You Have Obtained Data on Test Scores and Student-Teacher Ratios

question 56

Essay

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 $Y _ { i } = \mathcal { \beta } _ { 0 } + \mathcal { \beta } _ { 1 } X _ { 1 i } + \mathcal { \beta } _ { 1 } X _ { 2 i } + \beta _ { 3 } X _ { 3 i } + u _ { i }$ where $X _ { 1 }$ is the class size in region A, $X _ { 2 }$ is the difference in class size between region A and B, and $X _ { 3 }$ 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?

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Definitions:

Annually Compounded

Compound interest calculated and added to the principal once a year, affecting the total interest earned or paid.

Nominal Rate

The interest rate stated on a bond or loan before adjusting for inflation or other factors.

Lump Sum

A one-time payment executed at a specific moment, rather than several installments spread out over a period.

Nominal Rate

The advertised or stated interest rate on a loan or investment, not taking into account the effect of compounding or inflation.