Regression Line Calculator
Verified Calculation Engine
The online Regression Line Calculator helps you calculate instantly and solve problems related to Statistics Advanced. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Finds regression line y = a + bx where b = r(σᵧ/σₓ) and a = ȳ - bx̄. Regression of y on x predicts y from x.
Regression line of y on x:
y = a + bx
where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)²
and a = ȳ - bx̄
Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ)
Regression line predicts one variable from another
Inputs
Results
Worked Examples
Example 1: Basic
Find regression line of y on x for x = [1, 2, 3, 4, 5], y = [2, 4, 6, 8, 10]
- xValues: [ 1, 2, 3, 4, 5 ]
- yValues: [ 2, 4, 6, 8, 10 ]
- equation: y = 0 + 2x
- slope: 2
- intercept: 0
Example 2: Board Level
Find regression line of y on x for x = [1, 2, 3, 4], y = [3, 5, 7, 9]
- xValues: [ 1, 2, 3, 4 ]
- yValues: [ 3, 5, 7, 9 ]
- equation: y = 1 + 2x
- slope: 2
- intercept: 1
About this calculator
Overview
Regression Line Calculator evaluates Regression Line for the math / statistics-advanced library. Primary input cue: X Values [required]: Array of x values. Method anchor: Regression line of y on x: y = a + bx where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)² and a = ȳ - bx̄ Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ). Re.
When to use
Use this page when you need regression line from known inputs and want a transparent arithmetic or symbolic check.
Inputs explained
- X Values [required]: Array of x values
- Y Values [required]: Array of y values
- Regression Type [optional]: Type: 'y-on-x' or 'x-on-y' (default: y-on-x)
Formula / method
Regression line of y on x: y = a + bx where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)² and a = ȳ - bx̄ Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ). Regression line predicts one variable from another (calculator id: regression-line-calculator).
Worked example
Worked values: xValues = [1, 2, 3, 4, 5], yValues = [2, 4, 6, 8, 10] → equation = y = 0 + 2x, slope = 2, intercept = 0
Interpreting results
If regression line looks implausible, re-check units and which field is optional vs required.
Assumptions
- Empty required inputs are not silently replaced with zeros for regression line. [regression-line-calculator]
- Regression Line is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless regression line explicitly needs integers.
Limitations
- If multiple conventions exist for regression line, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to regression line.
- Complex/branch cuts and undefined points are not always interactively annotated for regression line.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Regression line of y on x: y = a + bx where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)² and a = ȳ - bx̄ Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ). Regression line predicts one variable from another (calculator id: regression-line-calculator).
Example Calculation
Worked values: xValues = [1, 2, 3, 4, 5], yValues = [2, 4, 6, 8, 10] → equation = y = 0 + 2x, slope = 2, intercept = 0
Frequently Asked Questions
What is Regression Line Calculator?
- Regression Line Calculator evaluates Regression Line for the math / statistics-advanced library. Primary input cue: X Values [required]: Array of x values. Method anchor: Regression line of y on x: y = a + bx where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)² and a = ȳ - bx̄ Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ). Re.
How does Regression Line Calculator work?
- Regression line of y on x: y = a + bx where b = r(σᵧ/σₓ) = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/Σ(xᵢ-x̄)² and a = ȳ - bx̄ Regression of x on y: x = a' + b'y where b' = r(σₓ/σᵧ). Regression line predicts one variable from another (calculator id: regression-line-calculator).
Why use this Math Numbers calculator?
- Use this page when you need regression line from known inputs and want a transparent arithmetic or symbolic check.