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.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=a/c with Durbin-Watson statistic=1.875 and sum of squared successive residual differences=180.
- residual sum of squares=96.
- 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
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
- Read Durbin-Watson statistic, sum of squared successive residual differences.
- Evaluate the principal relationship: b=a/c.
- 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))
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)));
}
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)));
}
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
MATLAB
function result = durbin_watson_statistic_solve_b(c, a)
result = (a / c);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a / c);
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 textbookCite 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 .