Expert answer:Multiple regression with dummy variables
Solved by verified expert:In this project, you will learn how to run and interpret an estimated multiple regression model
with a dummy variable. You will be given a data set called “Auto MPG Data Set” which you
can download in “Table of Contents – Project 3” in sakai. The data set contains 391 samples and
seven variables: six continuous variables mpg, cylinders, displayment, horsepower, weight,
acceleration and one dummy variable bin year. The dummy variable bin year equals 1 for
vehicles with model year before 1976 and 0 for those with model year in or after 1976.
The goal of the analysis is to develop a regression model for predicting mpg using the remaining
variables. That is, the response variable (y) is mpg and the explanatory variables (x) are cylinders,
displayment, horsepower, weight, acceleration, bin year.
project_description_2.pdf
data_set.xlsx
Unformatted Attachment Preview
Project 3. Multiple regression with dummy variables
Auto MPG Data Set
• The project is upto 2 percent points toward your final grade.
• It is due on October 29 11:55 pm.
Project description
In this project, you will learn how to run and interpret an estimated multiple regression model
with a dummy variable. You will be given a data set called “Auto MPG Data Set” which you
can download in “Table of Contents – Project 3” in sakai. The data set contains 391 samples and
seven variables: six continuous variables mpg, cylinders, displayment, horsepower, weight,
acceleration and one dummy variable bin year. The dummy variable bin year equals 1 for
vehicles with model year before 1976 and 0 for those with model year in or after 1976.
The goal of the analysis is to develop a regression model for predicting mpg using the remaining
variables. That is, the response variable (y) is mpg and the explanatory variables (x) are cylinders,
displayment, horsepower, weight, acceleration, bin year.
Assignments
Please fill out the blanks in the next page and save the document. Prepare an excel file with
the data you collected in one tab and the regression output in another tab. Upload two files in
“Assignments – Project 3” in sakai.
Note
Please feel free to contact me if you need any question, concern, and advise. I will be happy to
assist you. My office is MCOB 341 and email address is jinhakkim@southalabama.edu.
1
Project report
Name:
J Number:
1. (0.2 pt) What is the R-square?
2. (0.6 pt) What is the resulting multiple regression model?
mpg
ˆ =
+
× cylinder +
× displayment
+
× weight
× acceleration +
+
× horsepower
+
× bin year
3. (0.3 pt) Check all SIGNIFICANT explanatory variables at 5% significant level.
(In other words, find explanatory variables that has p-value less than 0.05).
cylinder
displayment
horsepower
weight
acceleration
bin year
4. (0.5 pt) The following sample has a missing mpg value:
mpg
cylinder
weight
=
=
=
?,
8,
4278,
displacement
acceleration
=
=
400,
9.5,
horsepower
bin year
=
=
230,
1
What is the predicted mpg for the above sample?
5. (0.4 pt) Is there a significant mpg difference between vehicles before 1976 and those in or after
1976 at 5% significance level?
Yes,
No
2
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car name
amc ambassador brougham
amc ambassador dpl
amc ambassador sst
amc concord
amc concord
amc concord d/l
amc concord dl 6
