Mathematics · Statistics

Durbin–Watson Residual Statistic residual sum of squares Solver

Rearrange the durbin–watson residual statistic relationship and solve for residual sum of squares.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
residual sum of squares96
Reconstructed Durbin-Watson statistic1.875

Calculation steps

  1. Use b=a/c with Durbin-Watson statistic=1.875 and sum of squared successive residual differences=180.
  2. residual sum of squares=96.
  3. Substitution into c=a/b reconstructs 1.875.

Understand Durbin–Watson Residual Statistic: solve residual sum of squares

One idea, three depths

Choose how deeply to explain Durbin–Watson Residual Statistic: solve residual sum of squares

Durbin–Watson Residual Statistic: solve residual sum of squares: Rearrange the durbin–watson residual statistic relationship and solve for residual sum of squares.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Durbin–Watson Residual Statistic: solve residual sum of squares to answer this question: rearrange the durbin–watson residual statistic relationship and solve for residual sum of squares? Enter Durbin-Watson statistic and sum of squared successive residual differences; the calculator shows residual sum of squares. For example: sum of squared successive residual differences=180 and residual sum of squares=96 produce Durbin-Watson statistic=1.875. The answer tells you residual sum of squares.

Age 15Explain it to a 15-year-oldConnect it to the formula

The Durbin-Watson statistic compares squared successive residual differences with residual sum of squares. This page isolates residual sum of squares and verifies it in the original relationship. The rule is b=a/c. Its input values are Durbin-Watson statistic, sum of squared successive residual differences, and the main result is residual sum of squares. For example: sum of squared successive residual differences=180 and residual sum of squares=96 produce Durbin-Watson statistic=1.875.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated durbin–watson residual statistic: solve residual sum of squares relation over the valid real-number domain stated below. The implemented relation is b=a/c, evaluated from Durbin-Watson statistic, sum of squared successive residual differences to produce residual sum of squares. The Durbin-Watson statistic compares squared successive residual differences with residual sum of squares. This page isolates residual sum of squares and verifies it in the original relationship. Its usual interpretation assumes ordered residuals and a regression model with an intercept.

Inputs and valid domain

  • Durbin-Watson statistic must be a finite real number.
  • sum of squared successive residual differences must be a finite real number.

Important boundary: Its usual interpretation assumes ordered residuals and a regression model with an intercept.

The formula

b=a/c

How the calculator works through it

It substitutes Durbin-Watson statistic, sum of squared successive residual differences into the formula and exposes every numerical step above. The main output is residual sum of squares, accompanied by Reconstructed Durbin-Watson statistic.

Read the result correctly

The residual sum of squares is the direct answer to “rearrange the durbin–watson residual statistic relationship and solve for residual sum of squares.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

sum of squared successive residual differences=180 and residual sum of squares=96 produce Durbin-Watson statistic=1.875.

Where this model stops being reliable

Its usual interpretation assumes ordered residuals and a regression model with an intercept.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Durbin–Watson Residual Statistic: solve residual sum of squares works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Durbin–Watson Residual Statistic: solve residual sum of squares uses b=a/c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Averages and representative values

    Representative values help you judge what the Durbin–Watson Residual Statistic: solve residual sum of squares inputs summarise and what the result can legitimately describe.

    Review this foundation about 5 min

Optional enrichment

  • Spread and measurement variation

    Variation is not always part of the Durbin–Watson Residual Statistic: solve residual sum of squares formula, but it helps you judge how stable a reported result may be.

    Review this foundation about 6 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read Durbin-Watson statistic, sum of squared successive residual differences.
  2. Evaluate the principal relationship: b=a/c.
  3. Return residual sum of squares and check the domain conditions described above.
Python
            from math import *

def durbin_watson_statistic_solve_b(c, a) -> float:
    return (a / c)

assert abs(durbin_watson_statistic_solve_b(1.875, 180) - 96) < 1e-6 * max(1.0, abs(96))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double durbin_watson_statistic_solve_b(double c, double a) {
    return (a / c);
}

int main(void) {
    const double expected = 96;
    const double actual = durbin_watson_statistic_solve_b(1.875, 180);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double durbin_watson_statistic_solve_b(double c, double a) {
    return (a / c);
}

int main() {
    constexpr double expected = 96;
    const double actual = durbin_watson_statistic_solve_b(1.875, 180);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double durbin_watson_statistic_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global durbin_watson_statistic_solve_b
section .text

durbin_watson_statistic_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-16]
    divsd xmm0, [rbp-8]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = durbin_watson_statistic_solve_b(c, a)
    result = (a / c);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a / c);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Introductory Statistics 2e

Read the free OpenStax statistics textbook
Cite this book
APA 7
Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
MLA 9
Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
Chicago author-date
Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Durbin–Watson Residual Statistic residual sum of squares Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver

MLA 9

MW SysArc. “Durbin–Watson Residual Statistic residual sum of squares Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Durbin–Watson Residual Statistic residual sum of squares Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver.

Harvard

MW SysArc (2026) ‘Durbin–Watson Residual Statistic residual sum of squares Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_durbin_watson_statistic_solve_b_2026,
  author = {{MW SysArc}},
  title = {Durbin–Watson Residual Statistic residual sum of squares Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Durbin–Watson Residual Statistic residual sum of squares Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/statistics/durbin-watson-statistic-residual-sum-of-squares-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Durbin–Watson Residual Statistic: solve residual sum of squares do?

Rearrange the durbin–watson residual statistic relationship and solve for residual sum of squares.

How does the Durbin–Watson Residual Statistic: solve residual sum of squares work?

The calculator applies b=a/c. The Durbin-Watson statistic compares squared successive residual differences with residual sum of squares. This page isolates residual sum of squares and verifies it in the original relationship.

What can I learn from the Durbin–Watson Residual Statistic: solve residual sum of squares?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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