// File MIT-Lab-10-01-02-01.txt. Edition 1/19/2013.

// Title
Random_Influences_and_the_Sum_of_Coefficient_Estimates

// 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
0

// Constant
  10 40 10 30

// Coef1
  -1.1 -.1 .1 -.5

// Coef2
  -.2 .6 .1 .4

// Coef3
  -.2 .6 .1 .1

// Error Term Var
  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 .6536 24 -.5 .4 .1
Two Objectives:
_
First, show that we cannot expect the sum of the coefficient estimates to equal the
 the sum of the actual coefficient values.
_
Second, show that the sum of the coefficient estimates is a random varaible.
_
To do so, we consider a regression with three explanatory variables. In each
 repetition, the three coefficient estimates and their sum are reported beneath
 the Coef Ests: 1, 2, 3, and Sum line.
 
 
` -1 .6536 24 -.5 .4 .1
1. By default, the actual values of the three coefficients are -.5, .4, and .1.
 What does the sum of the actual coefficient values equal?
_
2. Now, click Start to run the first repetition.
_
2a. Individually, does each
 of the coeficient estmates equal the actual value of the coefficient?
_
2b. Does the sum of the coefficient estimates equal the sum of the actual
 coefficient values in the first repetition?
 

`
3. Click Continue to run the second repetition. Does the sum of the
 coefficient estimates equal the sum of the actual coefficient values
 in the second repetition?
_
4. Click Continue a few more times. Can we expect the sum of the coefficient
 estimates to equal the sum of the actual coefficient values?
_
5. Is the sum of the coefficient estimates a random variable? Explain.