3216

Statistics Statistics Level: University

Rubax, a US manufacturer of athletic shoes, estimates the following linear trend model for shoe sales:

Qt = a + bt + c1D1 +c2D2 +c3D3

Where

Qt = sales of athletic shoes in the tth quarter

T + 1, 2,….., 28[j2001(I), 2001(II)….,2007{IV}

D1 = 1 if t is quarter I (winter); 0 otherwise

D2 = 1 if t is quarter II (spring); 0 otherwise

D3 = 1 if t is quarter III (summer); 0 otherwise

The regression analysis produces the following results:

Dependent Variable: QT R-Square F-Ratio P-Value on F
Observations: 28 0.9651 159.01 0.0001
Variable Parameter Estimate Standard Error T-Ratio P-Value
Intercept 184500 10310 17.90 0.0001
T 2100 340 6.18 0.0001
D1 3280 1510 2.17 0.0404
D2 6250 2220 2.82 0.0098
D3 7010 1580 4.44 0.0002

a. Is there sufficient statistical evidence of an upward trend in shoe sales?

b. Do these data indicate a statistically significant seasonal pattern of sales for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?

c. Using the estimated forecast equation, forecast slates of Rubax shoes for 2008(III) and 2009 (II).

d. How might you improve this forecast equation?


3215

Statistics Statistics Level: University

The British Columbia Tourist Association distributes pamphlets, maps, and other tourist-related information to people who call a toll-free number and request information. The marketing manager decided to develop a multiple regression model to predict the number of calls that will be received in the coming week. A random sample of 20 weeks is selected. The collected data are summarized below.
Calls ReceivedAds Place Previous WeekCalls Received the Previous WeekAirline Bookings
345 12 297 3,456
456 14 502 3,456
356 13 340 3,600
605 16 450 5,500
209 14 350 2,400
306 10 340 2,890
457 15 401 3,757
259 12 340 2,590
540 13 480 4,840
460 16 440 3,560
378 14 348 3,460
456 16 518 3,679
209 14 350 2,400
306 10 340 2,890
457 15 401 3,757
259 12 340 2,590
540 13 480 4,840
460 16 440 3,560
356 13 340 3,600
605 16 450 5,500

a. Specify a suitable multiple regression equation to estimate with the data.

b. What percentage of the total variation in the number of calls is explained by the regression model?

c. Is the overall multiple regression equation statistically significant? Explain.

d. Which, if any, of the independent variables is statistically significant? Test using a significance level of 0.05.


3214

Statistics Statistics Level: University

The following log-linear demand curve for a price-setting firm is estimated using the ordinary least squares method: where Q and P are the quantity and price respectively for good X, M is consumer income, and is the price of good R.

a.Express the estimated demand equation in logarithms.

b.Is X a normal or an inferior good? And how are goods X and R related? Explain.

c.Estimate the own-price elasticity for good X, the cross-price elasticity for goods X and R, and the income elasticity for good X.

d.Holding all other things constant, if household income were to fall by 22%, what would we expect to happen to quantity demanded? Explain.

e.Holding all other things constant, if own price were to increase by 22%, what would we expect to happen to quantity demanded? Explain.

f.Holding all other things constant, if the price of R were to fall by 8%, what would we expect to happen to quantity demanded? Explain.


The estimation results are presented below:
DEPENDENT VARIABLE:LNQR-SQUAREF-RATIOP-VALUE ON F
OBSERVATIONS: 64 0.8464 110.25 0.0001
PARAMETER STANDARD---
VARIABLE ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT 5.65 3.20 1.77 0.0825
LNP -1.02 0.59 -1.73 0.0890
LNM 0.45 0.22 2.05 0.0452
LNPR -2.0 0.75 -2.67 0.0098

3213

Statistics Statistics Level: University

The 1998 GSS states, "There are always some people whose ideas are considered bad or dangerous by other people. For instance, somebody who is against all churches and religion...If such a person wanted to make a speech in myour (city/town/community) against churches and religion, should he/she be allowed to speak or not?" Among the male GSS respondents, 631 said they would allow the speech and 154 would not allow it. Among the female respondents, 762 would allow and 303 would not allow the speech. What are the conditional odds in favor of allowing an atheist to speak?

3212

Statistics Statistics Level: University

In several presedential elections, researchers have observed a "gender gap" in which men and women vote for candidates in different proportions. Test this hypothesis by calculating X2 and Yule's Q for these frequencies from the 1998 General Social Survey:

Did you vote for Clinton or Dole?

Gender
Men Women
Clinton 351 572
Dole 283 306

3199

Statistics Statistics Level: University

Using economic theory explain the rationale for having a fixed monthly tariff, as well as charges for each call, in the market for mobile phones.

3198

Statistics Statistics Level: University

Baseball Controversy

In recent years a controversy has arisen in major league baseball. Some players have been accused of "doctoring" their bats to increase the distance the ball travels. However, a physics professor claims that the effect of doctoring, no matter how it is done, is negligible. A major league manager decides to test the professor's claim considering two different types of doctoring. He doctors two bats by inserting cork into one and rubber into another. He then selects five players on his team and has them each hit a ball with an un-doctored bat and with each of the doctored bats. The distances are measured and listed below. Distance Ball Travels (in feet)
Player Un-doctored Bat Bat with Cork Bat with Rubber
1. 275 265 280
2. 315 335 320
3. 425 435 440
4. 380 375 370
5. 450 460 450
We can assume that the data are normally distributed and that the variances for each treatment are equal. BE SURE TO USE THE CORRECT EXPERIMENTAL DESIGN

a.) Do these data provide sufficient evidence at a 5% level of significance to refute the professor's claim?

b.) Does our result indicate the need for any multiple comparison testing? Why? If yes, do it. Use α = 0.05). You must show all seven steps.


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