ECON 2B03 Lecture Notes - Lecture 10: Exclusive Or, Bernoulli Process, Central Limit Theorem
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TABLE 66 Stock Prices and Consumer Prices | |||
CITY | |||
Y = Rate of Change, Stock Prices, Percent Per Year | |||
X = Rate of Change, Consumer Prices, Percent Per Year | |||
CITY | Y | X | |
A | 5 | 4.3 | |
B | 11.1 | 4.6 | |
C | 3.2 | 2.4 | |
D | 7.9 | 2.4 | |
E | 25.5 | 26.4 | |
F | 3.8 | 4.2 | |
G | 11.1 | 5.5 | |
H | 9.9 | 4.7 | |
I | 3.3 | 2.2 | |
J | 1.5 | 4 | |
K | 6.4 | 4 | |
L | 8.9 | 8.4 | |
M | 8.1 | 3.3 | |
N | 13.5 | 4.7 | |
O | 4.7 | 5.2 | |
P | 7.5 | 3.6 | |
Q | 4.73. | 6 | |
R | 8 | 4 | |
S | 7.5 | 3.9 | |
T | 9 | 2.1 |
Table 66 gives data on percent change per year stock prices (Y) and consumer prices (X) for a cross section of 20 cities.
******************* answer in "SAS format" please********************* (if possible)
1) Plot the data in scattergram
2) Regress Y on X and examine the residuals from this regression. What do you observe?
3) Since the data for city(E) is unusual, repeat the regression in (2) dropping the data on city(E). Now examine the residuals from this regression. What do you observe?
4) If on the basis of the results in (2) you conclude that there was heteroscedasticity in the error variance but on the basis of the results in (3) you reverse your conclusion, what general conclusions do you draw?
State whether the following statements are true or false. Breifly justify your answer:
5) When autocorrelation is present, OLS estimators are biased as well as inefficient;
6) The R squared values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable.
7) In the presence of heterscedasticity the usual OLS method always overestimates the standard errors of estimators.
8) If a regression model is mis-specified (e.g., an important variable is ommitted), the OLS residuals will show a distinct pattern.
1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.
Quarter Seasonal Index Seasonally Adjusted Data
Q1 .80 295
Q2 .85 299
Q3 1.15 270
Q4 --- 271
2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?
A. Alpha and Delta
B. Delta and Gamma
C. Alpha and Gamma
D. Standard Deviation and Mean
3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.
A. Ho: r = .05 p < .5
B. Ho: r = 0 p >.05
C. Ho: r ? 0 p?.05
D. Ho: r = 0 p?.05
In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable? |
A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.
5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied? |
A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right
A. The rejection region and the t-table value generally gets smaller for sample size below 31. |
A. Yes. The data are significantly correlated through the 12th lag. C. No. Only the 12 lag period is not correlated. D. You cannot tell since the number of sample observations is not provided. E. The p-value is above .05 so the data is correlated. |
A. Type 2 error |
A. Yes. They move in the same direction as statistical significance. |
A. The weight cannot be calculated since the data observation is not given. |
A. Yes. The correlation coefficient is .873 that is greater than .05. |
A. Yes, since the residuals randomly vary in magnitude. |
A. -101.0 |
|
(Please show as much work as possible)
1. You are bidding in a second-price auction for a painting that you value at $800. You estimate that other bidders are most likely to value the painting at between $200 and $600. Which of these is likely to be your best bid?
a. $1,000
b. $800
c. $600
d. $400
2. Which of the following is true about different ways of conducting a private-value auction?
a. A first-price auction is strategically equivalent to a second-price auction.
b. A first-price auction is strategically equivalent to an English auction.
c. A second-price auction is strategically equivalent to an English auction.
d. None of the above
3. Suppose that five bidders with values of $500, $400, $300, $200, and $100 attend an oral auction. Which of these is closest to the winning price?
a. $500
b. $400
c. $300
d. $200
4. In the above auction, if the bidders with the first- and third-highest values ($500 and
$300) collude, which of these is closest to the winning price?
a. $500
b. $400
c. $300
d. $200
5. If a seller is concerned about collusion among bidders, which of the following changes to the auction, should the seller make?
a. Hold frequent, small auctions instead of infrequent large auctions.
b. Conceal the amount of winning bids.
c. Publically announce the name of each auction's winner.
d. Hold a second-price instead of a first-price auction.
