- Consider the following two least-squares estimates of the relationship between interest rates and the federal budget deficit in the United States:
Model 1:
N = 56, R2 = 0.00
where: = Interest rate on AAA corporate bonds
= Federal budget deficit as percentage of GNP
Model 2: .369
N = 38, R2 = 0.40
where: = Interest rate on 3 – month Treasury bills
= Federal budget deficit in billions of dollars
= Rate of inflation (in percent)
- What does “least squares” estimates mean? What is being estimated? What is being squared? In what sense are the squares “least”?
- What does it mean to have an R2 of 0.00? Is it possible for R2 to be negative? What about ?
- R2 tells us what percent of variation in the dependent variable from its mean can be explained by a regression model (regression equation). How does an increase in R2 impact TSS, ESS, and RSS for a given regression equation?
- What signs would you have expected for the estimated slope coefficients of the two models?
- Comparing the two equations, which model has estimated signs corresponding to your prior expectations?
- Can one argue that model 2 is preferred on the basis of fit?