amc gremlin
amc gremlin
amc gremlin
amc gremlin
amc hornet
amc hornet
amc hornet
amc hornet
amc hornet sportabout (sw)
amc matador
amc matador
amc matador
amc matador
amc matador
amc matador (sw)
amc matador (sw)
amc pacer
amc pacer d/l
amc rebel sst
amc spirit dl
audi 100 ls
audi 100ls
audi 100ls
audi 4000
audi 5000
audi 5000s (diesel)
audi fox
bmw 2002
bmw 320i
buick century
buick century
buick century 350
buick century limited
buick century luxus (sw)
buick century special
buick electra 225 custom
buick estate wagon (sw)
buick estate wagon (sw)
buick lesabre custom
mpg cylinders displacement horsepower weight
13
8
360
175
3821
15
8
390
190
3850
17
8
304
150
3672
19,4
6
232
90
3210
24,3
4
151
90
3003
18,1
6
258
120
3410
20,2
6
232
90
3265
21
6
199
90
2648
19
6
232
100
2634
18
6
232
100
2789
20
6
232
100
2914
18
6
199
97
2774
18
6
232
100
2945
19
6
232
100
2901
22,5
6
232
90
3085
18
6
258
110
2962
18
6
232
100
3288
14
8
304
150
3672
16
6
258
110
3632
15
6
258
110
3730
15,5
8
304
120
3962
15
8
304
150
3892
14
8
304
150
4257
19
6
232
90
3211
17,5
6
258
95
3193
16
8
304
150
3433
27,4
4
121
80
2670
24
4
107
90
2430
20
4
114
91
2582
23
4
115
95
2694
34,3
4
97
78
2188
20,3
5
131
103
2830
36,4
5
121
67
2950
29
4
98
83
2219
26
4
121
113
2234
21,5
4
121
110
2600
17
6
231
110
3907
22,4
6
231
110
3415
13
8
350
175
4100
25
6
181
110
2945
13
8
350
150
4699
20,6
6
231
105
3380
12
8
455
225
4951
14
8
455
225
3086
16,9
8
350
155
4360
13
8
350
155
4502
47
48
49
50
51
52
53
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60
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93
buick opel isuzu deluxe
buick regal sport coupe (turbo)
buick skyhawk
buick skylark
buick skylark
buick skylark 320
buick skylark limited
cadillac eldorado
cadillac seville
capri ii
chevroelt chevelle malibu
chevrolet bel air
chevrolet camaro
chevrolet caprice classic
chevrolet caprice classic
chevrolet caprice classic
chevrolet cavalier
chevrolet cavalier 2-door
chevrolet cavalier wagon
chevrolet chevelle concours (sw)
chevrolet chevelle malibu
chevrolet chevelle malibu
chevrolet chevelle malibu classic
chevrolet chevelle malibu classic
chevrolet chevette
chevrolet chevette
chevrolet chevette
chevrolet chevette
chevrolet citation
chevrolet citation
chevrolet citation
chevrolet concours
chevrolet impala
chevrolet impala
chevrolet impala
chevrolet impala
chevrolet malibu
chevrolet malibu
chevrolet malibu classic (sw)
chevrolet monte carlo
chevrolet monte carlo landau
chevrolet monte carlo landau
chevrolet monte carlo s
chevrolet monza 2+2
chevrolet nova
chevrolet nova
chevrolet nova
30
17,7
21
20,5
26,6
15
28,4
23
16,5
25
16
15
27
13
17,5
17
28
34
27
13
18
17
16
17,5
29
30,5
30
32,1
28,8
28
23,5
17,5
14
14
13
11
13
20,5
19,2
15
15,5
19,2
15
20
15
18
22
4
6
6
6
4
8
4
8
8
4
6
8
4
8
8
8
4
4
4
8
8
6
6
8
4
4
4
4
6
4
6
6
8
8
8
8
8
6
8
8
8
8
8
8
6
6
6
111
231
231
231
151
350
151
350
350
140
250
350
151
400
305
305
112
112
112
307
307
250
250
305
85
98
98
98
173
151
173
250
454
350
350
400
350
200
267
400
350
305
350
262
250
250
250
80
165
110
105
84
165
90
125
180
92
105
145
90
150
145
130
88
88
88
130
130
100
100
140
52
63
68
70
115
90
110
110
220
165
165
150
145
95
125
150
170
145
145
110
100
105
105
2155
3445
3039
3425
2635
3693
2670
3900
4380
2572
3897
4440
2950
4464
3880
3840
2605
2395
2640
4098
3504
3329
3781
4215
2035
2051
2155
