| № |
Condition |
free/or 0.5$ |
| m68684 | For Example 2.3, relating stock prices to interest rates, are the regression results given in Eq. (2.24) statistically significant? Show the necessary calculations. |
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| m68685 | For Example 4.3, compute the F value. If that F value is significant, what does that mean? |
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| m68700 | For Problem A. 13, find out the var (X + Y). How would you interpret this variance? |
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| m68702 | For regression (5.39) compute the raw r2 value and compare it with that given in Eq. (5.40). |
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| m68735 | For the models considered in Table 7-1, find out if these models suffer from the problem of heteroscedasticity. The raw data are given in Table 9-6, found on the textbook s Web site. State the tests you use. How would you remedy the problem? Show the necessary calculations. Also, present the results based on White s heteroscedasticity-corrected standard errors. What general conclusion do you draw from this exercise?
For Information: Refer to the life expectancy example (Example 7.4) |
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| m68738 | For the PC / printer sales example discussed in this appendix compute the conditional variance of Y (printers sold) given that X (PCs sold) is 2. |
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| m68739 | For the Phillips curve regression Equation (5.29) given in Chapter 5, the estimated d statistic would be 0.6394.
a. Is there evidence of first-order autocorrelation in the residuals? If so, is it positive or negative?
b. If there is autocorrelation, estimate the coefficient of autocorrelation from the d statistic.
c. Using this estimate, transform the data given in Table 5-6 and estimate the generalized difference equation (10.15) (i.e., apply OLS to the transformed data).
d. Is there autocorrelation in the regression estimated in part (c)? Which test do you use? |
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| m68774 | Four economists have predicted the following rates of growth of GDP (%) for the next quarter:
E1 = below 2%, E2 = 2 or greater than 2% but below 4%, E3 = 4 or greater than 4% but less than 6%, and E4 = 6% or more.
Let Ai be the actual rate of % GDP growth rate according to the same four classifications as Ei (e.g., A1 = GDP growth rate of less than 2%).
a. Are the events E1 through E4 mutually exclusive? Are they collectively exhaustive?
b. What is the meaning of the events (1) E1A2 (or E1 ∩ A2), (2) E3 + A3 (or E3 ⋃ A3), (3) Ei + Ai (or Ei ⋃ Ai) where I = 1 through 4, and (4) EiAj (or Ei ∩ Aj) where i > j? |
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| m68796 | From the data given in the preceding problem, a random sample of Y was drawn against each X. The result was as follows:
a. Draw the scatter gram with Y on the vertical axis and X on the horizontal axis.
b. What can you say about the relationship between Y and X?
c. What is the SRF for this example? Show all your calculations in the manner of Table 2-4.
d. On the same diagram, show the SRF and PRF.
e. Are the PRF and SRF identical? Why or why not? |
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| m68797 | From the regression (12.36), compute the probability of owning a house for each income level shown in Table 12-3. |
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| m68798 | From the total cost function given in the NYSE regression (9.31), how would you derive the average cost function? And the marginal cost function? But if Eq. (9.32) is the true (i.e., heteroscedasticity-adjusted) total cost function, how would you derive the associated average and marginal cost functions? Explain the difference between the two models. |
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| m68840 | Give examples where the chi-square and F probability distributions can be used. |
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| m68933 | Given X ~ N(µX,σ2X), prove that ~ N(µX, σ2X / n). |
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| m69088 | How do you perceive the role of econometrics in decision making in business and economics? |
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| m69139 | How would you modify this equation to allow for the possibility that the coefficient of Tuition also differs from region to region? Present your results.
For Information: Refer to Eq. (6.17) in the text. |
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| m69256 | If there is collinearity in Problem 8.14, estimate the various auxiliary regressions and find out which of the X variables are highly collinear.
Problem 8.14
You are given the annual data in Table 8-5 for the United States for the period 1971 to 1986. Consider the following aggregate demand function for passenger cars:
InYi = B1 + B2InX2t + B3InX3t + B4InX4t + B5InX5t + B6InX6t + ut
where In = the natural log
DEMAND FOR NEW PASSENGER CARS IN
THE UNITED STATES, 1971 TO 1986 |
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| m69271 | If X ~ N(10, 3) and Y ~ N(15, 8), and if X and Y are independent, what is the probability distribution of
a. X + Y
b. X - Y
c. 3X
d. 4X + 5y |
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| m69344 | In a regression of average wages (W) on the number of employees (N) for a random sample of 30 firms, the following regression results were obtained
a. How would you interpret the two regressions?
b. What is the author assuming in going from Eq. (1) to (2)? Was he worried about heteroscedasticity?
c. Can you relate the slopes and the intercepts of the two models?
d. Can you compare the R2 values of the two models? Why or why not? |
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| m69345 | In a regression of weight on height involving 51 students, 36 males and 15 females, the following regression results were obtained:15
1.
2.
3.
where weight is in pounds, height is in inches, and where
Dum sex = 1 if male
= 0 if otherwise
Dumht. = the interactive or differential slope dummy
a. Which regression would you choose, 1 or 2? Why?
b. If 2 is in fact preferable but you choose 1, what kind of error are you committing?
c. What does the dum sex coefficient in 2 suggest?
d. In Model 2 the differential intercept dummy is statistically significant whereas in Model 3 it is statistically insignificant. What accounts for this change?
e. Between Models 2 and 3, which would you choose? Why?
f. In Models 2 and 3 the coefficient of the height variable is about the same, but the coefficient of the dummy variable for sex changes dramatically. Do you have any idea what is going on?
To answer questions (d), (e), and (/) you are given the following correlation matrix.
The interpretation of this table is that the coefficient of correlation between height and dum sex is 0.6276 and that between dum sex and dumht. is 0.9971. |
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| m69363 | In a study of population density as a function of distance from the central business district, Maddala obtained the following regression results based on a sample of 39 census tracts in the Baltimore area in 1970.
where V = the population density in the census tract and X = the distance in miles from the central business district.
a. What assumption, if any, is the author making about heteroscedasticity in his data?
b. How can you tell from the transformed WLS regression that heteroscedasticity, if present, has been removed or reduced?
c. How would you interpret the regression results? Do they make economic sense? |
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