Answer to Question #48403 in Economics for darren

Question

1. In a simple regression model (one X variable only), if the t statistic for the slope is 2.5, what is the value of F. State the null and alternative hypothesis for both tests. How important is the assumption of a normal error term in using the t test?

Answer 1

Simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible.
In a simple regression model (one X variable only), if the t statistic for the slope is 2.5, F = 2.5X
The relative error in the normal approximation a distribution may be huge even when the absolute error is small.