The t test for the simple regression coefficient
Fortunately, it turns out that the t test is applicable to a variety of problems. In particular, it is applicable to the problem of testing the statistical significance of a regression coefficient. Under a set of assumptions that are usually referred to as the Gauss-Markov conditions, the t test can be used to test the significance of a regression coefficient. We will defer a detailed discussion of these assumptions and the consequences of violating them to a later point. For the time being, it is enough to know that these assumptions have to do with the distribution of the errors of prediction. In regression analysis, we are often interested in the simple question of whether or not there is a linear relationship between two variables in the population. Stated in statistical jargon, we wish to test the null hypothesis that the population regression coefficient for the regression of a dependent variable on an independent variable is equal to zero.
KeywordsStandard Error Null Hypothesis Regression Coefficient Probability Density Function Error Variance
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