---
title: "Curve Fit Analysis"
slug: "curve-fit-analysis"
updated: 2025-12-22T15:52:24Z
published: 2025-12-22T15:52:24Z
canonical: "docs.sightmachine.com/curve-fit-analysis"
---

> ## Documentation Index
> Fetch the complete documentation index at: https://docs.sightmachine.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Curve Fit Analysis

## Overview

Curve Fit Analysis is a multivariate tool used to investigate the relationship between two parameters in exploratory processes. It uses linear least-squares regression and scatterplots, providing metrics like Pearson-R correlation coefficient and r-squared. It can be performed on Cycle and Part models, enabling high-granularity and lower-granularity comparisons. This data-driven decision ensures accurate predictions and efficient process optimization in manufacturing operations.

**Before You Begin**

Ensure you have:

- Access to the Application tab
- Permission to view selected assets or part types
- Two numeric parameters available (X and Y)
- At least 30 observations in the selected date range (100+ recommended)

**Create a Curve Fit Analysis**

**1. Open Curve Fit Analysis**

- Navigate to the **Application** tab.
- Select **Curve Fit Analysis**.
- The configuration panel opens.

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764171682125.png)

**2. Select a Data Model**

Select how you want the tool to group data:

- **Cycles** – cycle-level parameters from the same asset type
- **Parts** – part-level data across machines producing the same part type

💡 Tip: Use Cycles for equipment behavior and Parts for final product characteristics.

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764171743086.png)

**3. Select Assets**

- Choose an Asset (Cycles) or Part Type (Parts).
- Select one or more assets of the same type.
- Confirm selections in the left panel.

📝 Note: Using multiple similar assets increases data volume and regression stability ![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764171813559.png) **4. Set the Time Range**

Choose:

- Relative ranges (Last 7/30/90 days)
- Absolute ranges (manual dates)

📝 Note: Larger ranges provide more data but may include process changes.

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764171896106.png)

**5. Select X and Y Parameters**

- Choose the X-axis parameter (independent variable).
- Choose the Y-axis parameter (dependent variable).

Both must be numeric fields.

Example:

- X: Oven Temperature
- Y: Cure Time

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764171957121.png)

**6. Add Stratification (Optional)**

To compare different conditions:

- Select a categorical field (e.g., Shift, Product Type).
- Each category generates its own regression line.
- Leave blank for a single-line regression.

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764172015774.png)

**7. Configure Carry-Forwards**

Choose how forward-filled values should be handled:

- **Keep All (default)**
- **First**
- **Last**

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764172069800.png)

**8. Generate Results**

- Select Update.
- Wait for the scatter plot and regression line to load.
- Review statistical metrics and visuals

![](https://cdn.us.document360.io/c65001f1-30e3-4f1d-b335-57abf64ebd31/Images/Documentation/image-1764172110953.png)

**How Linear Regression Works**

#### **Least-Squares Method**

Curve Fit Analysis uses linear least-squares regression, which fits the line that minimizes the squared distance between each data point and the regression line:

- y = mx + b
- m = slope
- b = intercept

**Calculation Formulas**

**Slope (m):**

m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)

**Intercept (b):**

b = (Σy - m × Σx) / n

**Statistical Metrics Provided**

#### **1. Pearson-R**

Measures linear correlation strength.

**Range:** –1.0 to +1.0

- **≥ 0.7** strong
- **0.4–0.7** moderate
- **< 0.4** weak

💡 Tip: Pearson-R only measures linear patterns.

#### **2. R-squared (R²)**

Explains how much of Y’s variance is predicted by X.

**Range:** 0.0–1.0

- **≥ 0.7** strong predictor
- **0.4–0.7** moderate
- **< 0.4** weak

**Formula: R² = r²**

#### **3. P-value**

Indicates statistical significance.

**p < 0.05** → significant

**p < 0.01** → highly significant

**p ≥ 0.05** → not significant

⚠️ Warning: Significance ≠ causation.

#### **4. Standard Error**

Measures how far points deviate from the regression line.

