Classic “Oakland A’s” Case Study in Statistics – Linear Regressions with Dummy Variables

I have attached the problem – reading the case study isn’t necessary – only a long reading about the Oakland A’s and the decisions they made. This problem is really about doing the linear regressions in Excel with the data given and making conclusions based on those regressions.

I need this problem done by1pm tomorrow (Wednesday, 10/2) central standard time.

PLEASE NOTE: The Excel regression tables must be included. This is a multi-variable regression model, so plotting each variable separately in charts is not the solution. I need the regression analysis which comes in the data analysis toolpak in Excel.

Problem 3A

Read the “Oakland As (A)” case in the course pack. The data is available in the course website. The tab in the spreadsheet labeled Full Data Set contains the data in Exhibit 1 of the case while the tab labeled Nobel Data contains the attendance ﬁgures for the games Nobel pitched in and those he did not pitch in.

(a) Compute the descriptive statistics for the attendance at the games Nobel pitched in and those he did not pitch in. What is the diﬀerence in the average attendance for these two sets of games? Does this provide meaningful evidence that Nobel should be paid more because attendance was higher in the games he pitched in?

(b) Plot Ticket against Time (i.e. create a time series plot of Ticket). Do you see any patterns in the data?

Tickett = β0 + β1*Nobelt + εt

where Nobel is a dummy variable that takes the value 1 when Nobel starts on day t.

What are the estimates of β0 and β1? How do these relate to the average attendance ﬁgures computed in part (a)?

(d) Do the residuals from the regression in part (c) appear to be independent? Why or why not? If they are not independent, what factors might explain the pattern?

(e) Run the regression

Tickett = β0 + β1Post + β2GBt + β3Tempt + β4Prect + β5TOGt + β6TVt + +β7Promot + β8Nobelt + β9Yankst + β10Weekendt + β11ODt + β12DHt + εt

Do the residuals from this regression appear to be independent? (It is a close call but assume they are independent.) Why would these residuals be independent while the residuals from the model in part (c) are dependent?

(f) What evidence is there about Nobel pitching in a game being related to the attendance at the game? Do you have more conﬁdence in drawing a conclusion from the model in part (c) or the model in part (e) to answer this question? Why?

(g) Do you think Nobel’s agent has a legitimate case that Nobel should be paid more because he brings fans to the games?

Problem 3B

Read the “Oakland As (B)” case in the course packet. The data ﬁle is attached to this problem.

(a) Run a regression of Attendance against Wins. What is the interpretation of the coeﬃcient associated with Wins? What is the interpretation of R2 in this regression? What is the practical problem associated with using this model to forecast Attendance for the next season (i.e. to forecast attendance in the 1981 season)?

(b) Now run a regression of Attendance against Roddey’s forecast of the number of wins for that season. Why is the R2 value obtained from this regression so much lower than the R2 obtained from the regression in part (a)?

(d) Before the 1981 season starts Roddey forecasts 95 wins for the season. Using the model from part (b), what is the prediction for attendance in the 1981 season? What is the standard deviation associated with the prediction?

(e) Using the prediction and standard deviation for the prediction from the model in part (b), what is the probability associated with a bonus to Nobel of $0, $50,000, $100,000 and $150,000? What is the mean of this distribution?

(e) Using the probability distribution from part (d), what is the expected cost if the lump-sum incentive plan is used?

>Full Data Set

2 5 1 4

0 2 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0

2 3 1 5

0 2 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

2 7 1 6

0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

2 5 1 7

0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

1 7 2 1 60 0 2 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 6 1 2 60 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 4 1 3