2120
2595
2678
2725
3520
4354
4209
4274
4997
3988
3155
3605
3761
4165
3425
4082
3221
3336
3459
3353
94
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chevrolet nova custom
chevrolet vega
chevrolet vega
chevrolet vega
chevrolet vega (sw)
chevrolet vega 2300
chevrolet woody
chevy c10
chevy c20
chevy s-10
chrysler cordoba
chrysler lebaron medallion
chrysler lebaron salon
chrysler lebaron town @ country (sw)
chrysler new yorker brougham
chrysler newport royal
datsun 1200
datsun 200sx
datsun 200-sx
datsun 210
datsun 210
datsun 210 mpg
datsun 280-zx
datsun 310
datsun 310 gx
datsun 510
datsun 510 (sw)
datsun 510 hatchback
datsun 610
datsun 710
datsun 710
datsun 810
datsun 810 maxima
datsun b210
datsun b-210
datsun b210 gx
datsun f-10 hatchback
datsun pl510
datsun pl510
dodge aries se
dodge aries wagon (sw)
dodge aspen
dodge aspen
dodge aspen 6
dodge aspen se
dodge challenger se
dodge charger 2.2
16
20
21
25
22
28
24,5
13
10
31
15,5
26
17,6
18,5
13
13
35
32,9
23,9
31,8
40,8
37
32,7
37,2
38
27,2
28
37
22
32
24
22
24,2
31
32
39,4
33,5
27
27
29
25,8
18,6
19,1
20,6
20
15
36
6
4
4
4
4
4
4
8
8
4
8
4
6
8
8
8
4
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4
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6
4
4
4
4
4
4
4
4
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6
4
4
4
4
4
4
4
4
6
6
6
6
8
4
250
140
140
140
140
140
98
350
307
119
400
156
225
360
440
400
72
119
119
85
85
85
168
86
91
119
97
119
108
83
119
146
146
79
85
85
85
97
97
135
156
225
225
225
225
383
135
100
90
72
75
72
90
60
145
200
82
190
92
85
150
215
190
69
100
97
65
65
65
132
65
67
97
92
92
94
61
97
97
120
67
70
70
70
88
88
84
92
110
90
110
100
170
84
3278
2408
2401
2542
2408
2264
2164
4055
4376
2720
4325
2585
3465
3940
4735
4422
1613
2615
2405
2020
2110
1975
2910
2019
1995
2300
2288
2434
2379
2003
2545
2815
2930
1950
1990
2070
1945
2130
2130
2525
2620
3620
3381
3360
3651
3563
2370
141
142
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187
dodge colt
dodge colt
dodge colt
dodge colt (sw)
dodge colt hardtop
dodge colt hatchback custom
dodge colt m/m
dodge coronet brougham
dodge coronet custom
dodge coronet custom (sw)
dodge d100
dodge d200
dodge dart custom
dodge diplomat
dodge magnum xe
dodge monaco (sw)
dodge monaco brougham
dodge omni
dodge rampage
dodge st. regis
fiat 124 sport coupe
fiat 124 tc
fiat 124b
fiat 128
fiat 128
fiat 131
fiat strada custom
fiat x1.9
ford country
ford country squire (sw)
ford country squire (sw)
ford escort 2h
ford escort 4w
ford f108
ford f250
ford fairmont
ford fairmont (auto)
ford fairmont (man)
ford fairmont 4
ford fairmont futura
ford fiesta
ford futura
ford galaxie 500
ford galaxie 500
ford galaxie 500
ford gran torino
ford gran torino
28
26
27,9
28
25
35,7
33,5
16
15
14
13
11
15
19,4
17,5
12
15,5
30,9
32
18,2
26
26
30
29
24
28
37,3
31
12
13
15,5
29,9
34,4
13
10
26,4
20,2
25,1
22,3
24
36,1
18,1
15
14
14
14
16
4
4
4
4
4
4
4
8
8
8
8
8
8
8
8
8
8
4
4
8
4
4
4
4
4
4
4
4
8
8
8
4
4
8
8
4
6
4
4
4
4
8
8
8
8
8
8
90
98
156
98
97,5
98
98
318
318
318
318
318
318
318
318
383
318
105
135
318
98
116
88
68
90
107
91
79
400
400
351
98
98
302
360
140
200
140
140
140
98
302
429
351
351
302
302
75
79
105
80
80
80
83
150
150
150
150
210
150
140
140
180
145
75
84
135
90
75
76
49
75
86
69
67
167
170
142
65
65
130
215
88
85
88
88
92
66
139
198
153
153
137
140
2125
2255
2800
2164
2126
1915
2075
4190
