Find a 90% prediction interval for the log-transformed price when the weight is
ID: 3319640 • Letter: F
Question
Find a 90% prediction interval for the log-transformed price when the weight is 0.75 carats. Find a 90% prediction interval for the untransformed price when the weight is 0.75.
DATASET: diamonds
"wt" "color" "clarity" "cert" "price"
0.3 "D" "VS2" "GIA" 1302
0.3 "E" "VS1" "GIA" 1510
0.3 "G" "VVS1" "GIA" 1510
0.3 "G" "VS1" "GIA" 1260
0.31 "D" "VS1" "GIA" 1641
0.31 "E" "VS1" "GIA" 1555
0.31 "F" "VS1" "GIA" 1427
0.31 "G" "VVS2" "GIA" 1427
0.31 "H" "VS2" "GIA" 1126
0.31 "I" "VS1" "GIA" 1126
0.32 "F" "VS1" "GIA" 1468
0.32 "G" "VS2" "GIA" 1202
0.33 "E" "VS2" "GIA" 1327
0.33 "I" "VS2" "GIA" 1098
0.34 "E" "VS1" "GIA" 1693
0.34 "F" "VS1" "GIA" 1551
0.34 "G" "VS1" "GIA" 1410
0.34 "G" "VS2" "GIA" 1269
0.34 "H" "VS1" "GIA" 1316
0.34 "H" "VS2" "GIA" 1222
0.35 "E" "VS1" "GIA" 1738
0.35 "F" "VS1" "GIA" 1593
0.35 "G" "VS1" "GIA" 1447
0.35 "H" "VS2" "GIA" 1255
0.36 "F" "VS1" "GIA" 1635
0.36 "H" "VVS2" "GIA" 1485
0.37 "F" "VS2" "GIA" 1420
0.37 "H" "VS1" "GIA" 1420
0.4 "F" "VS1" "GIA" 1911
0.4 "H" "VS1" "GIA" 1525
0.41 "F" "VS1" "GIA" 1956
0.43 "H" "VVS2" "GIA" 1747
0.45 "I" "VS1" "GIA" 1572
0.46 "E" "VVS2" "GIA" 2942
0.48 "G" "VVS2" "GIA" 2532
0.5 "E" "VS1" "GIA" 3501
0.5 "E" "VS1" "GIA" 3501
0.5 "F" "VVS2" "GIA" 3501
0.5 "F" "VS1" "GIA" 3293
0.5 "G" "VS1" "GIA" 3016
0.51 "F" "VVS2" "GIA" 3567
0.51 "G" "VS1" "GIA" 3205
0.52 "D" "VS2" "GIA" 3490
0.52 "E" "VS1" "GIA" 3635
0.52 "F" "VVS2" "GIA" 3635
0.52 "F" "VS1" "GIA" 3418
0.53 "D" "VS1" "GIA" 3921
0.53 "F" "VVS2" "GIA" 3701
0.53 "F" "VS1" "GIA" 3480
0.53 "G" "VVS2" "GIA" 3407
0.54 "E" "VS1" "GIA" 3767
0.54 "F" "VVS1" "GIA" 4066
0.55 "E" "VVS2" "GIA" 4138
0.55 "F" "VS1" "GIA" 3605
0.55 "G" "VVS2" "GIA" 3529
0.56 "F" "VS1" "GIA" 3667
0.56 "I" "VVS2" "GIA" 2892
0.57 "G" "VVS2" "GIA" 3651
0.59 "G" "VVS2" "GIA" 3773
0.6 "F" "VS1" "GIA" 4291
0.62 "E" "VVS1" "GIA" 5845
0.63 "G" "VVS2" "GIA" 4401
