Analyze slope significance with dependable regression t statistic outputs. Enter coefficients, errors, and assumptions once. Download tables, verify findings, and explain decisions with confidence.
| Observation | X | Y |
|---|---|---|
| 1 | 1 | 2.1 |
| 2 | 2 | 3.9 |
| 3 | 3 | 6.2 |
| 4 | 4 | 7.8 |
| 5 | 5 | 10.4 |
| 6 | 6 | 11.7 |
Use this sample in raw data mode to estimate a simple regression slope and test whether the slope differs from zero.
Summary mode: t = (b - b0) / SE(b)
Degrees of freedom: df = n - k - 1
Raw data slope: b1 = Sxy / Sxx
Slope standard error: SE(b1) = sqrt(MSE / Sxx)
Confidence interval: estimate ± t critical × standard error
Here, b is the estimated coefficient, b0 is the hypothesized value, n is sample size, and k is the number of predictors excluding the intercept.
This calculator helps you test whether a regression coefficient is statistically different from a chosen hypothesis. It works for summary inputs and raw paired data. That makes it useful for quick validation, code experiments, model reviews, and debugging. You can estimate the t statistic, p value, critical t, confidence interval, and decision in one place.
A regression coefficient shows how much the response changes when a predictor moves by one unit. The t statistic checks whether that estimated effect is large relative to its uncertainty. A large absolute t value suggests the coefficient is far from the hypothesized value. A small absolute t value suggests the observed effect may be noise.
Software teams review model outputs during testing, feature analysis, experimentation, and reporting. This tool supports that workflow. You can verify a single coefficient from an exported model summary. You can also paste raw x and y values to estimate a simple linear regression slope automatically. That helps when you need a fast quality check before shipping dashboards, scripts, or decision rules.
The p value measures how compatible the observed coefficient is with the null hypothesis. The critical t value gives a threshold for rejection at the selected significance level. The confidence interval shows a plausible range for the true coefficient. When the interval excludes the hypothesized value, the result is usually statistically significant for the same confidence level.
The page shows results above the form after submission. It also includes export options for CSV and PDF files. That makes it easier to document findings, share outputs with teammates, and keep records for audits, notebooks, and notes. The example table and formula guide make the calculator easier to learn and reuse.
Because regression testing appears in pipelines, the calculator keeps assumptions visible. You can choose alpha, set a nonzero null value, and switch between two sided and one sided tests. Those details matter when analysts compare model releases, evaluate refactors, or justify threshold changes more clearly.
The t statistic measures how far a coefficient estimate is from a hypothesized value after scaling by its standard error. Larger absolute values usually indicate stronger evidence against the null hypothesis.
The usual null hypothesis is that the coefficient equals zero. That means the predictor has no linear effect on the response after controlling for the rest of the model.
Use raw data mode when you have paired x and y values and want the calculator to estimate the slope, intercept, error terms, and t statistic for simple linear regression.
Use summary mode when your regression software already provides the coefficient estimate and standard error. You only need sample size, predictor count, alpha, and the hypothesized coefficient value.
Predictor count is needed to compute degrees of freedom in summary mode. The rule is df = n - k - 1, where k excludes the intercept term.
A small p value means the observed coefficient would be unlikely if the null hypothesis were true. Analysts often treat values below alpha as statistically significant evidence.
Yes. Enter any hypothesized coefficient value in the null value field. The calculator will test whether the estimated coefficient differs from that target.
They help you save the result, share it with teammates, attach it to reports, and keep a lightweight audit trail for model reviews or experiment documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.