How is the P-value computed in multiple linear regression analysis?

In multiple linear regression analysis, the p-value for each independent variable is computed using a hypothesis test, most often the t-test. The formula requires dividing the coefficient estimate for each independent variable by its standard error. This ratio has a t-distribution with degrees of freedom equal to the sample size less the number of independent variables. The p-value indicates the likelihood of seeing a t-statistic that is as severe as, or more extreme than, the computed value under the null hypothesis (no influence of the independent variable). Lower p-values indicate more evidence against the null hypothesis, implying a meaningful association.
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