6. You're holding an auction to license a new technology that your company has developed. One of your assistants raises a concern that bidders' fear of the winner's curse may encourage them to shade their bids. How might you address this concern?
a. Release your analyst's positive scenario for the technology's future profitability.
b. Release your analyst's negative scenario for the technology's future profitability.
c. Use an oral auction.
d. All of the above
7. In a first-price auction, you bid ________ your value, and in a second-price auction you bid _________ your value.
a. at; above
b. below; above
c. below; at
d. below; below
8. You hold an auction among three bidders. You estimate that each bidder has a value of either $16 or $20 for the item, and you attach probabilities to each value of 50%. What is the expected price? If two of the three bidders collude, what is the price?
9. In Sweden, firms that fail to meet their debt obligations are immediately auctioned off to the highest bidder. (There is no reorganization through Chapter 11 bankruptcy.) The current managers are often high bidders for the company. Why?
10. When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, representatives of other museums that have no chance of winning are actively wooed by the auctioneer to attend anyway. Why?
11. The deities Mars and Venus often do battle to create the weather conditions on Earth. Venus prefers extreme temperatures (especially heat), while Mars prefers temperate conditions. The payoffs (expressed in Points of Wrath) are given below.
|
|
Venus |
|
|
|
Warm |
Chill |
Mars |
Warm |
20 , 0 |
0 , 10 |
Chill |
0 , 90 |
20 , 0 |
What is the unique mixed-strategy equilibrium of the above game?
(Let p be the probability of "Warm" for Mars, and q the probability of "Warm" for Venus.)
a) p=9/10, q=1/2
b) p=1/2, q=1/10
c) p=1/2, q=1/2
d) p=1/10, q=1/10
Player 2
|
|
H |
D |
Player 1 |
H |
0 , 0 |
4 , 1 |
D |
1 , 4 |
2 , 2 |
12. The above game is the title of the hawk-dove game and used by evolutionary biologists to describe evolutionary processes. It is also used to model how a business should grow. In the above game, what is the Nash equilibrium in pure strategies and mixed strategies.?
Assume the cost of producing the goods is zero and that each consumer will purchase each good as long as the price is less than or equal to value. Consumer values are the entries in the table.
|
Good 1 |
Good 2 |
Consumer A |
$2,300 |
$1,700 |
Consumer B |
$2,800 |
$1,200 |
13. Suppose the monopolist only sold the goods separately. What price will the monopolist charge for good 1 to maximize revenues for good 1?
a. $2,300
b. $2,800
c. $1,200
d. $1,700
14. What is the total profit to the monopolist from selling the goods separately?
a. $4,500
b. $6,300
c. $7,000
d. $6,000
15. What is a better pricing strategy for the monopolist? At this price, what are the total profits to the monopolist?
a. Bundle the goods at $2,800; Profits = $5,600
b. Bundle the goods at $4,000; Profits = $8,000
c. Charge $2,800 for good 1 and charge $1,700 for good 2; Profits = $4,500
d. Charging the lowest price for each good individually is the best pricing strategy; Profits = $7,000
16. The prisoners' dilemma is an example of
a. a sequential game.
b. a simultaneous game.
c.a shirking game.
d. a dating game
17. Nash equilibrium
a. is where one player maximizes his payoff, and the other doesn't.
b. is where each player maximizes his own payoff given the action of the other player.
c.is where both players are maximizing their total payoff.
d. is a unique prediction of the likely outcome of a game.