//  File New-Lec2-03-01-01-04.txt. Edition 7/14/2010.


//  Lab Specs
//    Window Title
         Estimating_Variances
//    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: Show that the ordinary least squares (OLS) estimation procedure for the
 variance of the coefficient estimate's probability distribution is unbiased.
_
The OLS estimate for the variance of the coefficient estimate's probability
 distribution equals the OLS estimate for the variance of the error term's
 probability distribution divided by the sum of squared x deviations.
`
The following two lines provide the information needed to calculate the
 estimates:
___Sum Sqr XDev: Sum of squared x deviations
___SSR: Sum of Squared Residuals
_
After a repetition is completed, the estimate for the variance of the
 coefficient estimate's probability distribution is reported in the
 Coef Dist Var Est line. The Mean line immediately below updates
 the mean (average) of the estimates for all repetitions.


` 3 -1 2 500 50 2 0 30 0 -1
1a. First, we shall show that the simulation is calculating the OLS
 estimates for the coefficient estimates probability distribution
 correctly. To do so, click Start to run the first repetition.
 Now, we shall calculate the estimate for the variance of the error
 term's probability distribution. What is the sum of squared residuals
 (SSR) from the first repetition? Note that the sample size is 3.
 Using this information calculate the OLS estimate for the variance
 of the error term's probability distribution?
`
1b. What is the sum of the square x deviations? Based on this sum and the
 OLS estimate for the variance of the error term's probability distribution,
 calculate the OLS estimate for the variance of the coefficient estimate's
 probability distribution. Focus your attention on the Coef Dist Var Est
 line. Is the simulation calculating this OLS variance estimate correctly?


` 3 -1 2 500 50 2 0 30 0 -1
2. Next, click continue to run the second repetition. 
 Calculate the second repetition's estimate for the variance of the error
 term's probability distribution. Calculate the second repetition's estimate
 for the variance of the coefficient estimate's probability distribution?
 Focus your attention on the Coef Dist Var Est line. Is the
 simulation calculating this OLS variance estimate for the second 
 repetition correctly? Is the simulation calculating the mean of the
 variance estimates correctly?


` 3 0 2 500 50 2 0 30 0 -1
3. Note that Pause checkbox is now cleared. Click Continue and then, after
 many, many repetitions click Stop. Focus attention on the Mean line
 immediately below the Coef Dist Var Est line. What is the mean of the
 estimates for variance of the coefficient estimate's probability
 distribution? What is the actual variance of the coefficient estimates?
 Is the OLS estimation procedure for the variance of the coefficient
 estimate's probability distribution unbiased? Explain.