Linearized Equation Calculator
Linearized equation calculator works out Fitted equation and Slope (b) from X values (predictor), Y values (response) and Model. The default figures on this page give fitted equation of y = 2.197121 e^(0.183258x); change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
7 steps
- n = 5 observations.
- Taking logs turns y = a e^(bx) into ln y = ln a + b x, a straight line fitted by ordinary least squares.
- Fitted parameters: a = 2.19712109, b = 0.18325815.
- Fitted model: y = 2.197121 e^(0.183258x)
- SST = 0.56785112 splits into SSR = 0.33583548 explained and SSE = 0.23201564 unexplained, so R^2 = 0.59141467.
- Standard error of the estimate s = sqrt(SSE / 3) = 0.27809809.
- Prediction at 6: 6.59753955.
All coefficientstable
Fitted valuestable
Residualstable
Scatter points with the fittable
| x | y | fitted | residual |
|---|---|---|---|
| 1 | 2 | 2.639016 | -0.639016 |
| 2 | 4 | 3.169786 | 0.830214 |
| 3 | 5 | 3.807308 | 1.192692 |
| 4 | 4 | 4.573051 | -0.573051 |
| 5 | 5 | 5.492803 | -0.492803 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the linearized equation calculator calculates
Fits a least-squares model to paired data and reports the equation, slope, intercept, correlation, R squared, adjusted R squared, standard errors, t and F tests, the ANOVA sums of squares, residuals and a prediction at any chosen x. Handles simple, multiple, weighted, exponential, power, logarithmic and binary logistic fits.
How to use this linearized equation calculator
Enter X values (predictor), Y values (response), Model and Predict y at x =. Fitted equation updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Fitted equation, Slope (b) and Intercept (a).
The method follows NIST/SEMATECH e-Handbook of Statistical Methods, 4.1 Introduction to Process Modeling and 1.3.5.11 Linear Regression, Draper, N.R. & Smith, H. (1998), Applied Regression Analysis, 3rd edition, Wiley, McCullagh, P. & Nelder, J.A. (1989), Generalized Linear Models, 2nd edition, Chapman & Hall and Kay, S.M. (1993), Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, chapter 12.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What information do I need for the linearized equation calculator?
You need X values (predictor), Y values (response), Model, Predict y at x = and Confidence level. The page opens with default figures that give fitted equation of y = 2.197121 e^(0.183258x), so you can see the scale before entering your own.
What does this linearized equation calculator show?
It shows Fitted equation, Slope (b), Intercept (a), All coefficients, Number of observations, Correlation r, R squared and Adjusted R squared, with the working and any warnings for your entries.
Can I check how the linearized equation calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.