Question

Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d. Using Algebra, show that y= Bo + B1X1 + B2X2 + y; is the true population equation but if only y= Bo + Bixi + ui is estimated, Bi will be biased.

Answer 1

1. Ui is the error term that basically shows the difference between actual and predicted values of the dependent variable which is individual university GPA. This basically represents the impact that is not being captured by the independent variable which is individual high school grade.

2. The expected sum of error terms are assumed to be zero in OLS. This is due to the fact that we assume that the best fit regression line passes through the middle of the points. Other then the individual high school grade other variables that can affect individual university GPA can be Age of the student, IQ level and Number of lectures attended.

3. As we are only considering a single independent variable to explain the dependent variable thus a negative bias is assumed to occur. The reason being that single variable, in this case, won't be that much efficient to reflect the variability in the dependent variable and thus will always underpredict the dependent variable.

4. If the correct function form includes two variables x1 and x2 and if we are only using a single variable instead then it will cause a negative bias. That is the model will underpredict the dependent variable as the impact of the other variable i.e x2 will not be observed.