Econometrics Homework

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consider the multiple regression model
E(y) = β₁ + β₂x₂ + β₃x₃
Use the following observations.
y
154
112
80
22
53
106
78
28
74
82
143
90
58
141
86
77
107
76
23
49
102
72
22
62
77
157
82
21
71
88
104
84
24
114
128
26
64
60
75
104
1
a
b
c
d
2
x₂
1837
2422
1697
1216
1520
1563
1196
1095
1277
2099
1559
3018
943
1568
1189
2116
1476
1453
925
1474
1454
1335
1314
1088
2608
1774
3552
1091
1121
2011
1571
1564
1073
1189
1641
960
1919
854
1567
2214
x₃
5
13
38
55
35
20
33
40
36
16
17
26
50
5
29
14
17
36
59
35
19
37
44
37
18
20
23
44
33
16
17
37
50
22
55
47
23
46
36
27
The estimated coefficients of the regression equation is,
b₁
b₂
b₃
148.0796 -0.00171
-1.8275
141.0282 -0.00156
-1.9237
134.3125 -0.00142
-2.0249
127.9167 -0.00129
-2.1315
Given x₂ = x̅ ₂ and x₃ = x̅ ₃, ŷ = ________.
a
b
c
d
3
71.659
75.430
79.400
83.579
a
b
c
d
The variance of the error term is,
680.190
694.071
708.236
722.690
a
b
c
d
The test statistic for the null hypothesis β₂ = 0 is,
-0.159
-0.169
-0.180
-0.191
a
b
c
d
R² = _______
0.4320
0.4596
0.4889
0.5201
a
b
c
d
The margin of error for a 95% interval estimate for β₃ is
0.7430
0.7214
0.7004
0.6800
a
b
c
d
The 95% interval estimate for the expected value of y given x₂ = x̅ ₂ and x₃ = x̅ ₃ is,
67.70
91.10
71.04
87.76
73.43
85.37
75.14
83.66
4
5
6
7
Questions 8-13 are based on the following
Consider the following model which relates the fraction (weight) of a household’s budget spent on alcoholic
beverages (BSALC) to total expenditure (BUDGET), age of the household head (AGE), and the number of
children in the household (NKIDS).
E(BSALC) = β₁ + β₂ln(BUDGET) + β₃AGE + β₄NKIDS
BSALC
BUDGET
AGE
NKIDS
8
a
b
c
d
Budget Share (fraction) for alcohol expenditure
total household BUDGET (rounded to the nearest 10 UK pounds sterling)
age of household head
number of children
The value of coefficient b₂ = ______. This implies …
if BUDGET increases by
1%
the alcohol share will increase by
if BUDGET increases by
1%
the alcohol share will increase by
if BUDGET increases by
1%
the alcohol share will increase by
Both a and b are correct
0.000297
0.0297
0.0297
9
a
b
c
d
The variance of the error term is,
0.00743
0.00595
0.00476
0.00380
10
a
b
c
d
A 95% interval for β₃ is _____ to _____.
-0.00207 -0.00078
-0.00186 -0.00100
-0.00171 -0.00114
-0.00162 -0.00124
11
a
b
c
d
To test the hypothesis that the budget proportion for alcohol does not depend on AGE , the test statistic is …
-6.521
-7.672
-8.026
-9.618
12
To test the hypothesis that the budget proportion for alcohol does not depend on the number of children in the
household, the p-value is …
0.000485 Conclude BSALC does not depend on the number of children
0.000231 Conclude BSALC does not depend on the number of children
0.000110 Conclude BSALC decreases with each additional child.
0.000052 Conclude BSALC decreases with each additional child.
a
b
c
d
13
a
b
c
d
Commodities are regarded as luxuries if β₂ > 0 and necessities if β₂ < 0. For alcoholic beverages, test H₀: β₂ ≤ 0 against H₁: β₂ > 0. The t-statistic for the test is:
6.783 Reject H₀. Alcoholic beverage is a luxury.
5.427 Reject H₀. Alcoholic beverage is a luxury.
4.341 Reject H₀. Alcoholic beverage is a luxury.
3.473 Do not reject H₀. Alcoholic beverage is a necessity.
Questions 14-17 are based on the following
The data in the previous question is used again. This time it is used to estimate how the proportion of
household budget spent on transportation (WTRANS) depends on ln(BUDGET), AGE, NKIDS.
E(BSTRANS) = β₁ + β₂ln(BUDGET) + β₃AGE + β₄NKIDS
14
a
b
c
d
15
a
b
c
d
The predicted proportion of a budget that will be spent on transportation, for two-children households, when
BUDGET and age are set at their sample means is ______.
0.1675
0.1537
0.1410
0.1294
SSE = _______
13.667
14.386
15.144
15.941
16
a
b
c
d
Are there any variables that you might exclude from the equation?
NKIDS should be excluded. The p-value is
0.0090
NKIDS should be excluded. The p-value is
0.0129
AGE should be excluded. The p-value is
0.2072
AGE should be excluded. The p-value is
0.8289
17
a
b
c
d
The fraction of the variations in the budget proportion allocated to transport explained by this equation is:
0.1004
0.0609
0.0369
0.0224
Question 18-20 are based on the following
Data on per capita consumption of beef, the price of beef, the price of lamb, the price of pork, and per capita
disposable income for Australia, for the period 1990-2006, are given in this worksheet. All prices and income
have been deflated with 1986 as the base year. Consider the log-log demand function.
E[ln(QBEEF)] = β₁ + β₂ln(PBEEF) + β₃ln(PLAMB) + β₄ln(PPORK)+ β₅ln(INCM)
The variables are defined as:
QBEEF = per capita consumption of beef in year t (pounds)
PBEEF = price of beef in year t (pence per pound)
PLAMB = price of lamb in year t (pence per pound)
PPORK = price of pork in year t (pence per pound)
INCM = per capita income in year t (Australian currency pounds)
Determine the estimated coefficients and fill in the blanks below.
