Praca domowa #2 z SAD (laboratorium)
Zadanie 1:
W oparciu o podane wykresy diagnostyczne i informację o wielkości próby oceń i skomentuj, czy są spełnione założenia KMRL dotyczące składnika losowego (łącznie z założeniem o normalności rozkładu) oraz czy występują obserwacje wpływowe.
(a) n = 38
15 20 25 30 35 40
−505
Fitted values
Residuals
Residuals vs Fitted
25
38 37
−2 −1 0 1 2
−505
norm quantiles
reg$residuals
25
38
Time
ts(reg$residuals)
0 10 20 30
−505
0.00 0.05 0.10 0.15
−2−1012
Leverage
Standardized residuals
Cook's distance
0.5 0.5
Residuals vs Leverage
38 37 36
(b) n = 204
2000 4000 6000 8000
−150−100−50050100150
Fitted values
Residuals
Residuals vs Fitted
127125 190
−3 −2 −1 0 1 2 3
−100−50050100150
norm quantiles
reg$residuals
125127
Time
ts(reg$residuals)
0 50 100 150 200
−100−50050100150
0.00 0.01 0.02 0.03 0.04
−2−10123
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
204 190
1
(c) n = 203
−50 0 50 100
−100−50050100
Fitted values
Residuals
Residuals vs Fitted
128 151 113
−3 −2 −1 0 1 2 3
−100−50050
norm quantiles
reg$residuals
128
113
Time
ts(reg$residuals)
0 50 100 150 200
−100−50050
0.00 0.02 0.04 0.06 0.08 0.10 0.12
−4−202
Leverage
Standardized residuals
Cook's distance
0.5 0.5
Residuals vs Leverage
200 113
199
1
(d) n = 1000
5 10 15 20 25 30 35
−4−202
Fitted values
Residuals
Residuals vs Fitted
498 245
133
−3 −2 −1 0 1 2 3
−3−2−10123
norm quantiles
reg$residuals
498 245
Time
ts(reg$residuals)
0 200 400 600 800 1000
−3−2−10123
0.000 0.005 0.010 0.015
−4−202
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
764 106
241
(e) n = 1000
5 10 15 20 25 30 35
−4−202
Fitted values
Residuals
Residuals vs Fitted
283 447 498
−3 −2 −1 0 1 2 3
−4−3−2−1012
norm quantiles
reg$residuals
283 498
Time
ts(reg$residuals)
0 200 400 600 800 1000
−4−3−2−1012
0.00 0.05 0.10 0.15
−4−202
Leverage
Standardized residuals
Cook's distance
1 0.5 0.5
Residuals vs Leverage
283 447
385
(f) n = 1285
10000 20000 30000 40000 50000 60000
−1e+050e+001e+052e+053e+054e+05
Fitted values
Residuals
Residuals vs Fitted
853
693
205
−3 −2 −1 0 1 2 3
0e+001e+052e+053e+05
norm quantiles
reg$residuals
853
693
Time
ts(reg$residuals)
0 200 400 600 800 1000 1200
0e+001e+052e+053e+05
0.00 0.02 0.04 0.06 0.08
0510
Leverage
Standardized residuals
Cook's distance
0.5 1
Residuals vs Leverage
693 853
205
(g) n = 100
10000 20000 30000 40000
−200000200004000060000
Fitted values
Residuals
Residuals vs Fitted
449
606 1111
−2 −1 0 1 2
−200000200004000060000
norm quantiles
reg$residuals
449
606
Time
ts(reg$residuals)
0 20 40 60 80 100
−200000200004000060000
0.0 0.2 0.4 0.6
−2−1012345
Leverage
Standardized residuals
Cook's distance
1 0.5 0.5 1
Residuals vs Leverage
826 1111
449
(h) n = 100
−100 0 100 200 300 400 500
−20020406080
Fitted values
Residuals
Residuals vs Fitted
1232 227719
−2 −1 0 1 2
−20020406080
norm quantiles
reg$residuals
2271232
Time
ts(reg$residuals)
0 20 40 60 80 100
−20020406080
0.00 0.02 0.04 0.06 0.08 0.10 0.12
−101234
Leverage
Standardized residuals
Cook's distance
0.5
Residuals vs Leverage
719227 199
2
(i) n = 100
0 100 200 300 400 500 600
−2−1012
Fitted values
Residuals
Residuals vs Fitted
509 936 719
−2 −1 0 1 2
−2−1012
norm quantiles
reg$residuals
936509
Time
ts(reg$residuals)
0 20 40 60 80 100
−2−1012
0.00 0.05 0.10 0.15 0.20
−2−1012
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
