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

// Title
F-Statistic_Distribution

// Print F-statistics results (0 no)
1
// 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
Objective: Confirm that the restricted sum of squared residuals is never less
 than the unrestricted sum of squared residuals.
_
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.
_
Note that the actual coefficient values do indeed sum to 0. The
 restriction on the coefficient sum is actually true.


`
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


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

`
3. Click Continue to run the second repetition. How are the restricted and
 unrestricted sum of squared residuals related?
_
4. Click Continue a few more times.Is the restricted sum of squared residuals ever less than
 the unrestricted sum?