Lower values = better fit.

**Data Requirements**

**Numeric Fields Only**

- X and Y must be continuous numeric fields.
- Categorical fields can only be used for stratification.

**Cycles vs. Parts**

- Cycles → machine cycle data
- Parts → part-level comparisons

**Date Ranges:** Use relative or absolute windows.

💡 Tip: Be cautious of long ranges that include process or equipment changes.

**Interpreting Results**

**Scatter Plot:** Shows:

- Distribution of data points
- Regression line alignment
- Concentration or spread
- Outliers

**Histograms:** Display data distributions for X and Y:

- Identify skew
- Spot outliers
- Check data ranges

**Common Use Cases**

**1. Predict Outcomes:** Use regression equations to estimate results (e.g., predict Cycle Time from Temperature).

**2. Identify Drivers:** Understand how inputs relate to outputs.

**3. Validate Expectations:** Confirm whether expected relationships hold true.

**4. Compare Conditions:** Use stratification to test differences across shifts, operators, products, or machines.

**Limitations & Considerations**

**Linearity Requirement:** Relationships must be linear. Non-linear patterns require other methods.

**Outliers:** Large deviations can distort the regression line. Always inspect visually.

**Causation:** Regression describes correlation; it does not prove cause-and-effect.

**Sample Size**

- Minimum: 30 points
- Recommended: 100+

⚠️ Small datasets can produce misleading slopes or R².

## Feature Benefits

- **Detailed Relationship Validation:** Allows for in-depth investigation of the relationship between two specific parameters, confirming whether a high correlation value is meaningful or just a data artifact.
- **Linear Regression Computation:** Computes and visualizes a linear least-squares regression between the two parameters, providing a precise, quantifiable fit line.
- **Comprehensive Scatterplot Visualization:** Provides a clear visual representation via a scatterplot, complete with histograms along each axis to simultaneously show the individual distributions of the two parameters.
- **Stratification Capability:** Allows users to select a categorical field for stratification, enabling the breakdown of data points into separate traces to analyze how the relationship differs across various categories (e.g., product type).
- **Validation Metrics (R-squared & Pearson-R):** Delivers a table of key regression metrics, including the [Pearson-R correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient) and the R-squared value (see note below). The R-squared value provides a simple estimate of how well the independent variable determines the dependent variable (closer to 1.0 indicates a stronger fit). **NOTE:** Statisticians can speak volumes on the finer points of interpreting the r-squared value, but it is basically an estimate of how well the independent variable (the variable on the X axis of your chart) determines the dependent variable (the variable on the Y axis of your chart). Small numbers close to zero indicate a weak relationship. Bigger numbers close to one indicate a stronger relationship.
- **Strategic Exploratory Tool:** Most helpful later in the exploratory process; serves as an excellent follow-up tool after identifying key pairs using the Correlation Heatmap or Time-Series Correlation.
- **Model Flexibility (Cycle & Part):** Supports multivariate analysis on Cycle and Part data models, enabling high-granularity analysis within a machine (Cycle model) or cross-machine comparison (Part model).
- **Integrated Summary Statistics:** Includes a table of summary statistics (Count, Standard Deviation, Min, Max) for both selected parameters, providing immediate contextual data for the analysis.

## Summary

The Curve Fit tool outputs a scatterplot with a regression line and two histograms, one for each parameter. This enables you to gain a deeper understanding of the relationship between the two parameters.

For example, the stratification that you set applied a different color for the data points for each machine, allowing you to see if the machine impacted the relationship.

The value of correlation is represented by the [Pearson-R correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient), and you can see other useful statistical metrics displayed, such as r-squared (see note below), p-value, and standard error.NOTE: Statisticians can speak volumes on the finer points of interpreting the r-squared value, but it is basically an estimate of how well the independent variable (the variable on the X axis of your chart) determines the dependent variable (the variable on the Y axis of your chart). Small numbers close to zero indicate a weak relationship. Bigger numbers close to one indicate a stronger relationship.