//  File New-Lec2-02-06-01-04.txt. Edition 7/14/2010.


//  Lab Specs
//    Window Title
         Explanatory_Variable_Range
//    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 as the range of the explanatory variable's values
 decreases, the variance of the coefficient estimate's
 probability distribution increases thereby decreasing an estimate's reliabiilty.
_
As before, the sample size equals 5, the range of the x's is from 0 to 30; hence 
 the values of the x's are 3, 9, 15, 21, and 27. 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 equals 50.
 Using the appropriate equation, calculate the variance of the coefficient
 estimate's probability distribution.
_

1b. The Pause checkbox is cleared. 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 1a)?
_
1c. In what percent of the repetitions does the estimate lie within 1.0 and 3.0 range?


` 5 0 2 50 50 2 10 20 0 1
Note that the value of X Min has been increased from from 0 to 10 and the value of 
 X Max has been decreased from 30 to 20; the range of the x's is now from 10 to 20.
 In the simulation, when the sample size is 5 and the 
 range of the x's is from 10 to 20, the values of the x's are 11, 13, 15, 17, and 19.
_
Calculate the sum of squared x deviations from their mean.



` 5 0 2 50 50 2 10 20 0 1
2a. 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 a decrease the range of the explanatory variable's values
 affect the variance of the coefficient estimate's probability
 distribution? How does a decrease the range of the explanatory
 variable's values affect the reliability of a coefficient estimate?
 Why does this make sense intuitively?