//  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 0 500 50 2 0 30 0 -1
Objective: Illustrate our third estimation procedure for the variance of the error term's
 probability distribution: SSR divided by the degress of freedom, T-2, the sample size less 2. 
 Show that this estimation procedure is unbiased.
_
In the Use line, select the Res radiobutton
In the Divide by line, select the T-2 radiobutton

` 3 -1 0 500 50 2 0 30 0 -1
Since you selected Res in the Use line, the residuals will be used to
 estimate the value of the error terms. Also, since you selected T-2
 in the Divide by line, the sum of squared residuals will be divided
 by T-2, the degrees of freedom.
_
In other words, after each repetition of the experiment, the variance of error
 term's probability distribution is estimated by summing the squared residuals
 and then dividing this sum by the degrees of freedom. 

` 3 -1 0 500 50 2 0 30 0 -1
Each repetition's estimate for the variance of the error term's probability
 distribution is reported on the Error Var Est line. The mean (average) of
 these estimates is reported on the Mean line immediately beneath the Error
 Var Est line.
_
1. Click Start. What is the sum of squared residuals for the first repetition?
 Based on this sum, calculate the estimate for the variance of the error's
 term probability distribution. Record its value. Focus on the Error Var Est
 line. Is the simulation calculating the variance estimate correctly? 


`
2a. Click Continue to run the second repetition. 
 What is the sum of squared residuals for the second repetition?
 Based on this sum, calculate the estimate for the variance of the error's
 term probability distribution. Record its value. Focus on the Error Var Est
 line. Is the simulation calculating the variance estimate for the second
 repetition correctly?
_
2b. Next, focus the Mean line immediately below the Error Var Est line. Is the
 simulation calculating the mean (average) of the variance estimates from
 the first two repetitions correctly?


` 3 0 0 500 50 2 0 30 0 -1
3. Note that the Pause checkbox is now cleared. Click Continue and
 then, after many, many repetitions click Stop. What is the mean
 (average) of the estimates for the variance of the error term's probability
 distribution? What is the actual variance of the error term's probability
 distribution? 

` 3 0 0 200 50 2 0 30 0 -1
4. Note that the actual variance of the error term's probability distribution
 has been reduced to 200. Click Continue and
 then, after many, many repetitions click Stop. What is the mean
 (average) of the estimates for the variance of the error term's probability
 distribution? What is the actual variance of the error term's probability
 distribution?

` 3 0 0 50 50 2 0 30 0 -1
5. Note that the actual variance of the error term's probability distribution
 has been reduced to 50. Click Continue and
 then, after many, many repetitions click Stop. What is the mean
 (average) of the estimates for the variance of the error term's probability
 distribution? What is the actual variance of the error term's probability
 distribution? 
 
`
6. Review your answers to questions 4, 5, and 6. Does this estimation
 procedure for the variance of the error term's probability distribution
 appear to be unbiased?