Variable Coefficient
Intercept
ln(PBEEF)
ln(PLAMB)
ln(PPORK)
ln(INCM)
18
a
b
c
d
The coefficient of ln(PBEEF) is ______. This implies …
-0.2616 A 1 currency unit increase in the price of beef leads to a 0.2616 pounds decrease in quantity of beef
consumed.
-0.2616 A 1% increase in the price of beef leads to a 0.2616% decrease in quantity of beef consumed.
-0.1105 A 1 currency unit increase in the price of beef leads to a 1.105 pounds decrease in quantity of beef
consumed.
-0.1105 A 1% increase in the price of beef leads to a 1.105% decrease in quantity of beef consumed.
19
a
b
c
d
The margin of error for a 95% confidence interval for β₂ is,
0.2791
0.3283
0.3863
0.4544
20
a
b
Elasticity of demand for beef with respect to the price of lamb (cross-price elasticity) is,
0.1062
0.1328
c
d
0.1660
0.2075
Questions 21-28 are based on the following
Use the data in the worksheet PRICE for the houses sold in a major city. Estimate the regression model,
E(PRICE) = β₁ + β₂SQFT + β₃YEARS
for all houses in the sample.
21 The estimated coefficients of the regression equation is,
b₁
b₂
b₃
a
-42.8791
0.2270
-1.9142
b
-44.2052
0.2183
-1.9734
c
-45.5724
0.2099
-2.0344
d
-46.9818
0.2018
-2.0974
22
a
b
c
d
23
a
b
c
d
Estimate the regression model E(PRICE) = β₁ + β₂SQFT + β₃YEARS for town houses (STYLE = 2).
The estimated coefficients of the regression equation are,
b₁
b₂
b₃
289.2014
0.0728
-5.1480
286.3380
0.0857
-4.2900
283.5030
0.1008
-3.5750
280.6960
0.1186
-2.9791
Estimate the regression model E(PRICE) = β₁ + β₂SQFT + β₃YEARS for French style (STYLE = 7).
The estimated coefficients of the regression equation are,
b₁
b₂
b₃
-461.9863
0.2250
-4.4333
-457.4122
0.2647
-3.6944
-452.8834
0.3114
-3.0786
-448.3994
0.3663
-2.5655
24
a
b
The price of which style, town-house or French style, is least affected by the age of the house?
French style
Town-house
25
Test the hypothesis that having an older house reduces the price by $1,350 for each year of age. Perform the test for
ALL houses. The p-value for the test is ______.
0.0472 Reject H₀ at α = 0.05, but do not reject at α = 0.01.
0.0590 Reject H₀ at α = 0.10, but do not reject at α = 0.05.
0.0737 Reject H₀ at α = 0.01, but do not reject at α = 0.05.
0.0921 Do not eject H₀ at α = 0.05, and do not reject at α = 0.10.
a
b
c
d
26
a
b
c
d
Test the hypothesis that having an older house reduces the price by $2,500 for each year of age. Perform the test for
STYLE = 2 houses only, at α = 0.05. The p-value for the test is ______.
0.0126 Reject H₀.
0.0209 Reject H₀.
0.0349 Reject H₀.
0.0581 Do not reject H₀
Questions 27-33 are based on the following
The RICE data in the QRICE worksheet contains 352 observations on 44 rice farmers in the Tarlac region of the
Philippines for 8 years 1990 to 1997. Variables in the data set are tons of freshly threshed rice (RICE),
hectares planted (AREA), person-days of hired and family labor (LABOR), and kilograms of fertilizer (FERT).
The RICE data in the QRICE worksheet contains 352 observations on 44 rice farmers in the Tarlac region of the
Philippines for 8 years 1990 to 1997. Variables in the data set are tons of freshly threshed rice (RICE),
hectares planted (AREA), person-days of hired and family labor (LABOR), and kilograms of fertilizer (FERT).
Treating the data set as one sample with n = 352, proceed with the following questions.
Estimate the production function:
27
a
b
c
d
E[ln(QRICE)] = β₁ + β₂ln(AREA) + β₃ln(LABOR) + β₄ln(FERT)
Which of the following is the correct estimated coefficients of the regression equation
b₁
b₂
b₃
b₄
-1.5495
0.3615
0.4327
0.2099
-1.6310
0.3443
0.4555
0.1999
-1.7168
0.3279
0.4794
0.1904
-1.8072
0.3122
0.5047
0.1813
28
a
b
c
d
The value of the estimated coefficient b₃ implies,
A 1% increase in labor input would result in 0.332% increase in rice output.
A 1% increase in labor input would result in 0.433% increase in rice output.
A one unit increase in labor input would result in 0.433 ton of rice.
A one unit increase in labor input would result in 43.3% increase in rice output.
29
From the data find the mean of AREA, LABOR and FERT.
Find the predicted QRICE using the mean values for the three independent variables.
Note: Find the “corrected” predictor.
8.791
7.991
7.265
6.604
a
b
c
d
30
a
b
c
d
31
a
b
c
d
Test the hypothesis that the elasticity of production with respect to AREA is equal to 0.5.
The p-value for the test is ______.
0.1185 Do not eject H₀ at a 10% level of significance.
0.0740 Reject H₀ at a 10% level of significance, but do not reject at a 5% level.
0.0463 Reject H₀ at a 5% level of significance; reject at a 10% level.
0.0289 Reject H₀ at a 5% level of significance; reject at a 10% level.
Test the hypothesis that the elasticity of production with respect to labor is at most 0.4.
The p-value for the test is ______.
0.0500
0.1251
0.3127
0.3818
32
a
b
c
d
The margin of error for a 95% interval estimate for the elasticity of production with respect to fertilizer is,
0.0752
0.0836
0.0928
0.1032
33
Compute the mean for AREA, LABOR and FERT. Find the 95% interval estimate for the mean RICE yield given the
means for the control variables.
