Regression Analysis

Fit mathematical curves to your experimental data using the Table shape's built-in regression tools, then visualize the results in Charts.

Overview

Regression analysis in Modellus lets you find the best-fit curve through a set of data points. This is essential for comparing experimental measurements with theoretical models. Modellus supports linear and quadratic regression.

Step-by-Step Workflow

1. Enter or compute data

Screenshot: Table with experimental data entered in columns

Start by having data in a Table shape. This can be:

Manually entered experimental measurements (data columns)
Computed values from model expressions

2. Select cells for regression

Screenshot: Table with highlighted cell selection across X and Y columns

Click and drag to select the range of cells you want to include in the regression. Select cells from both an X column and a Y column to define the data pair.

You can select a subset of rows to exclude extreme values or focus on a specific region of your data.

3. Choose regression method

Screenshot: Regression method dropdown showing Linear and Quadratic options

From the Table toolbar, open the regression method dropdown and choose:

Method	Model	Best for
Linear	y = ax + b	Data with a constant rate of change. Produces slope (a) and intercept (b).
Quadratic	y = ax² + bx + c	Data with acceleration or curvature. Produces three coefficients.

4. Review the regression term

After applying regression, Modellus creates a new term of type REGRESSION in the calculator. This term:

Stores the fitted coefficients
References the source data ranges
Can be plotted in any Chart shape
Automatically flags outlier iterations

5. Visualize in a Chart

Screenshot: Chart showing scatter data with overlaid regression line

Add the regression term to a Chart shape as a Y-axis series. The fitted curve will overlay on the original data scatter, allowing you to visually assess the quality of the fit.

Interpreting Results

Linear Regression (y = ax + b)

Coefficient	Meaning
a (slope)	Rate of change of Y per unit X. A steeper line means a larger slope.
b (intercept)	The Y value when X = 0. Where the line crosses the Y-axis.

Quadratic Regression (y = ax² + bx + c)

Coefficient	Meaning
a	Controls the curvature. Positive = opens upward, negative = opens downward.
b	Linear component affecting the slope at the origin.
c	Y-intercept (Y value when X = 0).

Clearing a Regression

To remove a regression from selected data, choose No Regression from the regression method dropdown. This removes the regression term and any associated outlier markers.

See Outliers to learn how outlier detection works with regression analysis.