0.64 "G" "VVS1" "GIA" 4759
0.66 "H" "VVS1" "GIA" 4300
0.7 "F" "VS1" "GIA" 5510
0.7 "G" "VS1" "GIA" 5122
0.7 "H" "VVS2" "GIA" 5122
0.7 "I" "VS2" "GIA" 3861
0.71 "F" "VVS2" "GIA" 5881
0.71 "F" "VS1" "GIA" 5586
0.71 "F" "VS2" "GIA" 5193
0.71 "H" "VVS2" "GIA" 5193
0.72 "F" "VS2" "GIA" 5263
0.8 "I" "VVS2" "GIA" 5441
0.82 "I" "VS2" "GIA" 4948
0.84 "H" "VS2" "GIA" 5705
0.85 "F" "VS2" "GIA" 6805
0.86 "H" "VVS2" "GIA" 6882
0.89 "H" "VS1" "GIA" 6709
0.9 "I" "VVS2" "GIA" 6682
0.5 "E" "VS1" "GIA" 3501
0.5 "G" "VVS1" "GIA" 3432
0.51 "F" "VVS1" "GIA" 3851
0.55 "H" "IF" "GIA" 3605
0.56 "E" "VS1" "GIA" 3900
0.57 "H" "VVS1" "GIA" 3415
0.6 "H" "IF" "GIA" 4291
0.63 "E" "IF" "GIA" 6512
0.7 "E" "VS1" "GIA" 5800
0.7 "F" "VVS1" "GIA" 6285
0.7 "F" "VS2" "GIA" 5122
0.7 "F" "VS2" "GIA" 5122
0.7 "G" "VS1" "GIA" 5122
0.7 "H" "VVS2" "GIA" 5122
0.71 "D" "VS1" "GIA" 6372
0.71 "E" "VS1" "GIA" 5881
0.71 "H" "VVS2" "GIA" 5193
0.72 "E" "VS1" "GIA" 5961
0.72 "H" "VVS1" "GIA" 5662
0.73 "E" "VS2" "GIA" 5738
0.73 "H" "VS1" "GIA" 5030
0.73 "H" "VS1" "GIA" 5030
0.73 "I" "VVS1" "GIA" 4727
0.73 "I" "VS1" "GIA" 4221
0.74 "G" "VVS2" "GIA" 5815
0.74 "H" "VS2" "GIA" 4585
0.75 "D" "VVS2" "GIA" 7368
0.75 "I" "VVS2" "GIA" 4667
0.75 "I" "VS1" "GIA" 4355
0.76 "D" "IF" "GIA" 9885
0.77 "F" "VVS1" "GIA" 6919
0.78 "H" "VS1" "GIA" 5386
0.8 "I" "VS2" "GIA" 4832
0.83 "E" "VS2" "GIA" 7156
0.9 "F" "VS1" "GIA" 7680
1 "D" "VVS1" "GIA" 15582
1 "D" "VS1" "GIA" 11419
1 "E" "VS1" "GIA" 10588
1 "E" "VS2" "GIA" 9757
1 "F" "IF" "GIA" 13913
1 "F" "VVS2" "GIA" 10588
1 "F" "VS1" "GIA" 10713
1 "F" "VS2" "GIA" 9480
1 "G" "VVS2" "GIA" 9896
1 "G" "VS1" "GIA" 9619
1 "G" "VS2" "GIA" 9169
1 "G" "VS2" "GIA" 9203
1 "H" "VS2" "GIA" 8788
1 "I" "VS1" "GIA" 8095
1 "I" "VS2" "GIA" 7818
1.01 "D" "VVS1" "GIA" 16008
1.01 "E" "VS1" "GIA" 10692
1.01 "E" "VS2" "GIA" 9853
1.01 "F" "VS1" "GIA" 10272
1.01 "F" "VS2" "GIA" 9573
1.01 "H" "VS1" "GIA" 9153
1.01 "H" "VS2" "GIA" 8873
1.01 "I" "VVS1" "GIA" 8873
1.01 "I" "VVS2" "GIA" 8455
1.01 "I" "VS2" "GIA" 7895
