Based on the US data for 1965-IQ to 1983_IVQ (n=76), James Doti and Esmael Abidi obtained the following regression to describe personal consumption expenditure (PCE) in the United States.
Yt=-10.96+0.93x2t-2.09X3t
t=(-3.33)(249.06)(-3.09)
R^2=0.9996
F=83,753.7
Where Y=the PCE ($, in billions)
X2=the disposable(i.e., after-tax) income ($, in billions)
X3-the prime rate (%) charged by banks
a. what is the marginal propensity to consume (MPC - the amount of additional consumption expenditure from an additional dollar's personal disposal income?
b. is the MPC statistically different from 1? Show the appropriate testing procedure.
c. What is the rationale for the inclusion of the prime rate variable in the model? A priori, would you expect a negative sign for this variable?
d. is b3 significantly different from zero?
e. test the hypothesis that R^2=0
f. compute the std. error of that coefficient