6.201
6.262
6.171
6.292
6.112
6.353
a
b
c
d
5.994
6.478
Question 34-39 are based on the following
Use the data in the WAGE tab to estimate the following wage equation.
E[ln(WAGE)] = β₁ + β₂EDUC + β₃EXPER + β₄HRSWK
WAGE
EDUC
EXPER
HRSWK
Earnings per hour
Years of schooling
Post education years experience
Usual hours worked per week
34
a
b
c
d
The estimate b₂ = ________ implies that holding other variables constant,
an additional year of education increases wage by
6.08%
on average.
an additional year of education increases wage by
$6.08
on average.
an additional year of education increases wage by
8.19%
on average.
an additional year of education increases wage by
$8.19
on average.
35
a
b
c
d
The estimate b₃ = ________ implies that holding other variables constant,
extra year of related work experience increases wage on average by
extra year of related work experience increases wage on average by
extra year of related work experience increases wage on average by
extra year of related work experience increases wage on average by
36
Test the hypothesis that an extra year of education increases the wage rate by at least 7.5%.
The P-value for the test is,
0.0670 At a 5% level of significance, do not reject H₀.
0.0258 At a 5% level of significance, reject H₀.
0.0099 At a 5% level of significance, reject H₀.
0.0038 At a 5% level of significance, reject H₀.
a
b
c
d
$0.70
0.70%
$0.51
0.51%
37
a
b
c
d
Find a 95% confidence interval for the percentage increase in wage from working an additional hour per week.
0.719%
1.126%
0.632%
1.214%
0.507%
1.338%
0.329%
1.516%
38
a
b
c
d
From the data find the mean of the control variables, and then determine the “corrected” predicted wage.
22.04
20.99
19.99
18.44
39
Find the 95% interval estimate for the mean wage at the mean values of the control variables in the previous
question.
16.98
17.55
16.70
17.85
16.16
18.45
15.12
19.71
a
b
c
d
Question 40-46 are based on the following
Re-estimate the above model with the following additional variables,
EDUEXP
EDUSQ
EXPSQ
EDUC×EXPER
EDUC²
EXPER²
E[ln(WAGE)] = β₁ + β₂EDUC + β₃EXPER + β₄HRSWK + β₅EDUEXP + β₆EDUSQ + β₇EXPSQ
40
a
b
c
d
41
a
b
c
d
42
a
b
c
d
43
a
b
c
d
44
a
b
c
d
45
Bob has
16 years of education
10 years of experience
What is the marginal effect of education on Bob’s wage?
Wage increases by
Wage increases by
Wage increases by
Wage increases by
8.16%
7.42%
6.74%
5.13%
for each additional year of education
for each additional year of education
for each additional year of education
for each additional year of education
Tom has
12 years of education
10 years of experience
What is the marginal effect of education on Tom’s wage?
Wage increases by
Wage increases by
Wage increases by
Wage increases by
5.63%
4.69%
3.91%
3.26%
for each additional year of education
for each additional year of education
for each additional year of education
for each additional year of education
Test the hypothesis, at α = 0.05, that Bob’s marginal effect of education is greater than that of Tom’s.
The P-value for the test is,
0.0934 Do not reject H₀. Bob’s marginal effect is not greater than that of Tom’s.
0.0718 Do not reject H₀. Bob’s marginal effect is not greater than that of Tom’s.
0.0453 Reject H₀. Bob’s marginal effect is greater than that of Tom’s.
0.0325 Reject H₀. Bob’s marginal effect is greater than that of Tom’s.
Sam has
16 years of education
20 years of experience
What is the marginal effect of experience on Sam’s wage?
Wage increases by
Wage increases by
Wage increases by
Wage increases by
Pam has
1.29%
2.23%
3.84%
6.62%
16
25
for each additional year of experience
for each additional year of experience
for each additional year of experience
for each additional year of experience
years of education
years of experience
What is the marginal effect of experience on Pam’s wage?
Wage increases by
2.02% for each additional year of experience
Wage increases by
1.26% for each additional year of experience
Wage increases by
0.79% for each additional year of experience
Wage increases by
0.49% for each additional year of experience
When EDUC = 16, after how many years does the marginal effect of experience become negative?
a
b
c
d
46
a
b
c
d
35.02
34.18
33.51
32.85
Build a 95% interval estimate for the marginal effect of experience on wage when EDUC = 16 and EXPER = 20.
