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QMB 3250 Fall 2010 Final Exam FormBD December 14, 2010

* Page 1 of 10

1. To test the overall significance of the model, we would perform an F test. What is the value of the F statistic we would use?

F=R2/(1-R2)*(n-k-1)/k = (.5553/.4447)(45-4-1)/4 = 12.487

10.2 11.2 12.2 13.2

Choose one answer: <------+------+------+------+------>

A B C D E

1. If you test each of the four predictor variables individually for significance, using two-sided T-tests and an  = .05 significance level, what general conclusion would you reach?

With n-k-1=40 df the critical T is  2.040. Only X1 is NOT significant

A. None of the individual predictors are significant.

B. Only one of the individual predictors is significant.

C. Exactly two of the individual predictors are significant.

D. Exactly three of the individual predictors are significant.

E. All four of the individual predictors are significant.

1. What net revenue level (in thousands) does this model predict for a store that had these characteristics: shipping costs of $9.00 per unit, 35 thousand dollars spent on print advertising, 43 thousand dollars spent on internet advertising, and offered a rebate of 10 percent of the retail price?

Yhat = - 32.5 + 1.07(9) + 2.60(35) + 2.52(43) + 17.6(10) = 352.49

351.5 354.5 357.5 360.5

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A B C D E

1. For a particular store, this model has predicted a net revenue level of 420 thousand dollars. For this store, the shipping costs were $9.00 per unit, 35 thousand dollars were spent on print advertising, and 43 thousand dollars spent on internet advertising. What was the rebate as a percent of the retail price?

Yhat = - 32.5 + 1.07(9) + 2.60(35) + 2.52(43) + 17.6*Rebate

420 = - 32.5 + 1.07(9) + 2.60(35) + 2.52(43) + 17.6*Rebate

420 + 32.5 - 1.07(9) - 2.60(35) - 2.52(43) = 17.6*Rebate

Rebate = 243.51/17.6 = 13.836

11.3 12.2 13.1 14.0

Choose one answer: <------+------+------+------+------>

A B C D E

1. What is the R-square of the model, as a percentage?

R-sq = SSR/SST = 58199.5246/131607.8710 = .4422

43% 44% 45% 46%

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A B C D E

1. Note that the slope in the model is negative, which implies that coins do lose weight as they age. How much weight does the model predict that a nickel loses per year? To answer this, compute a 95% confidence interval estimate for the population slope, and then report the lowerendpoint (most negative) of the interval.

b1  t(29) s(b1) = -3.983  2.056(.83064) = -3.983  1.708 = -5.691 to -2.275

-5.7 -5.5 -5.3 -5.1

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A B C D E

1. What does the model predict for the weight of a brand new coin? To answer this, compute a 95% confidence interval for the average value of Y at X=0, and then report the upperendpoint of the interval.

Get this right from the intercept!

b0  t(29) s(b0) = 5021.015  2.056(13.65371) = 5021.015  28.072 = 4992.9 to 5049.1

5041 5044 5047 5050

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A B C D E

1. What does the model predict for the weight of a 20-year old coin? Because it is difficult to compute a predictive standard error by hand, just give a point estimate for this quantity.

Yhat = 5021.015 – 3.983(20) = 4941.355

4940 4944 4948 4952

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A B C D E

1. Note that the output contains information about predicting the weight of coins that are 11 years old. Now let’s compare the weight of 11-year oldcoinsto those 15 years old. The predicted weight of a 15-year old coin is 4961.27 and a 95% prediction interval for the weight is 4856.63 to 5065.92 milligrams. Based on these numbers, what would be the most that the weight of a coin could change in four years?

11 years old: 4872.63 to 5081.77 14 years old: 4856.63 to 5065.92

It could go from a high of 5081.77 to a low of 4856.63, or a change of 225.14

200 223 227 231

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A B C D E

1. On the graph showing the data, there are two coins (age 38 and 40) with an actual weight much higher than the one predicted by the Y-hat equation. These two coins were likely out of circulation for a period of time, so have much less wear than “normal”. The slope for the Y-hat equation is currently b1 = -3.983. If we re-ran the regression with these two coins eliminated, what would happen to the slope?

If these two points were out, the line would dip a lot lower as it tried to fit the other points more accurately. (It actually goes down to -6.1 or so)

A. It would be lower than -3.983

B. It would be higher than -3.983

C. It is really not possible to say.

1. In the table, what is the value of the missing moving average denoted ccccc? (Note: the ones labeled “other” are asked about on other versions of the exam, so are not listed.)

CMA=1411.33

1422 1455 1488 1521

Choose an interval: <------+------+------+------+------>

A B C D E

1. What is the value of the missing ratio denoted rrrrr?

RMA=.9608

.33 .36

Choose an interval: <------+------+------>

A B C

1. What production level does this model predict for first quarter1999?

This is t=32+5=37 TR(37) = 1407.486 + 5.861877(37) = 1624.3754

Y-hat = 1641.9611(1.0195) = 1656.0508

1642 1647 1652 1657

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A B C D E

1. Suppose you compare the seasonally adjusted production level in first quarter 1993 to the seasonally adjusted production level in second quarter 1993. What can you say about the comparison?

Q1 adjusts to 1542.1/1.0195 = 1512.641 Q2 adjusts to 1646.5/1.0986 = 1498.676

the difference is 13.965

A. The two are about equal (within 15 of each other).

B. First quarter is (15.1 or more) higher

C. First quarter is (15.1 or more) lower.

1. Simple exponential smoothing does not do a very good job in fitting this series because of the seasonality. But, just because something isn’t very good does not prevent people from trying it! Suppose you are applying SES with a smoothing constant of W = .330. After observing the value in 3rd quarter 1991, Y7 = 1261.8, you obtain a smoothed value of E7= 1378.91. What is the next smoothed value, E8?

