between interest rates and the federal budget deficit in the United States 3. Co
ID: 3354250 • Letter: B
Question
between interest rates and the federal budget deficit in the United States 3. Consider the following two least-squares estimates of the relationship R-.00 Model A: Yi = 0.103-0.079x, Y, = the interest rate on Aaa corporate bonds x, where: the federal budget deficit as a percentage of GNP (quarterly model: N 56) Model T: Y2 = 0.089 + 0.36%, +0.887% R-.40 Y2 = the interest rate on 3-month Treasury bills x, = the federal budget deficit in billions of dollars x, = the rate of inflation (in percent) where: (quarterly model: N 38) a. What does "least-squares estimates" mean? What is being estimated? b. What does it mean to have an R of.00? Is it possible for an R2 to be c. Based on economic theory, what signs would you have expected for d. Compare the two equations. Which model has estimated signs that What is being squared? In what sense are the squares "least"? negative? the estimated slope coefficients of the two models? correspond to your prior expectations? Is Model T automatically better because it has a higher R'? If not, which model do you prefer and why?Explanation / Answer
a) Least square estimate is the estimate between the actual data and the predicted value given by the regression line
the actual value is y and predicted value is denoted by a hat
in least square we are minimizing (y-y hat)^2 values hence the name least square
b) R ^2 is the coefficient of determination which tells us how well the regression line is able to fit to the actual data point
Higher the R^2 value better is the model
The R^2 value can never be below zero or negative it ranges between 0 to 1
R^2 of 0 means that the regression line is not able to predict any value of the original data
c) both the equations should have had a negative sign for the slope for the inverse relation
d) I would prefer the first model even though it has 0 R^2 value as it complies with the economic theory even though the second model has a R^2 of 0.4 it contradicts the economic models
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