1.20%
1.38%
1.11%
1.48%
0.92%
1.66%
0.55%
2.03%
0.4
0.001494
-0.0015
BSALC
BSTRANS BUDGET
0.0106
0.1458
50
0.0825
0.1215
90
0.0513
0.2063
180
0.0397
0.0652
80
0.1571
0.2403
90
0.021
0.0955
70
0.0153
0.0227
140
0.0161
0
50
0
0.0426
60
0.0354
0
90
0.1176
0.2903
150
0.0405
0.0983
120
0.1055
0.0681
160
0.0517
0.0608
90
0.05
0.0739
80
0.1488
0.0968
130
0
0.1168
100
0.0308
0.0121
80
0.0264
0.1704
90
0.0905
0.0175
40
0
0.012
50
0
0.0303
70
0.2525
0.117
90
0.0473
0.0372
130
0.1072
0.0761
40
0.0666
0.0008
90
0
0.0435
130
0.0465
0.1888
70
0.0313
0.134
110
0.2029
0.0061
80
0.1957
0.0461
360
0.0332
0.0443
60
0.0387
0.1496
90
0.0279
0.7638
310
0.0332
0.0381
170
0.0679
0.2598
210
0.0378
0.3145
70
0.0087
0.3588
100
0.1296
0.0271
70
0.0664
0.1597
130
0.0741
0.028
90
0.0578
0.0222
60
0.0807
0.1601
70
0
0.1151
50
0.153
0.0476
110
0
0.0503
70
0.0287
0.0508
160
0.1783
0.206
70
AGE
25
39
47
33
31
24
46
25
25
29
38
34
36
50
28
29
29
38
38
32
29
34
26
33
47
28
25
28
40
24
41
33
32
36
52
38
30
46
24
57
34
27
33
30
50
42
35
30
NKIDS
2
2
2
2
1
1
1
1
2
2
2
2
2
1
1
1
2
2
2
2
2
2
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
0.1115
0.207
0.0943
0
0.0635
0
0.0582
0.0483
0.0988
0.1356
0.1163
0.0999
0.0221
0.0665
0.1294
0.1055
0
0.0639
0.2099
0.0923
0.0148
0.0868
0.1071
0.0023
0
0.0771
0.0472
0.1609
0.012
0.244
0
0.0097
0.0068
0.0896
0.0973
0
0.0261
0.1148
0.1372
0
0.0315
0.0544
0.0261
0.0753
0.0318
0.1244
0
0.1431
0.0528
0.1062
0.04
0.0111
0.0521
0.0821
0.0165
0.1531
0.1561
0.019
0.0224
0.0973
0.0364
0.1984
0.157
0.066
0.1154
0.0418
0.0237
0.0424
0.0906
0.1399
0.1068
0.1136
0.1338
0.1349
0.1848
0.1516
0.056
0.0061
0.1121
0.1362
0.1072
0.3952
0.0545
0.0628
0.1992
0.3964
0.1058
0.1754
0.0218
0
0.2982
0.351
0.1529
0.0656
0.1577
0
0.1051
0.1569
90
50
60
40
70
50
70
70
80
80
70
80
100
80
110
150
70
50
70
130
90
70
100
60
80
230
170
100
80
80
80
180
220
80
110
90
110
120
170
60
50
60
130
90
140
70
90
190
50
27
21
19
37
31
31
28
21
41
28
32
24
39
49
42
42
53
27
33
49
33
38
41
34
36
47
31
37
37
24
34
40
33
47
43
26
36
35
35
37
34
26
34
30
37
28
31
52
33
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
2
2
1
2
1
2
1
1
2
2
1
2
2
2
1
2
2
1
2
2
2
2
2
1
2
1
1
2
2
2
2
2
1
2
0
0.0661
0.1012
0.0878
0.131
0.1035
0.1323
0.0259
0.0062
0.0336
0.1424
0.0297
0.0806
0.0928
0.0302
0.0316
0.0425
0.2666
0.1761
0.159
0.047
0.0367
0
0.0241
0.0113
0.0072
0.0615
0.0157
0.0416
0.0405
0.1318
0.0343
0.0179
0.0167
0.0129
0.0361
0.1774
0
0.0461
0.0034
0.2147
0.0997
0.1366
0.1369
0.013
0.1239
0.1044
0
0.0164
0.0103
0.0801
0.14
0.0158
0.0736
0.2401
0.1256
0.1495
0.1526
0.1568
0.1215
0.0785
0.4713
0.0692
0.0126
0.0765
0.1564
0.0003
0.1408
0.0848
0.0147
0.6134
0.0579
0.0402
0.1192
0.0646
0
0.3182
0.2383
0.1488
0.1477
0.2473
0.0665
0.2184
0.0914
0
0.2076
0.254
0
0.1327
0.1154
0.0131
0.1719
0.1459
0.4396
0.0668
0.1177
0.2681
0.1139
80
70
90
80
80
80
70
190
50
60
110
150
90
100
60
110
80
140
100
120
70
120
50
60
90
100
60
110
70
60
120
160
70
60
100
60
90
40
60
70
190
40
70
100
110
130
70
110
110
36
33
33
40
30
33
25
41
33
28
35
35
26
37
31
37
37
41
30
34
30
33
28
33
30
48
29
32
27
24
30
41
48
31
55
30
27
43
35
37
25
50
39
44
41
30
34
33
39
2
2
2
2
1
2
2
1
1
1
2
2
1
2
2
2
2
2
1
2
2
1
1
2
2
2
1
2
1
1
1
2
2
1
1
2
2
1
2
2
2
1
1
2
2
2
2
1
1
0.1632
0.0814
0.0289
0.0142
0.0147
0.1029
0.0202
0.2126
0
0.0657
0.1573
0.0684
0.0264
0.0095
0.0347
0.0213
0.1024
0.0602
0.0663
0
0.0907
0.0461
0.0581
0.136
0
0.0078
0.0742
0
0.0333
0.0079
0.0622
0.142
0.0067
0.2351
0.016
0.1132
0.0363
0
0.0025
0.02
0.0782
0.092
0.0251
0
0.1736
0
0.1086
0
0
0.2485
0.1215
0.3735
0.2133
0.039
0.0063
0.2939
0.094
0.3031
0.1454
0.1401
0.4239
0.0471
0.0611
0.0817
0.1054
0
0.1312
0.16
0.1134
0.0979
0.2821
