//  File MIT-Lab-18-04-01-04.txt.  Edition 1/21/2013.


//  Lab Specs
//    Window Title
         Unbiased_and_Consistent_Estimation_Procedure:_Any_Two
//    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
         -2.0 6.0 2.0 2.0
//    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 0 2 500 50 2 0 30 0 0
Objective: Illustrate that an estimation procedure is unbaised but not consistent.
_
Focus your attention on the drop down box just above the Start button.
 Select the Any Two estimation procedure.
_
This simulation will show that the Any Two estimation procedure is unbiased
 but not consistent.


`
1. Be certain that the Any Two estimation procedure has been selected.
 Initially, the sample size is specified as 3. Click the Start button
 and after many, many repetitions click the Stop button.
1a. What does the mean of the coefficient estimates equal?
1b. What does the variance of the coefficient estimates equal?
_
2. Increase the sample size from 3 to 6. Click the Start button and after many,
 many repetitions click the Stop button. 
2a. What does the mean of the coefficient estimates equal?
2b. What does the variance of the coefficient estimates equal?


`
3. Based on these results, is the Any Two estimation procedure
________3a. unbiased?
________3b. consistent?