//  File 55-Lec2-03-01-01-02.txt. Edition 7/14/2010.


//  Lab Specs
//    Window Title
         Random_Influences_-_Coefficient_Estimates
//    Option (0 Normal, 1 Auto, 2 Heter, 3 X-e correlation, 4 Measurement, 5 Consistency (Is this used?)
         0
//    Constant List
         40 60 10 50
//    Coefficient List
         -2 6 2 2
//    iListVarErrors
         50 500 150 500
//    iListSamples
         3 250 1 5
//    iListSamplesAutocorrelation
         3 50 1 40
//    iListSamplesMeasurement
         3 50 1 5
//    iListXMinima
         0 10 10 0
//    iListXMaxima
         20 30 10 30
//    strListFromCoef
         -1.0 4.0 .5 1.0
//    strListToCoef
         1.0 6.0 .5 3.0
//    strListRho
         -.9 .9 .3 .0
//    strListHeter
         -2.0 2.0 1.0 .0
//    strListCoefXAndError
         -.9 .9 .3 .0
//    iListXMeasErrVar
         0 100 50 0


//  Problem Specs
//    SampleSize
//    PauseCheckbox (-1 checked, 0 cleared)
//    EstType (0 Error, 1 Constant, 2 Coefficient)
//    ErrorVar
//    ConstValue
//    CoefValue 
//    xMinValue
//    xMaxValue
//    ErrTermCheckbox (0 not visible and unchecked, -1 visible and checked, 1 visible and unchecked))
//    VarEstAndFromTo (-1 VarEst visible, 0 nothing visible, 1 From-To visible)



` 3 -1 2 500 50 2 0 30 -1 0
Objective: Show that as a consequence of random influences (the error term)
 the coefficient estimate is a random variable; that is, as a consequence
 of random influences we could not determine the value of the coefficient
 estimate with certainty even if we knew the actual value of the coefficient.
_
The Err Term checkbox is checked. The model now includes an error term, 
 reflecting the fact that random influences are present in the real world.
 The Act Err Var list above the Err Term checkbox reports that the
 variance of the error term's probability distribution equals 500.
`
Each repetition of the experiment represents a quiz from a single week.
 The quiz score for each student based on the actual constant, the actual
 coefficient, and the number of minutes the student studies; also, to be
 realistic, the simulation can add a random influence in the form of
 the error term. The ordinary least squares (OLS) estimation
 procedure is used to estimate the values of the constant and coefficient.
_
Since the Act Coef radiobutton is selected, the coefficient estimate will
 be reported.
`
1. Click Start. What is the numerical value of the coefficient estimate
 for the first repetition? Record its value.
_
2. Click Continue. What is the numerical value of the coefficient estimate
 for the second repetition? Record its value.
_
3. Click Continue. What is the numerical value of the coefficient estimate
 for the third repetition? Record its value.
_
4. Click Continue. What is the numerical value of the coefficient estimate
 for the fourth repetition? Record its value.


`
5. Click Stop. In the presence of random influences, can you predict
 the value of the coefficient estimate even if you knew the actual value of
 the coefficient? In the presence of an random influences, is the coefficient
 estimate a random variable? Explain.