3777
4457
3755
4382
3399
3735
4080
4955
4140
2230
2295
3830
2265
2246
2065
1867
2108
2464
2130
2000
4906
4746
4054
2380
2045
3870
4615
2870
2965
2720
2890
2865
1800
3205
4341
4154
4129
4042
4141
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
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219
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221
222
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225
226
227
228
229
230
231
232
233
234
ford gran torino
ford gran torino (sw)
ford gran torino (sw)
ford granada
ford granada ghia
ford granada gl
ford granada l
ford ltd
ford ltd
ford ltd landau
ford maverick
ford maverick
ford maverick
ford maverick
ford mustang
ford mustang gl
ford mustang ii
ford mustang ii 2+2
ford pinto
ford pinto
ford pinto
ford pinto
ford pinto
ford pinto (sw)
ford pinto runabout
ford ranger
ford thunderbird
ford torino
ford torino 500
hi 1200d
honda accord
honda accord
honda accord cvcc
honda accord lx
honda civic
honda civic
honda civic
honda civic (auto)
honda civic 1300
honda civic 1500 gl
honda civic cvcc
honda civic cvcc
honda prelude
maxda glc deluxe
maxda rx3
mazda 626
mazda 626
14,5
13
14
18,5
18
20,2
22
13
14
17,6
21
18
15
24
18
27
13
25,5
19
26
23
18
26,5
22
21
28
16
17
19
9
32,4
36
31,5
29,5
24
33
38
32
35,1
44,6
33
36,1
33,7
34,1
18
31,3
31,6
8
8
8
6
6
6
6
8
8
8
6
6
6
6
6
4
8
4
4
4
4
6
4
4
4
4
8
8
6
8
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3
4
4
351
302
302
250
250
200
232
351
351
302
200
250
250
200
250
140
302
140
122
122
140
171
140
122
122
120
351
302
250
304
107
107
98
98
120
91
91
91
81
91
91
91
107
86
70
120
120
152
140
140
98
78
88
112
158
148
129
85
88
72
81
88
86
129
89
85
80
83
97
72
86
86
79
149
140
88
193
72
75
68
68
97
53
67
67
60
67
53
60
75
65
90
75
74
4215
4294
4638
3525
3574
3060
2835
4363
4657
3725
2587
3021
3158
3012
3139
2790
3169
2755
2310
2451
2639
2984
2565
2395
2226
2625
4335
3449
3302
4732
2290
2205
2045
2135
2489
1795
1965
1965
1760
1850
1795
1800
2210
1975
2124
2542
2635
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
mazda glc
mazda glc 4
mazda glc custom
mazda glc custom l
mazda glc deluxe
mazda rx2 coupe
mazda rx-4
mazda rx-7 gs
mercedes benz 300d
mercedes-benz 240d
mercedes-benz 280s
mercury capri 2000
mercury capri v6
mercury cougar brougham
mercury grand marquis
mercury lynx l
mercury marquis
mercury marquis brougham
mercury monarch
mercury monarch ghia
mercury zephyr
mercury zephyr 6
nissan stanza xe
oldsmobile cutlass ciera (diesel)
oldsmobile cutlass ls
oldsmobile cutlass salon brougham
oldsmobile cutlass salon brougham
oldsmobile cutlass supreme
oldsmobile delta 88 royale
oldsmobile omega
oldsmobile omega brougham
oldsmobile starfire sx
oldsmobile vista cruiser
opel 1900
opel 1900
opel manta
opel manta
peugeot 304
peugeot 504
peugeot 504
peugeot 504
peugeot 504
peugeot 504 (sw)
peugeot 505s turbo diesel
peugeot 604sl
plymouth arrow gs
plymouth champ
46,6
34,1
31
37
32,8
19
21,5
23,7
25,4
30
16,5
23
21
15
16,5
36
11
12
15
20,2
20,8
19,8
36
38
26,6
19,9
23,9
17
12
11
26,8
23,8
12
28
25
24
26
30
25
23
19
27,2
21
28,1
16,2
25,5
39
4
4
4
4
4
3
3
3
5
4
6
4
6
8
8
4
8
8
6
8
6
6
4
6
8
8
8
8
8
8
6
4
8
4
4
4
4
4
4
4
4
4
4
4
6
4
4
86
91
91
91
78
70
80
70
183
146
168
122
155
302
351
98
429
429
250
302
200
200
120
262
350
260
260
260
350
350
173
151
350
116
116
116
97
79
110
120
120
141
120
141
