What does a smaller p-value in regression analysis signify?

A smaller p-value in regression analysis indicates stronger evidence against the null hypothesis. The null hypothesis in the context of regression typically asserts that there is no relationship between the independent and dependent variables being studied. When conducting a hypothesis test, researchers calculate the p-value to determine the likelihood of observing the data, or something more extreme, if the null hypothesis were true.

By having a smaller p-value, it suggests that the observed data is increasingly unlikely under the assumption that the null hypothesis holds true. This leads to the potential rejection of the null hypothesis in favor of an alternative hypothesis, which posits that there is indeed an effect or relationship present. Typically, a threshold such as 0.05 or 0.01 is used to establish statistical significance, where a smaller p-value suggests greater confidence in asserting that the relationship observed in the data is not due to random chance.

In contrast, other factors mentioned do not directly relate to the statistical significance indicated by the p-value in this context. Higher variance between forecast and actual does not correlate directly with the significance of the relationship; it simply pertains to the accuracy of predictions. Additionally, increased absolute percentage variation and higher location quotient pertain to different statistical measures or concepts that do not influence the interpretation of p-values.