04 Jun d. Is b3 significantly different from zero? e. Test the hypothesis that R2 = 0. f. Compute the standard error of each coefficient
Question
Week 3 Chapter 4 Homework
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Chapter 4
· Questions : 4.5 and 4.6
· Problems 4.11, 4.12, 4.13, and 4.21
Problem 4.11
To explain what determines the price of air conditioners: B. T. Ratchford24 obtained the following regression results based on a sample of 19 air conditioners: 66,236 i- 0.0 22 + 19,72.9Xx + 7.653X4,-R2 = se = 0,005) 0.992) (3.082)
where Y= the price: in dollars X2 = the BTU rating of air conditioner X3 = the energy efficiency ratio X4 = the number of settings se = standard errors
a. Interpret the regression results.
b. Do the results make economic sense?
c. At r 5%: test the hypothesis that the BTU rating has no effect on the price of an air conditioner versus that it has a positive effect.
Problem 4.12
Based on the U.S. data for 1965-IQ to 1963-IVO (n = 76): James Doti and Esmael Adibi25 obtained the following regression to explain personal consumption expenditure (POE) in the United States.
= —10.96 + O.93 2r 2.i9 3r t (-333)(249,06) (-3.09) R2 = 0.4996 F = 83,753,7
where V = the POE ($. in billions) X2 = the disposable (i_e.: after-tax) income (S: 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 disposable 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 R2 = 0. f. Compute the standard error of each coefficient
Problem 4.21
Refer to Example 4.5. a. Use the method of restricted least squares to find out if it is worth adding the Pop (population) variable to the model.
b. Divide both Educ and GDP by Pop to obtain per capita Educ and per capita GDP. Now regress per capita Educ on per capita GDP and compare your results with those given in Example 4_5_ What conclusion can you draw from this exercise?
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