//  File MIT-Lab-06-06-01-04.txt. Edition 1/18/2013.


//  Lab Specs
//    Window Title
         OLS_and_BLUE
//    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)


` 5 0 2 500 50 2 0 30 0 1
Objective: Illustrate that the OLS estimation procedure is the best linear unbiased
 estimation procedure (BLUE) when the standard ordinary least squares (OLS)
 premises are met.
_
Check to be certain that the sample size is 5 and the Pause checkbox is cleared.
_
A From value of 1.0 and a To value of 3.0 are specified. The
 From-To line reports the percent of repetitions in which the estimate lies
 within 1.0 of the actual value 2.0.


` 5 0 2 500 50 2 0 30 0 1
Focus your attention on the drop down box just above the Start button. We call
 this the Procedures box.
_
1. By default, the OLS estimation procedure is specified. Click Start and
 then after many, many repetitions click Stop.
_
1a. What is the mean of the coefficient estimates? Is the ordinary least squares (OLS)
 estimation procedure unbiased? Explain.
_
1b. What is the variance of the coefficient estimates? In what percent of the 
 repetitions does the estimate lie between 1.0 and 3.0?


` 5 0 2 500 50 2 0 30 0 1
2. Click on Procedures box, the drop down box just above the Start button. 
 Select Any Two rather than OLS. With this procedure two observations are 
 chosen randomly. The slope of the straight line passing through the two 
 points is used to estimate the coefficient. Click Start and then after
 many, many repetitions click Stop.
_
2a. What is the mean of the coefficient estimates? Is the ordinary least squares (OLS)
 estimation procedure unbiased? Explain.
_
2b. What is the variance of the coefficient estimates? In what percent of the 
 repetitions does the estimate lie between 1.0 and 3.0?


` 5 0 2 500 50 2 0 30 0 1
3. Again click on the Procedure box. Select Min-Max estimation procedure.
 With this procedure the two observations with the smallest and largest
 values of x are choosen. The slope of the straight line passing through
 the two points is used to estimate the coefficient. Click Start and then
 after many, many repetitions click Stop.
_
3a. What is the mean of the coefficient estimates? Is the ordinary least squares (OLS)
 estimation procedure unbiased? Explain.
_
3b. What is the variance of the coefficient estimates? In what percent of the 
 repetitions does the estimate lie between 1.0 and 3.0?


`
4. Compare your answers to questions 1, 2, and 3.
_
4a. How are the estimation procedures similar? 
_
4b. How do the estimation procedures differ? 
_
4c. Which estimation procedure is the "best?" Explain.