0.1504
0.1368
0.2188
0.0866
0.1195
0.2212
0.13
0.0992
0.1362
0.1209
0.0493
0.0533
0.0716
0.1111
0.2497
0.2474
0.0054
0.2983
0.3213
0.1467
0.1019
0.1802
0.1378
0.1167
0.0813
0.1406
0.0615
80
60
80
100
150
70
150
90
70
90
100
160
150
100
120
60
40
80
100
80
90
110
70
90
50
120
80
70
150
100
70
60
130
190
90
100
90
70
70
60
60
110
70
60
120
90
70
80
70
43
43
34
38
43
29
32
44
31
37
35
30
27
24
31
24
49
28
37
40
25
43
31
36
22
37
42
37
51
39
38
36
34
38
44
29
41
41
32
29
30
35
54
25
43
37
40
30
35
1
1
1
1
2
1
2
1
2
2
2
1
2
2
2
1
2
1
1
2
2
1
2
2
2
1
1
2
2
2
2
1
2
2
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
0
0.0587
0.1212
0.2092
0.1259
0.0304
0.0884
0
0.1488
0.0282
0.0775
0.0231
0.0696
0.0206
0.0603
0.0275
0.1915
0.0266
0.0456
0
0.1475
0.0133
0.0352
0.1057
0.0945
0
0.0483
0.1223
0.0412
0.0575
0.0364
0.0873
0.1798
0.0475
0.0373
0.0648
0.0248
0.1823
0
0.0759
0
0.0521
0.0716
0.063
0
0.0996
0.0249
0.023
0
0.1432
0.2009
0.0913
0.0686
0.0937
0.0839
0.1749
0.0408
0.087
0.1982
0.0115
0.5096
0.1763
0.1363
0.308
0.2563
0.1103
0.2576
0.1165
0.2608
0.1339
0.0482
0.0453
0.1684
0.0697
0.0092
0.1624
0.201
0.3479
0
0.0634
0.082
0.0209
0.1339
0.2484
0.1329
0.2103
0.157
0.0354
0.0582
0.0771
0.1039
0.1028
0.1721
0.0103
0.0231
0.1603
0.145
0.1367
50
80
90
80
100
90
100
100
100
80
60
110
70
130
50
100
90
60
290
50
190
60
50
50
60
110
80
70
140
50
120
50
80
90
90
60
60
90
50
90
40
50
70
100
50
90
70
110
120
25
57
32
53
27
31
40
55
36
32
33
38
31
35
32
42
34
36
32
28
35
44
28
38
32
32
27
35
32
29
50
37
34
27
45
28
30
55
26
45
30
24
30
41
26
38
30
54
39
2
2
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
2
2
2
1
2
1
2
1
1
1
2
1
2
2
2
2
2
2
2
1
2
2
2
0.0529
0.0856
0.0592
0.0652
0.1247
0
0
0.0222
0.0187
0
0.0586
0.1548
0.1654
0.0472
0.0857
0.1718
0
0
0.0176
0.1229
0.0491
0
0
0.0312
0.0718
0
0.0074
0.0773
0.0348
0.0449
0.0349
0.1466
0.027
0.1778
0.0038
0.0928
0.1173
0.0191
0.1369
0.0209
0.0152
0.0606
0.0111
0
0.0656
0.0285
0.0099
0.1983
0.0469
0.1094
0.1455
0.1056
0.0005
0.007
0.1945
0
0.1714
0.0717
0.1166
0.141
0.0978
0.1002
0.0113
0.0552
0.0369
0.127
0.1684
0.4701
0.0498
0.0497
0.09
0.0038
0.1319
0.1289
0.2111
0.2293
0.0512
0.5481
0.1411
0.1656
0.0653
0.1085
0.0745
0.0738
0.0442
0.1715
0.6373
0.1345
0.1199
0.5392
0.1354
0.1303
0.2175
0.2011
0.1814
0.0027
0
0.0519
70
80
110
70
110
70
60
80
60
160
70
90
110
50
90
70
70
70
110
80
80
80
80
100
50
50
120
70
190
100
100
70
40
150
60
50
60
80
90
100
250
100
70
70
70
150
80
80
90
31
25
57
25
39
41
26
49
36
54
33
33
56
30
22
20
57
25
36
40
29
34
22
44
60
35
36
40
32
38
33
45
25
34
40
36
22
35
25
34
35
42
34
41
38
35
39
35
40
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
2
2
1
2
2
2
1
2
2
0.0202
0
0.0652
0.0656
0.0477
0.0067
0.1538
0.0737
0.019
0.0212
0.1178
0.04
0.0305
0
0.1148
0.039
0.0537
0.0244
0.0586
0.02
0.1258
0.0154
0.068
0
0.0848
0.1287
0
0
0.0686
0.1162
0.0719
0.0475
0.165
0.014
0.0208
0.0723
0
0.0113
0.0997
0.0447
0
0
0.024
0
0.2106
0
0
0.0256
0.0048
0.0822
0.1133
0.056
0.1171
0.1871
0.1853
0.1111
0.1276
0.2595
0.0916
0.1667
0.0548
0.1068
0.2717
0.044
0.1124
0.0163
0.0838
0.106
0.2844
0.0912
0.0302
0.1687
0.0832
0.2262
0.0993
0.0375
0.1003
0.0786
0.0487
0.2244
0.1647
0.1774
0.0476
0.0833
0.1297
0.0303
0.1649
0.0319
0.1796
0.1539
0.0263
0.0316
0.066
0.0946
0.1599
0.0565
0.0982
0.1306
110
50
50
90
110
50
90
130
80
110
60
90
110
70
100
80
90
100
80
70
100
70
60
70
80
80
60
50
100
120
120
70
80
70
50
90
50
80
70
120
60
80
130
70
70
70
80
140
110
42
53
24
30
27
54
40
36
35
44
60
28
39
48
38
38
42
44
53
30
30
34
57
59
36
42
32
36
20
38
34
32
42
37
54
37
32
28
30
39
41
41
38
41
25
46
39
35
39
2
1
1
2
1
2
2
2
2
2
1
2
2
1
2
2
2
2
2
2
2
2
