You have obtained data on test scores and student-teacher ratios ...

[nummyann]

You have obtained data on test scores and student-teacher ratios in region A and region B of your state. Region B, on average, has lower student-teacher ratios than region A. You decide to run the following regression.
 
  Yi = 0+ 1X1i + 2X2i + 3X3i+ui
 
  where X1 is the class size in region A, X2 is the difference between the class size between region A and B, and X3 is the class size in region B. Your regression package shows a message indicating that it cannot estimate the above equation. What is the problem here and how can it be fixed? Explain the problem in terms of the rank of the X matrix.
  What will be an ideal response?

Question 2

All of the following are good reasons for an applied econometrician to learn some econometric theory, with the exception of
 
  A) turning your statistical software from a black box into a flexible toolkit from which you are able to select the right tool for a given job.
  B) understanding econometric theory lets you appreciate why these tools work and what assumptions are required for each tool to work properly.
  C) learning how to invert a 44 matrix by hand.
  D) helping you recognize when a tool will not work well in an application and when it is time for you to look for a different econometric approach.

[tranoy]

Answer to Question 1

Answer: There is perfect multicollinearity here, in that X2 = X1-X3, hence the X matrix (and the X'X) matrix does not have full rank (rank = 3 here, not 4). If the X'X is singular, you cannot invert it, since its determinant is zero. Dropping one of the three explanatory variables allows you to estimate the above equation.

Answer to Question 2

Answer: C

[nummyann]

Wow, this really help

[irishcancer18]

Great answer, keep it coming