A two-sample t-test has a lot in common with simple regression. This output summarizes the results of fitting a simple regression with only a dummy variable as the explanatory variable. The data are the same salary data used in the text, with salary regressed on Group.

(a) Interpret the estimated intercept and slope in the fitted simple regression.
(b) What is the relationship between the t-statistic for the slope in this simple regression and the t-statistic for the two-sample t-test? (See Table 25.1.)
(c) What assumption is needed in this simple regression approach to a two-sample t-test that we did not require previously?

170 16 150 140 130 120 110 0 0.25 0.5 0.75 1 Group 0.0312 12.402 174 /2 Estimate Std Error t-Stat p-Value Term Intercept 140.0339 16146 86.73 0.0001 Group 4.6705 .9860 2.35 0.0198