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
2
2
2
2
1
2
1
1
1
2
2
1
0.0216
0.0057
0.0374
0.099
0
0.0506
0.0067
0.2277
0.0342
0.0879
0.0292
0.2067
0
0.0213
0.1237
0.0861
0.0524
0.1291
0
0.006
0.3529
0.0989
0
0.0121
0.0578
0.1886
0.1243
0
0.0257
0.167
0
0.0058
0.0774
0
0.0046
0.0886
0.0956
0.0397
0.0517
0
0.0414
0.0263
0.1224
0.092
0.0504
0.0119
0.0469
0
0.0703
0.0817
0.1561
0.1665
0.155
0
0.0097
0.1616
0.1966
0.1557
0.1673
0.196
0.0444
0.1036
0.1239
0.0758
0.096
0.047
0.0005
0.1193
0.1331
0.0005
0.1322
0.1093
0.092
0.1283
0
0
0
0.2431
0.1024
0.2351
0.1176
0.0818
0.2113
0.262
0.1176
0.1654
0.0317
0.6046
0.4754
0.0945
0.0492
0.0974
0
0.115
0.1302
0.0186
0.1055
0.0922
140
60
50
80
130
270
80
110
120
110
80
80
100
200
150
70
60
190
60
150
80
90
120
120
70
70
80
100
80
160
90
70
230
60
120
80
80
120
320
100
110
190
130
60
150
90
120
50
130
28
31
34
34
50
41
35
33
37
43
27
55
60
25
49
37
24
38
38
40
28
34
42
38
38
24
24
39
36
27
39
46
36
35
37
30
29
45
45
27
39
40
40
33
37
34
39
30
32
2
2
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
2
2
2
1
1
2
1
2
2
2
1
2
2
2
2
1
2
2
1
2
2
2
2
2
1
2
0
0.027
0
0.0139
0.0845
0.0748
0.0208
0.0682
0.022
0.018
0.0319
0.0715
0.0391
0.0265
0.0255
0.0299
0
0.0388
0.0517
0.029
0.036
0.0155
0.0389
0.0166
0.2011
0.0124
0.0511
0.0804
0.0875
0.1006
0.0029
0
0.0283
0
0.0546
0
0.0504
0.173
0.0815
0
0.0546
0.0744
0.2649
0.0101
0
0.013
0.1405
0.0222
0.0192
0.0966
0.1422
0.0328
0.3017
0.0622
0.3799
0.3276
0.1401
0.1906
0.008
0.0517
0.0549
0.4638
0.1534
0.3133
0.1063
0.1559
0.2565
0.0239
0.116
0.1091
0.0349
0.211
0.1055
0.1034
0.0979
0.0095
0.1149
0.1515
0.062
0.1051
0.0229
0.1511
0.1399
0.0795
0.3017
0.1368
0.3624
0.1396
0.1611
0.0142
0.133
0.1128
0.1364
0.2968
0.0194
0.1569
0.2513
0.1629
50
60
50
80
100
80
70
70
70
60
70
90
90
150
110
90
110
160
110
70
80
60
100
80
100
100
110
80
100
90
80
60
80
120
110
70
60
90
110
90
50
150
90
100
100
50
80
140
90
37
40
30
42
26
37
38
35
36
39
29
42
38
32
39
25
57
46
21
39
35
26
26
43
33
38
27
40
40
27
41
28
52
37
35
35
25
37
46
36
28
47
21
29
27
39
27
32
31
1
2
2
2
1
1
2
2
2
2
2
2
2
2
2
2
2
2
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
2
2
2
2
2
2
2
1
2
1
2
2
2
1
2
2
0.2101
0.0863
0.1808
0.0629
0.0503
0
0
0.0469
0.0286
0.0132
0.0444
0.007
0.0067
0.0445
0
0.0291
0.0171
0
0.0261
0.0727
0.0344
0.0123
0.0767
0.026
0
0.125
0.085
0
0.0163
0.0085
0.0023
0.1737
0.0151
0.0023
0
0
0
0.0269
0.019
0.4281
0
0.0048
0.1024
0.0434
0.0754
0.0071
0.027
0.0379
0.0019
0.1362
0.0334
0.1217
0.2038
0.0271
0.2216
0.1528
0.0481
0.1446
0.0615
0.2228
0.1023
0.1485
0.0087
0
0.0753
0.1493
0.1926
0.1499
0.1512
0.2439
0.2147
0.2431
0.0297
0.0252
0.0315
0.3108
0.248
0.112
0.3647
0.1105
0.0477
0.2973
0.2632
0.2766
0.158
0.0928
0.0402
0.0798
0.0799
0.2955
0.1545
0.1276
0.0231
0.0832
0.3136
0.0845
0.0966
0.1528
110
80
120
160
50
70
50
40
70
100
120
90
90
70
60
80
100
100
140
40
70
80
120
210
60
60
90
130
70
190
110
60
70
100
50
60
90
70
60
150
50
60
50
140
90
70
110
90
70
30
25
22
33
32
33
34
34
28
31
51
38
45
27
36
28
40
34
37
42
26
45
47
37
33
29
25
33
49
29
28
25
34
38
52
40
39
28
40
40
34
30
36
38
37
40
37
37
50
2
2
1
2
1
2
1
1
2
2
1
2
1
2
2
2
2
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
2
2
2
2
1
0.0626
0.1335
0
0.0423
0.0051
0.0224
0.0428
0.0288
0.0364
0.064
0.0205
0.0094
0.0081
0.0102
0.0334
0.0597
0.1008
0.0146
0.0017
0
0.1344
0.0199
0
0.0783
0.0127
0.0199
0.2024
0
0
0.023
0.0111
0.0248
0.1288
0.0177
0.0166
0.058
0.0478
0.0666
0.1002
0.0209
0.0205
0.0188
0.0934
0.0168
0.0099
0.0375
0.0878
0.0048
0
0.0162
0
0.2836
0.1324
0.0481
0.0336
0.1905
0
0.1652
0.1664
0.2119
0.0043
0.1051
0.1826
0.0799
0.2075
0.1101
0.0565
0.2586
0
0.0356
0.1452
0.1398
0.2658
0.0012
0.0834
0.0989
