How to conduct hypothesis testing for regression analysis in data analysis?

Hypothesis testing in regression analysis evaluates whether predictor variables significantly relate to the outcome variable. This involves statistically testing if regression coefficients differ significantly from zero, typically using t-tests for individual coefficients and F-tests for overall model significance or groups of predictors. Key principles involve specifying null and alternative hypotheses (e.g., H₀: β₁ = 0 vs. H₁: β₁ ≠ 0). The t-test utilizes the coefficient estimate, its standard error, and degrees of freedom to calculate a test statistic, compared against a t-distribution to obtain a p-value. The F-test compares nested models. Essential conditions include meeting regression assumptions: linearity, independence, homoscedasticity, and normality of residuals. Significance level (α, e.g., 0.05) must be predetermined. To implement, formulate hypotheses based on the research question. Compute the test statistic (t or F) using regression output. Compare the p-value to α: reject H₀ if p ≤ α, indicating a significant relationship. Alternatively, check if the 95% confidence interval for the coefficient excludes zero. Always validate assumptions via residual analysis. This testing is fundamental across disciplines (economics, medicine, social sciences) for identifying meaningful predictors, evaluating model utility, and informing decisions based on data relationships.