//  File New-Lec2-02-05-01-04.txt. Edition 7/14/2010.


//  Lab Specs
//    Window Title
         Sample_Size
//    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 0 2 50 50 2 0 30 0 1
Objective: Show that an increase in the sample size reduces the variance
 of the coefficient estimate's probability distribution thereby increasing
 an estimate's reliability.
_
As before, the sample size equals 3, the range of the x's is from 0 to 30; hence 
 the values of the x's are 5, 15, and 25. As you did previously, calculate
 the sum of squared x deviations from their mean.
_
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.


` 3 0 2 50 50 2 0 30 0 1
1a. The variance of the error term's probability distribution still equals 50. 
 Using the appropriate equations, calculate the variance of the coefficient
 estimate's probability distribution.
_
1b. The Pause checkbox is cleared. Click Start and after many, many
 repetitions click Stop. What is the variance of the
 numerical values for the coefficient estimates? Is this consistent
 with the variance calculated from the equation (Question 1a)?
_
1c. In what percent of the repetitions does the estimate fall within 1.0 and 3.0 range?


` 5 0 2 50 50 2 0 30 0 1
Note that the sample size has been increased from 3 to 5. 
 Note that the value of X Min is still 0 the value of X Max is still 30;
 consequently, the range of the x's is from 0 to 30. In the simulation, when
 the sample size is 5 and the range of the x's is from 0 to 30, the values of the x's are
 3, 9, 15, 21, and 27.
_
Calculate the sum of squared x deviations from their mean.


` 5 0 2 50 50 2 0 30 0 1
2a. Again, the variance of the error term's probability distribution equals 50.
 Using the appropriate equation, calculate the variance of the coefficient
 estimate's probability distribution.
_

2b. Click Start and then after many, many repetitions, click Stop.
 What is the variance of the numerical values for the coefficient estimates?
 Is this consistent with the variance calculated from the equation (Question 2a)?
_
2c. In what percent of the repetitions does the estimate lie within 1.0 and 3.0 range?


`
3. How does an increase in the sample size affect the variance of the coefficient
 estimate's probability distribution? How does an increase in the sample size
 affect reliability of a coefficient estimate? Why does this make sense intuitively?