E8 = .33 Y8 + .67 E7 = .33(1419.1) + .67(1378.91) = 1392.17

1394 1399 1404 1409

Choose an interval: <------+------+------+------+------>

A B C D E

1. Table A above lists the average price per square foot of office space in a Midwestern city for three different years. The prices are categorized by how many rooms the office contains, and generally show that larger offices rent at a lower price per square foot. Using 1990 as the base year for an unweighted price index, what would be the value of this index in 1995?

Sum(1990 price)=56.95 Sum(1995 price)=58.90 Index = 100*58.90/56.95 = 103.42

103.00 103.60 104.00 105.40

Choose an interval: <------+------+------+------+------>

A B C D E

1. In addition to the price information in Table A, you also have the information in Table B, which shows you the proportion of all leases that fit into the four size categories. Again using 1990 as the base year, this time compute a Laspeyres price index. What is the value of this index in 1995?

Sum(1990 wtd price)=14.98 Sum(1995wtd price)=15.54 Index = 100*15.54/14.98 = 103.78

103.00 103.60 104.00 105.40

Choose an interval: <------+------+------+------+------>

A B C D E

1. During the last day of lecture in class, we discussed seasonal adjustment of a time series called NAICS series 4411, which was monthly sales at automobile dealers. What does the abbreviation “NAICS” stand for? Make sure you get this right. This is the bonus I said you would get for the class evaluations.

A. North American Industry Classification System (I hope you get this)

B. A popular TV show(NCIS)

C. The small-school division for college football(NAIA)

1. I have carefully reviewed my scantron and have correctly bubbled in my UF ID number, the exam form code and have used the “section number” field to record my exam location number.

A. No I didn’t B. No I didn’t C. No I didn’t D. No I didn’t E. Yes I did

1. In other national elections, the percentage of votes for the Republican candidate (like Bush) tended to increase by about 0.2 for each percent of the state’s population that was 65 or over. Using the output from the “full model”, test to see if this is true for the 2000 election. What is the value of the test statistic you obtain?

Test H0: B1 = .2 TStat = (b1 - .2)/SE(b1) = (.3117 - .2)/.0420 = .1117/.0420 = 2.659

1.90 2.20 2.50 2.80

Choose an interval: <------+------+------+------+------>

A B C D E

1. Suppose you drop the variables X2, X6 and X7 from the “full model”. What is the adjusted R2 of the model you obtain as a result? Note: answer is in decimal form, not percentage.

This leaves the model with X1, X3, X4 and X5. R2 = .71022, n=50 and k=4 variables left

Adj R2 = 1 – [(1-R2)(n-1)/(n-k-l)] = 1 – [(.28978)(49)/45] = 1 - .31554 = .68446

.652 .662 .672 .682

Choose an interval: <------+------+------+------+------>

A B C D E

1. Again, suppose you drop the variables X2, X6 and X7 from the “full model”. You perform an F test to determine if the three variables are significant as a group in the full model. What is the value of the F statistic you obtain?

Since R2 = .71022, SSR = .71022(SST) = .71022(3719.84) = 2641.9048

Numerator of Partial F = (SSRfull – SSRreduced)/3 = (2948.108 – 2641.9048)/3 = 102.068

F = 129.148/MSEFull = 102.068/18.375 = 5.5547

4.9 5.9 6.9 7.9

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A B C D E

THERE WERE A TOTAL OF 22 QUESTIONS ON THIS EXAM

MAXIMUM POSSIBLE SCORE IS 102 POINTS

THIS OUTPUT IS USED FOR QUESTIONS 20-22 ON PAGE 8

R-Square values of selected other models

USE THIS INFORMATION IN ANSWERING QUESTIONS 11-15

ON PAGE 4

USE THIS OUTPUT IN ANSWERING QUESTIONS 5-10

ON PAGE 3

------Time SeriesFormulae ------

Simple aggregate index: 100*Sum(Prices in period t)/Sum(prices in base period)

Laspeyres index: Use the weighted prices in period t and base period. The weights used are those for the base period.

Moving average of length L: MA = (Sum of L consecutive series values)/L

For a centered MA, it is located on the middle time period when L is odd.

If L is even (for example quarterly data), you can use the alternate direct centering form:CMAt = .25 {½ Yt-2 + Yt-1 + Yt + Yt+1 + ½ Yt+2}

Ratio to moving average: RMAt = Yt / CMAt

Simple exponential smoothing: Et = W Yt + (1 – W) Et-1 where E1 = Y1

Seasonal Adjustment: At = Yt / St where St = seasonal factor for time period t

----- RegressionFormulae ------

Sample size is n. Number of variables is k.

Sum of Squares: SST = SSR + SSE = SS(Total) + SS(Regression) + SS(Error)

F test for entire model:

F test has k d.f for numerator and (n-k-1) for denominator

T test forH0: j = Ø versus H1:j ≠ Ø Tj = (bj -Ø)/SE(bj)

T test has (n-k-1) d.f.

Interval estimate of j:bj t*SE(bj) t has n-k-1 d.f.

R2= SSR/SST

Adjusted R-square:

Partial F test on group of g variables

inside a model with k total variables:

Test has g d.f. for numerator and (n-k-1) for denominator.