Linear regression calculator evaluated example 1
Use the page’s labelled starter inputs to verify Linear regression calculator.
Inputs- X values: 1, 2, 3, 4, 5
- Y values: 2, 4, 5, 8, 10
Evaluated result: y = 2x − 0.2
Linear regression calculator
Calculate linear regression with explicit inputs, validation, and a documented formula.
Linear regression calculator
Resulty = 2x − 0.2
What this calculator answers
Fit an ordinary least-squares line to paired x and y observations and report slope, intercept, correlation, covariance, R², and sample size.
Variables, defaults, and limits
- X values
- X values is a number list input. The displayed starter value is 1, 2, 3, 4, 5; it is an example, not a hidden assumption.
- Default: 1, 2, 3, 4, 5
- Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result.
- Y values
- Y values is a number list input. The displayed starter value is 2, 4, 5, 8, 10; it is an example, not a hidden assumption.
- Default: 2, 4, 5, 8, 10
- Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result.
Formula and calculation rule
b=Σ(x₁ᵢ−x̄)(x₂ᵢ−ȳ)/Σ(x₁ᵢ−x̄)²; a=ȳ−bx̄; ŷ=a+bx; x₁=X values; x₂=Y valuesLinear regression calculator evaluates the registered expression “b=Σ(x₁ᵢ−x̄)(x₂ᵢ−ȳ)/Σ(x₁ᵢ−x̄)²; a=ȳ−bx̄; ŷ=a+bx; x₁=X values; x₂=Y values” with the validated inputs. Full calculation precision is retained until the result is formatted for display.
Worked examples
Linear regression calculator evaluated example 2
Enter x values = 0, 2, 5, 9, 14 and y values = 3, 4.2, 7.8, 10.5, 15.1 to fit a non-perfect upward trend.
Inputs- X values: 0, 2, 5, 9, 14
- Y values: 3, 4.2, 7.8, 10.5, 15.1
Evaluated result: y = 0.8706349206x + 2.8961904762
Assumptions
- Linear regression calculator uses the visitor-entered values exactly as labelled; it does not retrieve private records or current rates.
- The calculation is limited to the declared relationship: b=Σ(x₁ᵢ−x̄)(x₂ᵢ−ȳ)/Σ(x₁ᵢ−x̄)²; a=ȳ−bx̄; ŷ=a+bx; x₁=X values; x₂=Y values.
- Intermediate values are not rounded; display rounding is applied only at the presentation boundary.
- The deterministic calculation runs locally and does not upload calculator inputs to the application API.
- The result is an educational arithmetic result and excludes facts that are not represented by an input.
Validation and boundaries
- Every visible required input must be present; a missing value is never replaced with zero.
- NaN, positive or negative infinity, unsafe overflow, and a non-finite final result are rejected.
- Field-specific minimums, maximums, and choices apply to X values, Y values.
- Zero, negative values, and discrete counts are accepted only when the displayed field definition permits them.
- The x and y series must have the same length with at least two paired observations, and the x values must not all be identical.
Review and correction links
Common mistakes
- The lists must have equal length and x must vary; the model fits one straight line and does not handle weights, nonlinear structure, time dependence, measurement error, outlier treatment, or causal inference.
- Confirm the meaning and unit of X values, Y values before calculating; a numerically valid value can still use the wrong convention.
- Do not round intermediate values when checking the result, because early rounding can change the last displayed digits.
- Changing an unstated real-world assumption does not change the calculator until the corresponding displayed input is changed.
- Use the result as the answer to the displayed mathematical question, not to a different word problem with hidden conditions.
Frequently asked questions
- Does a high R² prove that x causes y?
- No. R² measures how much variation in the entered y values is described by this fitted line; it says nothing by itself about causation, omitted variables, or future validity.
- What question does Linear regression calculator answer?
- Calculate linear regression with explicit inputs, validation, and a documented formula. The implemented relationship is b=Σ(x₁ᵢ−x̄)(x₂ᵢ−ȳ)/Σ(x₁ᵢ−x̄)²; a=ȳ−bx̄; ŷ=a+bx; x₁=X values; x₂=Y values.
- Which inputs does Linear regression calculator use?
- It uses the visible fields X values, Y values. No hidden value is substituted for an omitted required input.
- What happens when Linear regression calculator receives an invalid or extreme value?
- The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.
- Why can Linear regression calculator differ from another result?
- Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.
- Can I use Linear regression calculator as professional advice?
- No. It answers the displayed mathematical question and cannot account for omitted real-world facts.
- How can I verify the Linear regression calculator result?
- Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with NIST/SEMATECH e-Handbook of Statistical Methods.
Source and review scope
NIST/SEMATECH e-Handbook of Statistical Methods
Scope: NIST/SEMATECH e-Handbook of Statistical Methods is used to check the formula, definition, or convention relevant to Linear regression calculator. The citation does not supply current personal, lender, tax, medical, or market data.
Source checked: