Testing linear hypotheses after regression
Channel: Mikko Rönkkö
Date: 2019-07-14

In this video, the focus is on the application of regression analysis in testing hypotheses beyond the basic assessment of whether regression coefficients differ from zero. It highlights the utility of regression analysis in exploring more complex questions, such as whether a coefficient differs from a non-zero value or if two coefficients are equivalent in the population. The video uses an example involving the Prestige data set, examining variables like prestige, education, women, and occupation types, specifically focusing on the professional and white-collar categories compared to a blue-collar reference category.

The video explains the use of the Wald test to determine the statistical significance of differences between coefficients. It elaborates on how to calculate the test by squaring the estimate of the difference between coefficients and dividing it by the squared standard error. The importance of considering the variance and covariance of the estimates is also discussed, emphasizing that the variance of the difference between two variables is the sum of their individual variances minus twice their covariance. The video concludes by stressing the necessity of logical reasoning in comparing regression coefficients, as statistical software will not determine the appropriateness or relevance of such comparisons. The proper application of these methods enables significant insights into the data, illustrated through the example provided.

Slides: https://osf.io/wmhxy