//  File New-Lec2-02-02-01-04.txt. Edition 7/21/2010.


//  Lab Specs
//    Window Title
         Distribution_of_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 0 0
Objective: Exploit the relative frequency interpretation of probability to
 show that the equation we derived for the mean of the coefficient estimate's
 probability distribution is correct. The equation indicates that the mean
 of the coefficient estimate's probability distribution equals the actual value
 of the coefficient. Therefore, we wish to show that the average of the
 numerical values of the coefficient estimates equals after many, many repetitions will
 equal the actual value of the coefficient. 


` 3 0 2 500 50 2 0 30 0 0
1a. Using the appropriate equation, calculate the mean of the coefficient
 estimate's probability distribution when the actual coefficient is 2.
_
1b. Be certain that the Pause checkbox is cleared. Click Start. After many,
 many repetitions click Stop. What is the mean of the numerical values of the
 coefficient estimates after many, many repetitions of the experiment?
 Is this consistent with the equation for the mean of the probability distribution (part 1a)?


` 3 0 2 500 50 4 0 30 0 0
2a. Note that the actual coefficient value has been reset to 4. 
 Using the appropriate equation, calculate the mean of the 
 coefficient estimate's probability distribution when the actual coefficient is 4.
_
2b. Click Start. After many,
 many repetitions click Stop. What is the mean of the numerical values of the
 coefficient estimates after many, many repetitions of the experiment?
 Is this consistent with the equation for the mean of the probability distribution (part 2a)?


` 3 0 2 500 50 6 0 30 0 0
3a. Note that the actual coefficient value has been reset to 6. 
 Using the appropriate equation, calculate the mean of the 
 coefficient estimate's probability when the actual coefficient is 6.
_
3b. Click Start. After many,
 many repetitions click Stop. What is the mean of the numerical values of the
 coefficient estimates after many, many repetitions of the experiment?
 Is this consistent with the equation for the mean of the probability distribution (part 3a)?

` 3 0 2 500 50 6 0 30 0 0
4. Review your answers to questions 1, 2, and 3. Does the ordinary least
 squares (OLS) estimation procedure systematically overestimate or
 underestimate the actual value of the coefficient? Is the ordinary
 least squares estimation procedure unbiased?