// File MIT-18-01-03-01.txt. Edition 5/15/2012. // Lab Specs // Window Title Distribution_of_Error_Terms // List of Error Variances 50. 500. 150. 500. // List of Heter Values -2.0 2.0 1.0 .0 // List of Rho's -.9 .9 .3 .0 // List of XECorr's -.90 .90 .30 .00 // Problem Specs // Hetero visible (0 not visible, -1 visible) // Rho visible (0 not visible, -1 visible) // XECorr visible (0 not visible, -1 visible) // Graph visible (0 none, -1 et versus et-1, 1 e versus x) // Pause checked (0 not checked, -1 checked) // ErrVar value // Hetero Factor value // Rho value // XECorr value ` 0 0 -1 1 -1 500 0 0 0 Objective: Illustrate the ordinary least sqaures' explanatory variable/error term independence premise: _ _ The explanatory variable and the error term are not correlated. _ That is, knowing the value of the explanatory variable does not help us predict the value of the error term. ` 0 0 -1 1 -1 500 0 0 0 1. Click Start to run the first repetition of the experiment. Three histogram's appear at the top of the window; one histogram for each student's error term. _ Also, a scatter diagram appears to the left. Notice that there are three points, representing the number of minutes each student studied, the explanatory variable, and the student's error term for the first repetition. ` Click Continue. Three different points now appear in the scatter diagram, representing the number of minutes each student studied, the explanatory variable, and the student's error term for the second repetition. _ Click Continue a few more times until that you are confident that you understand the scatter diagram. ` 0 0 -1 1 0 500 0 0 0 2. A correlation value of 0 is specified in the XECorr list; this means that the explanatory variable and the error term are not correlated. Also, the Pause checkbox has been cleared. Click Start and then after many many repetitions click Stop. ` Focus on the scatter diagram. _ 2a. When the explanatory variable is low, is the error term typically positive or negative? When the explanatory variable is high, is the error term typically positive or negative? _ 2b. Does knowing the value of the explantory variable help us predict the value of the error term? Explain. ` 0 0 -1 1 0 500 0 0 .6 3. A correlation value of .6 is specified in the XECorr list; the explanatory variable and the error term are positively correlated. Click Start and then after many, many repetitions click Stop. _ 3a. When the explanatory variable is low, is the error term typically positive or negative? When the explanatory variable is high, is the error term typically positive or negative? _ 3b. Does knowing the value of the explantory variable help us predict the value of the error term? Explain. ` 0 0 -1 1 0 500 0 0 -.6 4. A correlation value of -.6 is specified in the XECorr list; the explanatory variable and the error term are negatively correlated. Click Start and then after many, many repetitions click Stop. _ 4a. When the explanatory variable is low, is the error term typically positive or negative? When the explanatory variable is high, is the error term typically positive or negative? _ 4b. Does knowing the value of the explantory variable help us predict the value of the error term? Explain.