// File New-Lec3-02-02-02-01.txt. Edition 7/14/2010.

// Title
F-Statistic_Distribution

// Print F-statistics results (0 no)
2
// 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

// 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
Two Objectives:
_
First, show that the F-statistic is non-negative.
_
Second show that the F- statistic is a random variable.
_
To do so, we consider an unrestricted regression and a restricted regression.
 The unrestricted regression imposes no conditions on the coefficients. In the
 restricted regression, the sum of the coefficients must equal a specified
 value. By default, the specified sum value is 0.

`
For each repetition, the following information is reported to the left:
____Res: Estimates of the restricted coefficients and their sum
____SSRR: Restricted sum of squared residuals
____Unr: Eestimates of the unrestricted coefficients and their sum
____SSRU: Unrestricted sum of squared residuals
____F-statistic: The F-statistic
 
` -1 .64 24 -.5 .4 .1
We begin by showing that the simulation calculates the F-statistic correctly.
_
1. Click Start. In the first repetition: 
_  1a. What does the restricted and unrestricted sum of squares equal?
_  1b. What does the restricted and unrestricted degrees of freedom equal?
_  1c. What does the F-statistic equal?
Is the simulation calculating the F-statistic correctly?
_
2. By clicking Continue repeat this process until you are convinced that
 the simulation ia calculating the F-statistic correctly.

` -1 .64 24 -.5 .4 .1
3. Could the restricted sum of squared residuals ever be
 less than the unrestricted sum? Could the F-statistic ever be negative?
_
4. Now, confirm your answer to question 3 by using the simulation.
 Click Start to run the first repetition. How are the restricted and 
 unrestricted sum of squared residuals related? What is the sign of
 the F-statistic?

`
5. Click Continue to run the second repetition. How are the restricted and 
 unrestricted sum of squared residuals related? What is the sign of
 the F-statistic?
_
6. Click Continue a few more times. Is the restricted sum of squared residuals ever less than
 the unrestricted sum? Is the F-statistic ever negative?
_
7. Is the F-statistic a random variable? Explain.