0.0119
0.1086
0.1772
0.2547
0.1009
0.1153
0.1525
0.1721
0.1273
0.224
0.0376
0.0473
0.0807
0.0547
0.1301
0.1145
0.1032
0.2631
0.3486
0.1949
0.3681
0.2796
80
100
60
90
90
120
90
80
110
70
90
70
90
50
90
60
80
100
80
50
100
40
60
100
110
130
90
70
100
70
80
50
150
90
130
100
70
60
110
100
140
90
120
100
80
60
140
180
150
31
34
34
28
41
37
47
41
38
37
31
29
34
33
32
27
44
36
32
44
26
29
41
53
31
48
26
35
37
30
27
24
36
37
48
34
25
35
27
50
45
35
30
43
41
28
30
43
34
2
2
1
2
2
2
2
2
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
2
1
2
2
2
2
1
2
2
2
1
2
2
2
1
2
2
2
1
2
2
0
0.0345
0.0104
0.011
0.3563
0.0267
0.0215
0.1553
0
0.0413
0.15
0.0173
0.0311
0
0.1111
0.1223
0.0321
0.0091
0
0.0151
0
0
0.0153
0.0775
0
0
0.0214
0.0369
0.0672
0.0542
0.011
0
0.0988
0
0
0
0.0085
0.0715
0.0157
0.0115
0.0932
0.0986
0.021
0.0656
0.0176
0.1172
0.0036
0
0.0501
0.0819
0.0168
0.0015
0.0144
0.0437
0.2446
0.3292
0.0861
0.2313
0.2456
0.0167
0.1556
0.2032
0.0542
0
0.1174
0.4168
0.2439
0.213
0.2134
0.1289
0.2343
0.089
0.1796
0.3568
0.1143
0.0825
0.1035
0.1204
0.0999
0.0274
0.3557
0.0823
0.1127
0
0.2918
0.1688
0.0843
0.1376
0.1473
0.1419
0.0056
0.1575
0.1775
0.2358
0.033
0.0005
0.1948
0.126
110
40
70
100
120
60
130
130
110
160
120
150
70
60
50
80
80
220
130
80
80
50
80
80
100
70
110
110
110
80
70
100
100
100
50
40
100
100
100
130
260
100
80
140
90
70
80
80
120
45
35
32
37
33
37
30
37
48
46
42
30
27
47
26
30
37
40
47
35
45
40
32
27
38
36
36
32
32
28
40
37
34
47
33
29
33
40
35
48
48
49
34
45
34
29
36
43
36
2
2
1
2
2
2
1
2
1
2
2
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
2
2
2
1
2
1
2
2
2
2
2
2
2
2
2
1
2
1
1
2
2
2
2
0.2254
0.04
0
0
0
0.077
0.0188
0.0381
0.1704
0.0169
0.0105
0.0218
0
0.0164
0.0072
0.1818
0.0424
0.002
0.1134
0.0049
0.0121
0.0721
0.0395
0.1391
0.0478
0
0
0.0068
0.2384
0.0258
0.0354
0.1049
0.0216
0
0
0.0037
0.1212
0.0377
0.1278
0.0205
0.0155
0.0053
0.0416
0.0147
0.0762
0.0242
0.027
0.1297
0
0
0.1693
0.2436
0.1098
0.2717
0.0517
0.1369
0.2159
0.0869
0.1723
0.1488
0.0929
0.3189
0.2175
0.0879
0.0142
0.2103
0.1185
0.1361
0.0897
0.003
0.4114
0.075
0.0413
0.1975
0.1256
0.1094
0.1632
0.0776
0.0493
0.1408
0.2393
0.4372
0.1382
0.1739
0.5517
0.1112
0.1824
0.0988
0.3155
0.1417
0.0036
0.4806
0.1415
0.3546
0.1744
0.1642
0.0316
0.4296
70
80
130
90
150
210
120
70
160
120
100
100
80
190
90
70
110
170
90
70
80
110
110
60
90
130
70
130
100
60
90
90
90
110
60
80
140
60
90
110
110
170
170
90
120
80
80
120
110
38
54
33
45
34
49
32
27
38
34
34
33
42
39
31
32
30
45
38
38
28
25
28
33
32
49
46
44
40
36
32
40
34
36
49
38
42
36
32
44
43
37
34
29
32
33
36
40
43
2
2
1
1
2
1
2
2
2
2
2
2
2
1
2
1
1
1
2
2
2
2
2
2
2
1
2
2
2
2
2
2
2
2
1
2
2
2
2
2
1
2
2
2
1
2
1
2
2
0.0234
0
0.0586
0.022
0.0498
0.0909
0
0
0
0.1
0.1231
0.0607
0.0307
0.0957
0.0596
0
0.0545
0.0416
0.0447
0.0838
0
0.0452
0.0571
0.0228
0.0363
0.0696
0.034
0.0685
0.046
0.1465
0.0504
0.081
0.0431
0
0.0293
0
0.0431
0.1003
0.035
0.0756
0
0.0446
0.0243
0.1331
0
0
0.0593
0.1435
0.0692
0.2536
0.2199
0.162
0.1072
0.3905
0.1233
0.1862
0.0821
0.187
0.0051
0
0.2528
0.0913
0.0354
0.1354
0.192
0.1387
0.3532
0.2367
0.011
0.1548
0.1362
0.0483
0.1175
0.5621
0.1552
0.1153
0.0599
0.2416
0.0043
0.0703
0.1682
0.0985
0.1077
0.1236
0.1563
0.0456
0.0165
0.0107
0.1061
0.2838
0.1516
0.2633
0.1535
0.146
0.001
0.1745
0.1009
0.1938
110
60
120
60
90
90
110
80
120
50
70
160
50
80
90
130
90
300
140
170
90
60
80
50
130
60
70
90
70
80
110
100
120
90
60
100
80
180
110
90
50
100
120
150
80
100
80
120
60
52
36
36
35
43
38
54
46
40
37
53
38
25
27
35
50
38
37
31
41
46
24
32
25
33
35
36
37
33
30
45
36
38
43
29
45
22
36
36
27
28
37
34
32
33
39
32
30
38
1
2
2
2
2
2
2
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
2
2
2
2
