Mathematics · Statistics
Regression Coefficient of Determination residual sum of squares Solver
Rearrange the regression coefficient of determination 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 a=b(1−c) with coefficient of determination=0.8 and total corrected sum of squares=900.
- residual sum of squares=179.99999999999997.
- Substitution into c=1−a/b reconstructs 0.8.
Understand Regression Coefficient of Determination: solve residual sum of squares
One idea, three depths
Choose how deeply to explain Regression Coefficient of Determination: solve residual sum of squares
Regression Coefficient of Determination: solve residual sum of squares: Rearrange the regression coefficient of determination relationship and solve for residual sum of squares.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Regression Coefficient of Determination: solve residual sum of squares to answer this question: rearrange the regression coefficient of determination relationship and solve for residual sum of squares? Enter coefficient of determination and total corrected sum of squares; the calculator shows residual sum of squares. For example: residual sum of squares=180 and total corrected sum of squares=900 produce coefficient of determination=0.8. The answer tells you residual sum of squares.
Age 15Explain it to a 15-year-oldConnect it to the formula
Coefficient of determination is one minus residual sum of squares divided by total corrected sum of squares. This page isolates residual sum of squares and verifies it in the original relationship. The rule is a=b(1−c). Its input values are coefficient of determination, total corrected sum of squares, and the main result is residual sum of squares. For example: residual sum of squares=180 and total corrected sum of squares=900 produce coefficient of determination=0.8.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated regression coefficient of determination: solve residual sum of squares relation over the valid real-number domain stated below. The implemented relation is a=b(1−c), evaluated from coefficient of determination, total corrected sum of squares to produce residual sum of squares. Coefficient of determination is one minus residual sum of squares divided by total corrected sum of squares. This page isolates residual sum of squares and verifies it in the original relationship. Models without an intercept or evaluated out of sample can produce values below zero.
Inputs and valid domain
- coefficient of determination must be a finite real number.
- total corrected sum of squares must be a finite real number.
Important boundary: Models without an intercept or evaluated out of sample can produce values below zero.
The formula
a=b(1−c)
How the calculator works through it
It substitutes coefficient of determination, total corrected sum of squares into the formula and exposes every numerical step above. The main output is residual sum of squares, accompanied by Reconstructed coefficient of determination.
Read the result correctly
The residual sum of squares is the direct answer to “rearrange the regression coefficient of determination 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
residual sum of squares=180 and total corrected sum of squares=900 produce coefficient of determination=0.8.
Where this model stops being reliable
Models without an intercept or evaluated out of sample can produce values below zero.
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 Regression Coefficient of Determination: 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
Regression Coefficient of Determination: solve residual sum of squares uses a=b(1−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 Regression Coefficient of Determination: 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 Regression Coefficient of Determination: 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 coefficient of determination, total corrected sum of squares.
- Evaluate the principal relationship: a=b(1−c).
- Return residual sum of squares and check the domain conditions described above.
Python
from math import *
def regression_coefficient_determination_solve_a(c, b) -> float:
return (b * (1.0 - c))
assert abs(regression_coefficient_determination_solve_a(0.8, 900) - 179.99999999999997) < 1e-6 * max(1.0, abs(179.99999999999997))
C
#include <assert.h>
#include <math.h>
double regression_coefficient_determination_solve_a(double c, double b) {
return (b * (1.0 - c));
}
int main(void) {
const double expected = 179.99999999999997;
const double actual = regression_coefficient_determination_solve_a(0.8, 900);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double regression_coefficient_determination_solve_a(double c, double b) {
return (b * (1.0 - c));
}
int main() {
constexpr double expected = 179.99999999999997;
const double actual = regression_coefficient_determination_solve_a(0.8, 900);
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 regression_coefficient_determination_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global regression_coefficient_determination_solve_a
section .text
regression_coefficient_determination_solve_a:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x3ff0000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
subsd xmm0, [rbp-8]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = regression_coefficient_determination_solve_a(c, b)
result = (b * (1.0 - c));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, b_] := (b * (1.0 - 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). Regression Coefficient of Determination residual sum of squares Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/regression-coefficient-determination-residual-sum-of-squares-solver
MLA 9
MW SysArc. “Regression Coefficient of Determination residual sum of squares Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/regression-coefficient-determination-residual-sum-of-squares-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Regression Coefficient of Determination residual sum of squares Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/regression-coefficient-determination-residual-sum-of-squares-solver.
Harvard
MW SysArc (2026) ‘Regression Coefficient of Determination residual sum of squares Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/regression-coefficient-determination-residual-sum-of-squares-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_regression_coefficient_determination_solve_a_2026,
author = {{MW SysArc}},
title = {Regression Coefficient of Determination residual sum of squares Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/regression-coefficient-determination-residual-sum-of-squares-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Regression Coefficient of Determination 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/regression-coefficient-determination-residual-sum-of-squares-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Regression Coefficient of Determination: solve residual sum of squares do?
Rearrange the regression coefficient of determination relationship and solve for residual sum of squares.
How does the Regression Coefficient of Determination: solve residual sum of squares work?
The calculator applies a=b(1−c). Coefficient of determination is one minus residual sum of squares divided by total corrected sum of squares. This page isolates residual sum of squares and verifies it in the original relationship.
What can I learn from the Regression Coefficient of Determination: 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 .