163
122
86
65
68
68
68
52
97
110
100
77
67
120
86
107
130
138
70
208
198
72
139
85
85
88
85
105
110
90
110
160
180
115
85
180
90
81
75
78
70
87
88
88
71
87
80
133
96
64
2110
1985
1970
2025
1985
2330
2720
2420
3530
3250
3820
2220
2472
4295
3955
2125
4633
4952
3432
3570
3070
2990
2160
3015
3725
3365
3420
4060
4456
3664
2700
2855
4499
2123
2220
2158
2300
2074
2672
2957
3270
3190
2979
3230
3410
2300
1875
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
plymouth cricket
plymouth ‘cuda 340
plymouth custom suburb
plymouth duster
plymouth duster
plymouth duster
plymouth fury
plymouth fury gran sedan
plymouth fury iii
plymouth fury iii
plymouth fury iii
plymouth grand fury
plymouth horizon
plymouth horizon 4
plymouth horizon miser
plymouth horizon tc3
plymouth reliant
plymouth reliant
plymouth sapporo
plymouth satellite
plymouth satellite custom
plymouth satellite custom (sw)
plymouth satellite sebring
plymouth valiant
plymouth valiant
plymouth valiant custom
plymouth volare
plymouth volare custom
plymouth volare premier v8
pontiac astro
pontiac catalina
pontiac catalina
pontiac catalina
pontiac catalina brougham
pontiac firebird
pontiac grand prix
pontiac grand prix lj
pontiac j2000 se hatchback
pontiac lemans v6
pontiac phoenix
pontiac phoenix
pontiac phoenix lj
pontiac safari (sw)
pontiac sunbird coupe
pontiac ventura sj
renault 12 (sw)
renault 12tl
26
14
13
22
23
20
18
14
14
14
15
16
34,2
34,7
38
34,5
27,2
30
23,2
18
16
14
18
18
22
19
20,5
19
13
23
14
14
16
14
19
16
16
31
21,5
33,5
27
19,2
13
24,5
18,5
26
27
4
8
8
6
6
6
6
8
8
8
8
8
4
4
4
4
4
4
4
8
6
8
6
6
6
6
6
6
8
4
8
8
8
8
6
8
8
4
6
4
4
6
8
4
6
4
4
91
340
360
198
198
198
225
318
440
318
318
318
105
105
105
105
135
135
156
318
225
318
225
225
225
225
225
225
318
140
455
400
400
400
250
400
400
112
231
151
151
231
400
151
250
96
101
70
160
170
95
95
95
95
150
215
150
150
150
70
63
63
70
84
84
105
150
105
150
105
105
100
95
100
100
150
78
225
175
170
175
100
230
180
85
115
90
90
105
175
88
110
69
83
1955
3609
4654
2833
2904
3102
3785
4237
4312
4096
4135
4498
2200
2215
2125
2150
2490
2385
2745
3436
3439
4077
3613
3121
3233
3264
3430
3630
3940
2592
4425
4385
4668
4464
3282
4278
4220
2575
3245
2556
2735
3535
5140
2740
3645
2189
2202
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
renault 5 gtl
saab 99e
saab 99gle
saab 99le
saab 99le
subaru
subaru
subaru dl
subaru dl
toyota carina
toyota celica gt
toyota celica gt liftback
toyota corolla
toyota corolla
toyota corolla
toyota corolla
toyota corolla
toyota corolla 1200
toyota corolla 1200
toyota corolla 1600 (sw)
toyota corolla liftback
toyota corolla tercel
toyota corona
toyota corona
toyota corona
toyota corona
toyota corona hardtop
toyota corona liftback
toyota corona mark ii
toyota cressida
toyota mark ii
toyota mark ii
toyota starlet
toyota tercel
toyouta corona mark ii (sw)
triumph tr7 coupe
vokswagen rabbit
volkswagen 1131 deluxe sedan
volkswagen 411 (sw)
volkswagen dasher
volkswagen dasher
volkswagen dasher
volkswagen jetta
volkswagen model 111
volkswagen rabbit
volkswagen rabbit
volkswagen rabbit custom
36
25
21,6
24
25
26
32,3
30
33,8
20
32
21,1
29
28
32,2
32,4
34
31
32
27
26
38,1
25
31
24
27,5
24
29,8
24
25,4
20
19
39,1
37,7
23
35
29,8
26
22
26
25
30,5
33
27
29
29,5
29
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
6
6
6
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