1.02 "F" "VS1" "GIA" 10372
1.02 "F" "VS2" "GIA" 9666
1.02 "G" "VVS2" "GIA" 10090
1.03 "E" "VS1" "GIA" 10900
1.04 "F" "VS1" "GIA" 10571
1.04 "I" "IF" "GIA" 9563
1.05 "I" "VVS2" "GIA" 8781
1.06 "G" "VS2" "GIA" 9743
1.06 "H" "VS2" "GIA" 9302
1.07 "I" "VVS2" "GIA" 8945
1.1 "H" "VS2" "GIA" 9646
0.18 "F" "VVS1" "IGI" 823
0.18 "F" "VVS2" "IGI" 765
0.18 "G" "IF" "IGI" 803
0.18 "G" "IF" "IGI" 803
0.18 "G" "VVS2" "IGI" 705
0.18 "H" "IF" "IGI" 725
0.19 "D" "VVS2" "IGI" 967
0.19 "E" "IF" "IGI" 1050
0.19 "F" "IF" "IGI" 967
0.19 "F" "VVS1" "IGI" 863
0.19 "F" "VVS2" "IGI" 800
0.19 "G" "IF" "IGI" 842
0.19 "G" "VVS1" "IGI" 800
0.19 "H" "IF" "IGI" 758
0.2 "D" "VS1" "IGI" 880
0.2 "G" "IF" "IGI" 880
0.2 "G" "VS1" "IGI" 705
0.2 "G" "VS2" "IGI" 638
0.21 "D" "VS1" "IGI" 919
0.21 "E" "IF" "IGI" 1149
0.21 "F" "IF" "IGI" 1057
0.21 "G" "IF" "IGI" 919
0.22 "E" "IF" "IGI" 1198
0.23 "E" "IF" "IGI" 1248
0.23 "F" "IF" "IGI" 1147
0.23 "G" "IF" "IGI" 995
0.24 "H" "IF" "IGI" 1108
0.25 "F" "IF" "IGI" 1485
0.25 "G" "IF" "IGI" 1283
0.25 "H" "IF" "IGI" 1149
0.25 "I" "IF" "IGI" 1082
0.26 "F" "IF" "IGI" 1539
0.26 "F" "VVS1" "IGI" 1365
0.26 "F" "VVS2" "IGI" 1260
0.26 "I" "IF" "IGI" 1121
0.27 "F" "IF" "IGI" 1595
0.27 "H" "IF" "IGI" 1233
0.28 "I" "IF" "IGI" 1199
0.29 "G" "IF" "IGI" 1471
0.29 "I" "IF" "IGI" 1238
0.3 "E" "VVS2" "IGI" 1580
0.3 "F" "VVS2" "IGI" 1459
0.3 "G" "VVS1" "IGI" 1459
0.3 "H" "VVS2" "IGI" 1218
0.3 "I" "IF" "IGI" 1299
0.31 "E" "VVS2" "IGI" 1628
0.31 "F" "VVS1" "IGI" 1628
0.31 "I" "IF" "IGI" 1337
0.32 "H" "IF" "IGI" 1462
0.33 "H" "IF" "IGI" 1503
0.34 "F" "VVS1" "IGI" 1773
0.34 "F" "VVS2" "IGI" 1636
0.35 "F" "VVS1" "IGI" 1821
0.35 "G" "VVS2" "IGI" 1540
0.4 "G" "IF" "IGI" 2276
0.41 "I" "VVS1" "IGI" 1616
0.41 "I" "VVS2" "IGI" 1506
0.47 "F" "VVS2" "IGI" 2651
0.48 "F" "VS1" "IGI" 2383
0.5 "G" "IF" "IGI" 3652
0.51 "E" "VVS2" "IGI" 3722
0.51 "F" "VVS1" "IGI" 3722
0.52 "I" "IF" "IGI" 3095
0.55 "F" "VVS2" "IGI" 3706
0.56 "E" "VVS2" "IGI" 4070
0.56 "G" "VVS2" "IGI" 3470
