// File New-Lec3-02-03-02-01.txt. Edition 7/14/2010. // Title F-Statistic_Distribution // Print F-statistics results (0 no) // 0 Unrestricted estimates only // 1 Both sets of estimates // 2 Both sets of estimates and the F-statistic // 3 Both sets of estimates, the F-statistic, and the Probability 3 // Constant 10 40 10 30 // Coef1 -1.3 -.3 .1 -.5 // Coef2 -.2 1.5 .1 .4 // Coef3 -.3 .3 .1 .1 // Error Term Var // 200.0 500.0 150.0 200.0 1.0 5.0 1.0 2.0 // Sample Size 10 30 1 24 // Problem Specs // Pause // At Least FValue // SampleSize // Coef1, Coef2, Coef3 ` -1 .64 24 -.5 .4 .1 Objective: Use a simulation to calculate the probability that the F-statistic would be at least as large as the value that actually occurred, if the null hypothesis (and hence the restriction) were true. _ Begin by noting the default values are based on our null hypothesis: ____The sum of the actual coefficient values equals 0. ____The coefficient sum restriction equals 0. When calculating the coefficient estimates for the restricted regression, the simulation enforces the restriction imposed by the null hypothesis. ` An At Least F-Value of .64 is specified. The simulation will report the percent of repetitions in which the F-statistic is at least .64. Recall that .64 was the F-statistic we computed from our restricted and unrestricted regressions. _ This At Least Percent is just the information we need to determine the probability that the F-statistic would be at least as large as the value we obtained if the null hypothesis were true. ` -1 .64 24 -.5 .4 .1 We can apply the relative frequency interpretation of probability. After many, many repetitions, the At Least Percent equals the probability that the F-statistic is at least .64 in one repetition if the null hypothesis were true. _ But first we should convince ourselves that the simulation is computing the values correctly. ` -1 .64 24 -.5 .4 .1 1. Click Start. Based on the value of the restricted and unrestricted sums of squared errors is the simulation computing the F-statistic correctly for the first repetition. Is the simulation computing the At Least Percent correctly? _ 2. Click Continue a few times to convince yourself the the simulation is computing both the F-statistic and the At Least Percent correctly. ` 0 .64 24 -.5 .4 .1 3. Note that the Pause checkbox is now cleared. Click Continue and then after many, many repetitions, click Stop. In what percent of the repetitions does the F-statistic equal .64 or more? What is the probability that the F-statistic in any one repetition will be at least .64?