//  File 55-Lec2-01-02-01-02.txt. Edition 7/21/2010.


//  Lab Specs
//    Window Title
         Random_Influences_-_Coefficient_Estimates
//    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 1 0
Objective: Show that the ordinary least squares (OLS) coefficient estimate
 equals the actual coefficient value whenever there is no error term; that is,
 show that the estimate equals the actual value when random influences are absent.
_
This simulation allows us to specify the actual values of the constant,
 and the coefficient. Focusing on the left side of the screen you see that
 Act Const list and the Act Coef list. Initially, the actual value of the
 constant is 50, the actual value of the coefficient is 2.
`
The Error Term checkbox is cleared indicating that there will be no error term. 
 The Sample  Size list indicates that the sample size is 3 indicating that there
 are the three students in Professor Lord's class.
_ 
Each repetition of the experiment represents a quiz from a single week.
 The quiz score for each student
 based on the actual constant, the actual coefficient, and the number of
 minutes the student studies. The ordinary least squares (OLS) estimation
 procedure is used to estimate the values of the constant and coefficient.
`
The X Min and X Max lists specify the range of the explanatory variable,
 the number of minutes studied.
 The values of the explanatory variable are "evenly spaced" between the
 minimum and maximum. Intially, 0 and 30 are selected. When the sample size is 3,
 this means that the explanatory variable takes on the values 5, 15, and 25.
 That is, the three students study 5, 15, and 25 minutes respectively.
`
Since the Act Coef radiobutton is selected, we shall be focusing on the
 estimates for the coefficient. The value of coefficient estimate from
 each repetition of the experiment is reported. Also, the mean and
 variance of estimates from all the repetitions are continually updated
 and, as we shall see shortly, a histogram of the estimates will appear
 in the upper right hand portion of the window.
_
Since the Pause checkbox is selected, the simulation will pause after each repetition.


` 3 -1 2 500 50 2 0 30 1 0
1. Click Continue. What is the numerical value of the coefficient estimate
 for the first repetition? Record its value.
_
2. Click Continue. What is the numerical value of the coefficient estimate
 for the second repetition? Record its value.
_
3. Click Continue. What is the numerical value of the coefficient estimate
 for the third repetition? Record its value.
_
4. Click Continue. What is the numerical value of the coefficient estimate
 for the fourth repetition? Record its value.
`
5. Click Stop. In the absence of an error term, can you predict the value
 of the coefficient estimate with certainty?