719 783
1071
(j) n = 200
−1000 −500 0 500 1000 1500 2000
−100001000200030004000
Fitted values
Residuals
Residuals vs Fitted
1513 1084
6394
−3 −2 −1 0 1 2 3
−100001000200030004000
norm quantiles
reg$residuals
1513 1084
Time
ts(reg$residuals)
0 50 100 150 200
−100001000200030004000
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
−20246
Leverage
Standardized residuals
Cook's distance
0.5 1
Residuals vs Leverage
6394 1513 1084
(k) n = 200
−500 0 500 1000 1500 2000
−100001000200030004000
Fitted values
Residuals
Residuals vs Fitted
1513 1084
6394
−3 −2 −1 0 1 2 3
−100001000200030004000
norm quantiles
reg$residuals
1513 1084
Time
ts(reg$residuals)
0 50 100 150 200
−100001000200030004000
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
−20246
Leverage
Standardized residuals
Cook's distance
0.5 1
Residuals vs Leverage
6394 1084 1513
(l) n = 10000
0 200 400 600 800 1000 1200
−4−2024
Fitted values
Residuals
Residuals vs Fitted
1163
3248 3227
−4 −2 0 2 4
−4−2024
norm quantiles
reg$residuals
1163
3248
Time
ts(reg$residuals)
0 2000 4000 6000 8000 10000
−4−2024
0.000 0.005 0.010 0.015
−4−2024
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
3287 2280
5845
(m) n = 38
24 26 28 30 32 34
−15−10−50510
Fitted values
Residuals
Residuals vs Fitted
12 32
−2 −1 0 1 2
−10−50510
norm quantiles
reg$residuals
1 2
Time
ts(reg$residuals)
0 10 20 30
−10−50510
0.0 0.2 0.4 0.6 0.8 1.0
−1.5−1.0−0.50.00.51.01.5
Leverage
Standardized residuals
Cook's distance
1 0.5
Residuals vs Leverage
38
12
3
(n) n = 38
24 26 28 30 32 34
−15−10−50510
Fitted values
Residuals
Residuals vs Fitted
12 32
−2 −1 0 1 2
−10−50510
norm quantiles
reg$residuals
1 2
Time
ts(reg$residuals)
0 5 10 15 20 25 30 35
−10−50510
0.0 0.2 0.4 0.6 0.8 1.0
−2.0−1.5−1.0−0.50.00.51.01.5
Leverage
Standardized residuals
Cook's distance
1 0.5
Residuals vs Leverage
37 12
(o) n = 500
0 200 400 600 800 1000 1200
−3−2−101234
Fitted values
Residuals
Residuals vs Fitted
481 427
409
−3 −2 −1 0 1 2 3
−2−10123
norm quantiles
reg$residuals
481 427
Time
ts(reg$residuals)
0 100 200 300 400 500
−2−10123
0.00 0.05 0.10 0.15 0.20 0.25
−3−2−101234
Leverage
Standardized residuals
Cook's distance
0.5 0.5 1
Residuals vs Leverage
36 23
494
(p) n = 340
0 5 10 15
−15−10−50510
Fitted values
Residuals
Residuals vs Fitted
172171 173
−3 −2 −1 0 1 2 3
−15−10−50510
norm quantiles
reg$residuals
172 171
Time
ts(reg$residuals)
0 50 100 150 200 250 300 350
−15−10−50510
0.000 0.002 0.004 0.006 0.008 0.010 0.012
−2−1012
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
324325322
(q) n = 436
−1500 −1000 −500 0 500
−500−400−300−200−1000100
Fitted values
Residuals
Residuals vs Fitted
1 2 3
−3 −2 −1 0 1 2 3
−400−300−200−1000100
norm quantiles
reg$residuals
1 2
Time
ts(reg$residuals)
0 100 200 300 400
−400−300−200−1000100
0.000 0.005 0.010 0.015
−5−4−3−2−101
Leverage
Standardized residuals
Cook's distance
Residuals vs Leverage
1 2 3
(r) n = 3000
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−1.5−1.0−0.50.00.51.01.5
Fitted values
Residuals
Residuals vs Fitted
267 1198
859
−3 −2 −1 0 1 2 3
−1.0−0.50.00.51.01.5
norm quantiles
reg$residuals
2671198
Time
ts(reg$residuals)
0 500 1000 1500 2000 2500 3000
−1.0−0.50.00.51.01.5
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
−4−20246
Leverage
Standardized residuals
Cook's distance
1 0.5 0.5 1
Residuals vs Leverage
267 1198
2481
