Line Graph Trend & Linear Regression Calculator

Line Graph Analytics, Ordinary Least Squares (OLS) & Trendlines

A line graph connects a series of data points with straight line segments, ideal for continuous time series and mathematical functional relationships:

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• Ordinary Least Squares (OLS) Linear Regression Formulas**:

y = mx + b

m = (N Σ (xy) - (Σ x)(Σ y)) / (N Σ (x^2) - (Σ x)^2)

b = y - m x = (Σ y - m Σ x) / (N) (Y-Intercept)

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• Pearson Correlation Coefficient (r) & Goodness of Fit (R^2)**:

r = (N Σ (xy) - (Σ x)(Σ y)) / (√([N Σ x^2 - (Σ x)^2] [N Σ y^2 - (Σ y)^2]))

R^2 = r^2 (Fraction of variance in Y explained by X, 0 R^2 1)

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• Forecasting / Extrapolation**:

y_future = m · x_target + b

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• When to Use Line Graphs vs Bar Graphs**:

• Line Graphs: Best for continuous variables, time series (seconds, days, years), physical rates of change, and continuous mathematical functions.

• Bar Graphs: Best for discrete, non-continuous categories (departments, product names, countries).

How to Use This Calculator

Enter your Independent Variable X Values (comma-separated) (e.g. 1, 2, 3, 4, 5), Dependent Variable Y Values (comma-separated) (e.g. 100, 125, 145, 170, 205), Extrapolate / Predict at X Target (e.g. 6 in X), and Trend Dataset Benchmark — choose from Custom X-Y Data Pairs, Quarterly Sales Trend (X: 1..5, Y: 100, 125, 145, 170, 205) → m = +25.5/qtr, R² = 0.995, Hooke's Spring Law (X: 1..5 kg, Y: 9.8, 19.6, 29.4, 39.2, 49.0 N) → Perfect R² = 1.

• Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Line Graph Trend & Linear Regression Calculator (y = mx + b, R²)

Input variables:

xValuesInput — Independent Variable X Values (comma-separated)

yValuesInput — Dependent Variable Y Values (comma-separated)

predictAtXInput — Extrapolate / Predict at X Target

Computed outputs:

trendSlopeM — Best-Fit Slope (m in y = mx + b)

yInterceptB — Y-Intercept (b)

coefficientOfDeterminationR2 — Goodness of Fit (R²)

correlationCoefficientR — Pearson Correlation (r)

predictedYTarget — Extrapolated Value Y(X_target)

Mathematical relationships extracted from calculation logic:

meanX = sumX / N

meanY = sumY / N

denominatorM = N sumX2 - sumX sumX

slopeM = denominatorM === 0 ? 0 : (N sumXY - sumX sumY) / denominatorM

interceptB = meanY - slopeM * meanX

r = denominatorR === 0 ? 1.0 : (N sumXY - sumX sumY) / denominatorR

r2 = r * r

predictedY = slopeM * targetX + interceptB

Standard: NIST / ISO mathematical definitions

Worked Example

A laboratory physicist testing Hooke's Law records spring extensions under 5 masses and fits a line with slope m = 9.80 N/kg and R^2 = 1.000, confirming exact linear elasticity.

Understanding Your Result

Chemical calculations require careful attention to significant figures — your result is only as precise as your least precise input. For laboratory work, verify that temperature, pressure, and concentration conditions match the formula's assumed standard state (typically 25°C and 1 atm). Compare your result against published reference values for the specific compound or reaction. Safety note: laboratory chemical calculations should always be verified by a qualified chemist before practical application.