| Satisfaction | Hours | Age | Income |
|---|---|---|---|
| 4 | 38 | 29 | 45000 |
| 5 | 41 | 33 | 52000 |
| 3 | 36 | 27 | 39000 |
| 4 | 40 | 31 | 48000 |
| 2 | 30 | 24 | 32000 |
| 5 | 45 | 35 | 61000 |
This tool fits: Y = β₀ + β₁X₁ + … + βₖXₖ + ε
- β = (XᵀX)⁻¹ Xᵀy
- R² = 1 − SSE/SST with SSE = Σeᵢ² and SST = Σ(yᵢ − ȳ)²
- Robust HC1: Var(β)= (n/(n−p)) (XᵀX)⁻¹ (Xᵀ diag(e²) X) (XᵀX)⁻¹
- VIF: VIFⱼ = 1/(1 − R²ⱼ) from regressing Xⱼ on other predictors
- Paste your dataset into the CSV box.
- Pick the delimiter and header row option.
- Select dependent variable (Y) and predictors (X).
- Choose intercept, robust errors, and standardization options.
- Press “Run Regression” to show results above.
- Download CSV or PDF using the buttons.
Survey Model Setup
Upload or paste a CSV where each row is one respondent and each column is a numeric measure, such as a 1–5 satisfaction scale. This tool builds a design matrix from selected predictors and, when enabled, adds an intercept term to capture baseline response levels. With n observations and p parameters, the residual degrees of freedom are n−p, which drives standard errors and confidence ranges. Aim for at least 10 responses per predictor, and prefer listwise deletion when missingness is modest. Mean imputation can support quick exploratory checks.
Interpreting Coefficients
Each coefficient estimates the expected change in Y for a one‑unit increase in an X, holding other predictors constant. For example, β=0.25 on “Hours” implies a quarter‑point rise in satisfaction per additional hour, on the chosen scale. If you enable standardization, inputs become z‑scores, so β values compare influence across variables with different units. Use standardized inputs to compare effect magnitudes directly. The intercept is the expected Y when predictors equal zero.
Diagnostics That Matter
Model fit is summarized by R² and adjusted R². R² reports the share of variance explained, while adjusted R² penalizes extra predictors that do not add signal. RMSE reports typical prediction error in Y units. To flag multicollinearity, the calculator reports VIF for each predictor; values above 5 often suggest redundant overlap, and values above 10 can destabilize estimates. The F statistic summarizes overall model evidence using df model and df residual.
Robust Inference
Survey outcomes often show uneven variance across groups, such as income bands or age cohorts. Selecting robust (HC1) standard errors helps protect p‑values when residual variance is heteroskedastic. Coefficients stay the same, but standard errors, t‑statistics, and confidence intervals adjust. If robust and conventional results diverge, examine outliers and consider subgroup checks.
Reporting Outputs
Use the coefficient table to communicate estimates, uncertainty, and practical relevance. A p‑value below 0.05 is common, but confidence intervals convey effect size precision more clearly. The predictions preview shows how the fitted model tracks observed values and where residuals cluster. Export CSV for spreadsheets or PDF for documentation, and record options for transparent reporting. Include n, predictors, missing handling, and standard error type.