional weights let important observations count more. Set model parameters when you need residual standard error. Choose decimal places for reporting. Then calculate, export, or save the result. The table shows every residual and squared error for review.

FAQs

What is sum squared error?

Sum squared error is the total of squared residuals. A residual is the gap between an actual value and its predicted value. It shows total model error for the entered dataset.

Can SSE be zero?

Yes. SSE is zero when every predicted value equals its matching actual value. That means all residuals are zero for the data entered.

Is a lower SSE always better?

A lower SSE is better when models use the same dataset and target. Do not compare raw SSE values across different sample sizes without added context.

How is SSE different from MSE?

SSE adds all squared errors. MSE divides SSE by the number of data pairs. MSE is easier to compare when datasets have different sizes.

What is RMSE?

RMSE is the square root of MSE. It returns error to the original unit of the target variable, which makes results easier to read.

Why are residuals squared?

Squaring removes negative signs and gives larger mistakes more influence. This helps highlight predictions that miss the actual value by a wide margin.

When should I use weights?

Use weights when some observations are more important, more reliable, or represent larger groups. Leave weights blank for a standard unweighted calculation.

What does R squared show here?

R squared compares SSE with total variation in the actual values. It gives a fit indicator when the entered predictions are for the same response variable.