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

// 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:
 
 
` -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. Individually, does each
 of the coeficients equal its actual value? 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 sum of the actual coefficient values?
_
5. Is the estimate sum a random variable? Explain.