79
104
121
121
121
108
97
97
97
97
144
134
97
97
108
108
108
71
71
97
97
89
113
76
134
134
113
134
113
168
156
156
79
89
120
122
89
97
121
79
90
97
105
97
90
97
97
58
95
115
110
115
93
67
67
67
88
96
95
75
75
75
75
70
65
65
88
75
60
95
52
96
95
95
90
95
116
122
108
58
62
97
88
62
46
76
67
71
78
74
60
70
71
78
1825
2375
2795
2660
2671
2391
2065
1985
2145
2279
2665
2515
2171
2155
2265
2350
2245
1773
1836
2100
2265
1968
2228
1649
2702
2560
2278
2711
2372
2900
2807
2930
1755
2050
2506
2500
1845
1835
2511
1963
2223
2190
2190
1834
1937
1825
1940
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
volkswagen rabbit custom diesel
volkswagen rabbit l
volkswagen scirocco
volkswagen super beetle
volkswagen type 3
volvo 144ea
volvo 145e (sw)
volvo 244dl
volvo 245
volvo 264gl
volvo diesel
vw dasher (diesel)
vw pickup
vw rabbit
vw rabbit
vw rabbit c (diesel)
43,1
36
31,5
26
23
19
18
22
20
17
30,7
43,4
44
29
41,5
44,3
4
4
4
4
4
4
4
4
4
6
6
4
4
4
4
4
90
105
89
97
97
121
121
121
130
163
145
90
97
90
98
90
48
74
71
46
54
112
112
98
102
125
76
48
52
70
76
48
1985
1980
1990
1950
2254
2868
2933
2945
3150
3140
3160
2335
2130
1937
2144
2085
acceleration bin_year
11
1
8,5
1
11,5
1
17,2
0
20,1
0
15,1
0
18,2
0
15
1
13
1
15
1
16
1
15,5
1
16
1
16
1
17,6
0
13,5
1
15,5
1
11,5
1
18
1
19
1
13,9
0
12,5
1
15,5
1
17
1
17,8
0
12
1
15
0
14,5
1
14
1
15
1
15,8
0
15,9
0
19,9
0
16,5
1
12,5
1
12,8
0
21
1
15,8
0
13
1
16,4
0
14,5
1
15,8
0
11
1
10
1
14,9
0
13,5
1
14,8
13,4
15
16,9
16,4
11,5
16
17,4
12,1
14,9
18,5
14
17,3
12
12,5
15,4
19,6
18
18,6
14
12
15,5
17
13
22,2
17
16,5
15,5
11,3
16,5
12,6
16,4
9
12
12
14
13
18,2
15
9,5
11,4
13,2
13
13,5
17
16
14,5
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
18
19,5
19,5
17
19
15,5
22,1
12
15
19,4
12,2
14,5
16,6
13
11
12,5
18
14,8
14,9
19,2
19,2
19,4
11,4
16,4
16,2
14,7
17
15
16,5
19
17
14,5
13,8
19
17
18,6
16,8
14,5
14,5
16
14,4
18,7
18,7
16,6
17,7
10
13
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
14,5
17,7
14,4
15
17
14,4
15,9
13
12,5
13,5
14
13,5
11
13,2
13,7
11,5
13,7
14,5
11,6
15,2
15,5
14
14,5
19,5
15,5
15,5
14,7
16
12,5
12
14,3
20,7
16,2
15
14
18,1
15,8
15,4
17,3
16,4
14,4
11,2
10
13,5
13
14,5
14
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
12,8
16
16
19
21
17,1
14,7
13
13,5
13,4
16
16,5
19,5
17,6
14,5
15,6
12
15,8
18,5
16,5
17
14,5
13,6
16
16,5
18,6
14,5
10,5
15,5
18,5
17
14,5
18,5
16,6
15
17,4
15
15,7
16,1
13,8
17,5
16,4
14,4
15,2
13,5
17,5
18,3
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
17,9
16
17,6
18,2
19,4
13,5
13,5
12,5
20,1
21,8
16,7
14
14
14,9
13,2
17,3
11
11,5
21
12,8
16,7
18,2
14,5
17
19
15,5
22,2
19
13,5
11
12,9
17,6
12,5
14
16,9
15,5
14,5
19,5
17,5
17
21,9
24,8
19,5
20,4
15,8
15,5
16,4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
20,5
8
13
15,5
16
16,5
19
14,5
8,5
13
13,5
14,5
13,2
14,9
14,7
14,9
15,7
12,9
16,7
11
15,5
14
16,5
16,5
15,4
16
17,2
17,7
13,2
18,5
10
12
11,5
11,5
15
9,5
11,1
16,2
15,4
13,2
18
19,2
12
16
16,2
18
15,3
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
18,6
17,5
15,7
14
13,5
15,5
17,8
16,4
18
19
13,9
14,8
16
16,4
15,2
16,8
16,9
19
21
16,5
18,2
18,8
14
16,5
13,5
14,2
15,5
15,5
15
12,6
13,5
15,5
16,9
17,3
14,5
15,1
15,3
20,5
18
15,5
16,5
14,1
14,2
19
14
12,2
14,5
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
21,5
15,3
14,9
21
23,5
15,5
1 …
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