2
2
2
1
2
2
2
2
1
2
2
2
1
2
2
2
2
2
2
2
2
0.3347
0
0.2025
0.0068
0.0449
0.1365
0.022
0.071
0.0429
0.0257
0.078
0.0731
0
0.0131
0.0858
0.1125
0.1067
0.0528
0.0514
0.0234
0.0066
0.0359
0.0358
0.0731
0.1165
0.0243
0.165
0.137
0.0317
0.0616
0.0153
0.1513
0.154
0.1223
0.0036
0
0
0.0441
0.0185
0.0614
0.0388
0.1029
0.1864
0.0397
0
0.089
0.1199
0.0298
0.0514
0.0357
0.1043
0.0055
0.1835
0.2721
0.0748
0.1551
0.3594
0.0427
0.1069
0.0963
0.1037
0.5158
0.1612
0.0055
0.0077
0.0409
0.1849
0.257
0.1571
0.0614
0.1698
0.0899
0.0458
0.2
0.0443
0.0595
0.0399
0.2194
0.053
0.1252
0.261
0.0392
0.0768
0.0968
0.189
0.1853
0.0943
0.1652
0.0945
0.0847
0.0635
0.0375
0.2531
0.3218
0.0972
0.0648
0.0792
0.1031
100
80
80
90
90
90
60
100
80
90
170
90
100
70
150
60
70
100
130
70
80
80
60
70
150
180
120
70
70
70
80
150
90
70
130
120
110
50
50
60
90
90
110
110
90
100
40
170
100
20
29
35
54
35
31
37
49
27
39
36
53
35
35
31
43
24
34
26
32
43
31
26
29
30
44
37
37
23
28
43
24
54
28
32
36
37
42
23
31
39
44
25
36
32
38
26
26
32
1
1
2
1
2
2
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
2
2
2
2
1
1
1
2
2
1
2
2
1
1
1
2
0
0.0774
0.1323
0
0
0.0644
0.1556
0.0568
0.192
0.0407
0.0436
0.1004
0.0334
0.0271
0.0537
0.0548
0.0031
0.074
0.0181
0.044
0.0412
0.0747
0.0174
0.1225
0.0185
0.0658
0.0672
0.0072
0.0174
0.0242
0.0766
0.0108
0.0999
0.0317
0.0195
0.268
0
0
0.0486
0.0488
0.1016
0
0
0.1459
0.0592
0.0478
0.0515
0.1927
0.0949
0.0401
0.3584
0.0559
0.1198
0.0746
0.0912
0.0458
0.2725
0.2115
0.0154
0.1476
0.0042
0.1175
0.0276
0.0077
0.052
0.107
0.2342
0.1367
0.1818
0.0262
0.2362
0.1438
0.0243
0.1452
0.0705
0.1241
0.0093
0.0706
0.3054
0.0005
0.1887
0.0886
0.046
0.0079
0.0217
0
0.1945
0.0655
0.2264
0.0422
0.1282
0.0116
0.019
0.2133
0.0679
0.0473
0.0696
0.0764
120
70
60
60
30
80
40
120
90
260
50
120
90
120
60
60
100
200
110
100
130
130
80
120
40
130
70
90
60
70
80
190
110
100
90
50
80
60
60
100
80
70
40
100
80
100
150
160
90
43
28
23
34
24
28
24
40
31
25
26
32
34
34
38
45
39
33
36
35
35
24
42
34
31
32
45
42
32
32
23
50
23
42
58
28
38
40
34
29
38
27
48
31
31
44
26
45
22
2
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
2
2
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
2
2
2
2
2
1
1
1
2
2
2
1
2
0.1531
0.1178
0.0578
0.157
0.0442
0.1933
0.0623
0.3288
0.0669
0.0085
0.0663
0.177
0.0935
0.1649
0.1992
0.0843
0
0.0708
0.1058
0.0568
0
0.0459
0.2148
0
0.2824
0.2003
0.0554
0.0916
0.0568
0.0246
0.1911
0.2234
0.2073
0.1317
0.0141
0.3952
0.0164
0.0241
0.08
0
0.2791
0.11
0.3227
0.0039
0.0462
0.015
0.1435
0.0648
0.0342
0.0596
0.1858
0.1254
0.0609
0.1413
0.1819
0.1207
0.1374
0.0912
0.4146
0.0248
0.1165
0.0759
0.0779
0.0128
0.1829
0.0644
0.024
0.2232
0.0037
0.1401
0.0745
0.046
0.2353
0.0087
0.0739
0.1629
0.053
0.0569
0.3163
0.1056
0.2612
0.089
0.1091
0.003
0.0293
0.1184
0.0236
0.2556
0.0452
0.0007
0.0077
0.1304
0.2884
0.196
0.2337
0.0894
0.2644
0.2043
100
120
100
130
70
110
100
80
140
120
80
100
100
80
90
130
50
80
130
70
60
140
70
70
60
70
90
100
70
160
110
90
90
70
70
70
70
50
50
70
160
80
140
150
60
60
80
170
50
31
23
26
34
48
37
41
25
38
40
31
27
24
38
29
40
32
37
36
34
43
35
33
37
30
28
44
33
38
31
39
25
35
38
36
43
57
30
27
36
27
27
30
38
43
25
38
35
24
2
2
1
1
1
2
2
1
2
1
2
1
1
2
1
2
2
2
1
2
1
2
2
1
2
2
2
2
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
0.0783
0.0942
0.0529
0
0.0759
0.2053
0.09
0
0.0437
0.0779
0
0.0104
0.1261
0
0.1206
0.0923
0.0828
0.063
0.0176
0.0511
0.0108
0.0168
0.1129
0.0325
0.0964
0
0.0336
0.0454
0.0657
0.0583
0
0.0869
0.1233
0.0756
0.1079
0.0899
0.0052
0.2276
0.0119
0.0611
0.0312
0.0735
0
0.2919
0.15
0.0573
0.1156
0.1241
0.0393
0.0137
0.177
0.0797
0.0207
0.0117
0.0069
0.0662
0.1702
0.0956
0.0693
0.0464
0.1393
0.0167
0.0987
0