//  File New-Lec2-02-03-01-04.txt. Edition 9/24/2012.


//  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 1
Objective: Exploit the relative frequency interpretation of probability to
 show that the equation we derived for the variance of the coefficient
 estimate's probability distribution is correct. That is, show that
 the equation tell us what the variance of the numerical values of the
 coefficient estimates will equal after many, many repetitions.
_
1. In the simulation, when the sample size is 3 and the range of the x's is from 0 to 30,
 the values of the x's are 5, 15, and 25. Click Start and then Continue to convince yourself
 that this is correct. Calculate the sum of squared x deviations from their mean.


` 3 0 2 500 50 2 0 30 0 0
2a. Using the appropriate equation, calculate the variance of the coefficient
 estimate's probability distribution.
_
2b. Be certain that the Pause checkbox is cleared and click Start. After
 many, many repetitions, click Stop. What is the variance of the numerical
 values for the coefficient estimates? Is your answer consistent with the
 variance you calculated for the probability distribution (part 2a)?