Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 10

Take as given the properties of the chi-square distribution listed in the text. Show how those properties, along with the definition of an F random variable, imply the stated property of the F distribution (concerning ratios of quadratic forms).

Step 1 of 2

Chi-Square distribution consists of a chi-square random variable as the sum of squared independent standard normal random variables.

The most important property of chi-square distribution () is that if a variable u is normally distributed such as N(0,I) and A is a n×n symmetric idempotent matrix with rank q, then .