0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

3 3 1 5

0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

3 2 1 6

0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

3 1 0 7 57 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0

5 1 0 5 57 0 2 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

5 1 0 6 59 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

5 1 0 7 58 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0

11 1 0 1 60 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

11 1 0 2 60 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

11 1 0 3 60 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

7 1 0 6

1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

7 1 0 7 57 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

12 4 2 5

0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

12 3 2 6 55 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

12 5 3 7 57 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

13 4 2 1 58 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1
23

13 4 3 2 58 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

13 3 2 3 59 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

9 3 6 5 59 0 2 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

9 3 6 6 61 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

9 3 7 7 63 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

10 3 7 1 61 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

10 3 7 2 59 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

10 3 7 3 60 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

4 3 7 5 60 0 2 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

4 3 7 6 63 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

294

4 3 8 7 64 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

6 3 9 1 62 0 2 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

6 4 10 2 62 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

6 4 11 3 63 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

8 4 11 5

0 2 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

8 4 12 6 69 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

8 4 12 7 63 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

3 5 12 4 66 0 2 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0

3 5 12 5 62 0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

5 5 13 3 65 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

5 3 12 4 65 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

11 3 12 5 60 1 2 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

11 3 11 6 65 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

11 3 11 7 65 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

7 3 12 1 65 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

7 3 12 2 63 0 2 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0

7 3 12 3 64 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

2 2 12 1 65 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

2 2 12 2 67 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

2 2 12 3 63 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

1 2 13 5 62 0 2 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 2 12 6 63 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 2 13 7 63 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0

9 2 15 2 67 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

9 2 15 3 65 0 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

9 2 15 4 61 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

10 2 15 5 62 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

10 2 16 6 64 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

10 2 17 7 63 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

4 2 17 1 62 0 2 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

4 2 17 2 62 0 2 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

12 3 19 1 65 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

12 3 18 2 63 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

12 2 17 3 64 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

13 2 17 5 62 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

13 2 16 6 61 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

13 2 17 7 63 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

8 2 15 2 70 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

8 2 14 3 69 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

8 2 14 4 64 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

6 2 14 5 64 0 2 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

6 2 13 6 62 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

6 2 12 7 65 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

															NUMBER	TICKET	OPP	POS	GB	DOW	TEMP	PREC	TOG	TV	PROMO	NOBEL	YANKS	WKEND	OD	DH	0	1	O2	O	3	O	4	O	5	O	6	O	7	O	8	O	9	O	10	O	11	O	12	O	13
	24						15					57
57	29			66
	5783								64
											63			62
	52									60
2				14
24		18						61
										65	70		58
5	23						59
	9014
86	36
	7062
182							17
1	26
24	27
		16		47	31
	49			55
78	39
	19		41		56
20		50
21	10	54
22		21882
	44
	40
25		15947
	12990
187	53
28		20162
	38	73
30		5628
477	68
32		27312
33		46
34		17666
35		48
	6856
37		8482				69
	5204
	7369
	11337
	7696
42		74
43		6370
	5949
45		6506
	10606
	14588
	8645
	4765
1			67
51		4651
	6697
	6283
	13629
	13062
	11934
	75
	10947
	11532
	10578
	18745
	47946
	32905
	9731
	2443
	3598
	17440
	11253
	10756
	3069
71		3836
72		3180
	5099
	4581
	10662

Nobel Data

5783

15947

27312

8482 9014
11337

5949 7062
8645

13629

47946

3598

5099

21882
12990
20162
5628
17666
6856
5204
7369
7696
6370
6506
10606
14588
4765
4651
6697
6283
13062
11934
10947
11532
10578
18745
32905
9731
2443
17440
11253
10756
3069
3836
3180
4581
10662

TICKET when Nobel pitches	TICKET when Nobel does not pitch
5260	24415
5239	5729
18217
7839	6300
10549	2140
2418
6570
8636
12605
24272
7569	4731
4929
4141
5061
4488
4094
18753
3873
47768
46294
4899
7413
16741

Nobel Data

NOBEL
Residuals
NOBEL Residual Plot
1

1 1

#REF!
#REF!
Game
Residual
Residuals vs. Game

Sheet1

7466

93 89

593

63 70

83 80

Year	Attendance	Wins	Forecasted Wins
1968		83	82	79
19	69	778232		88	90
19	70	778355		89	91
1971	9149	93	101	106
1972	962931
1973	10007	63	94	84
1974	845693	92
1975	1075518	98
1976	7	80	87
1977	49	54
1978	526412	67
1979	306763	65
1980	843319

Sheet2

Sheet3

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