Analyze regression slope evidence with clear hypothesis testing. Review degrees of freedom, alpha, and effect. Download outputs and visualize significance regions with confidence quickly.
The calculator tests whether the slope coefficient differs from a hypothesized value. Most users test against zero.
Test statistic: t = (b₁ − β₁₀) / SE(b₁)
Degrees of freedom: df = n − 2
Two tailed p value: p = 2 × [1 − Ft(|t|, df)]
Right tailed p value: p = 1 − Ft(t, df)
Left tailed p value: p = Ft(t, df)
The slope is significant when the p value is less than or equal to alpha. Critical values come from the t distribution.
| Scenario | Estimated Slope | Standard Error | Sample Size | Alpha | Null Slope | Alternative |
|---|---|---|---|---|---|---|
| Advertising spend vs sales | 2.1500 | 0.4800 | 20 | 0.05 | 0.0000 | β₁ ≠ β₁₀ |
| Hours studied vs exam score | 4.1800 | 0.7300 | 16 | 0.05 | 0.0000 | β₁ > β₁₀ |
| Price vs quantity demanded | -1.2200 | 0.3100 | 24 | 0.01 | 0.0000 | β₁ < β₁₀ |
This test checks whether the predictor has a measurable linear relationship with the response. A significant slope suggests that changes in the predictor are associated with changes in the outcome, beyond random noise alone.
Use this result together with residual checks, context knowledge, and effect size interpretation. Statistical significance does not guarantee practical importance.
It tests whether a regression slope is statistically different from a hypothesized value, usually zero. The output includes the t statistic, p value, critical value, confidence interval, and decision.
Simple linear regression estimates two parameters: the intercept and the slope. Because of that, the slope significance test uses n − 2 degrees of freedom.
Use a two tailed test when you only care whether the slope differs from the null value in either direction. It is the most common default choice.
Use a one tailed test only when your research question and theory specify a direction before analyzing the data. Switching afterward can bias conclusions.
The p value measures how surprising your observed t statistic would be if the null slope were true. Smaller values indicate stronger evidence against the null hypothesis.
No. A significant slope shows evidence of a linear association within the model. It does not, by itself, prove that the predictor causes the outcome.
Yes. Enter any hypothesized slope under the null hypothesis field. The calculator will compare your estimated slope against that reference value.
The usual assumptions are linearity, independent observations, constant error variance, and roughly normal residuals. Serious violations can make p values and intervals misleading.
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.