0.58 "E" "VVS1" "IGI" 4831
0.58 "F" "VVS1" "IGI" 4209
0.58 "G" "VVS1" "IGI" 3821
0.7 "G" "VVS1" "IGI" 5607
0.7 "G" "VVS2" "IGI" 5326
0.71 "D" "VS1" "IGI" 6160
0.76 "F" "VVS2" "IGI" 6095
0.78 "G" "VVS2" "IGI" 5937
1 "H" "VVS2" "IGI" 9342
1.01 "G" "VS1" "IGI" 9713
1.01 "H" "VS2" "IGI" 8873
1.01 "I" "VS1" "IGI" 8175
0.5 "F" "VVS1" "HRD" 3778
0.5 "G" "VVS1" "HRD" 3432
0.51 "F" "VVS1" "HRD" 3851
0.52 "E" "VS2" "HRD" 3346
0.52 "H" "VVS1" "HRD" 3130
0.53 "F" "VVS1" "HRD" 3995
0.53 "F" "VVS2" "HRD" 3701
0.55 "G" "VVS2" "HRD" 3529
0.56 "F" "VS1" "HRD" 3667
0.56 "F" "VS2" "HRD" 3202
0.57 "F" "VS2" "HRD" 3256
0.57 "H" "VVS1" "HRD" 3415
0.58 "H" "IF" "HRD" 3792
0.6 "G" "VS1" "HRD" 3925
0.6 "G" "VS2" "HRD" 3421
0.6 "H" "VVS1" "HRD" 3925
0.61 "H" "VVS2" "HRD" 3616
0.62 "I" "VVS2" "HRD" 3615
0.64 "H" "VVS2" "HRD" 3785
0.65 "I" "VVS2" "HRD" 3643
0.66 "H" "VVS1" "HRD" 4300
0.7 "E" "VVS1" "HRD" 6867
0.7 "E" "VVS2" "HRD" 6285
0.7 "G" "VVS1" "HRD" 5800
0.7 "G" "VVS2" "HRD" 5510
0.7 "H" "VS2" "HRD" 4346
0.71 "G" "IF" "HRD" 6372
0.71 "H" "VVS2" "HRD" 5193
0.72 "H" "VVS1" "HRD" 5662
0.73 "F" "VS2" "HRD" 5333
0.73 "G" "VVS1" "HRD" 6041
0.74 "H" "VVS1" "HRD" 5815
0.8 "F" "IF" "HRD" 8611
0.8 "F" "VS1" "HRD" 6905
0.8 "G" "VVS2" "HRD" 6905
0.8 "H" "VVS2" "HRD" 6416
0.8 "H" "VS1" "HRD" 6051
0.81 "E" "VVS1" "HRD" 8715
0.81 "E" "VS2" "HRD" 6988
0.81 "F" "VS1" "HRD" 6988
0.81 "G" "VS1" "HRD" 6495
0.81 "H" "IF" "HRD" 7358
0.82 "F" "VS2" "HRD" 6572
0.82 "G" "VVS2" "HRD" 7072
0.85 "F" "VVS1" "HRD" 8359
0.85 "F" "VS2" "HRD" 6805
0.85 "G" "VVS1" "HRD" 7711
0.86 "H" "VS2" "HRD" 5835
1 "D" "VVS2" "HRD" 13775
1 "E" "VVS1" "HRD" 14051
1 "E" "VVS2" "HRD" 11419
1 "E" "VS1" "HRD" 10588
1 "F" "VVS1" "HRD" 11696
1 "F" "VVS2" "HRD" 10588
1 "G" "VVS1" "HRD" 10450
1 "G" "VVS2" "HRD" 9896
1 "G" "VS2" "HRD" 9203
1 "H" "VVS1" "HRD" 9480
1 "H" "VS1" "HRD" 9065
1 "H" "VS2" "HRD" 8788
1 "I" "VVS1" "HRD" 8788
1 "I" "VVS2" "HRD" 8372
1 "I" "VS1" "HRD" 8095
1 "I" "VS2" "HRD" 7818
1.01 "D" "VVS2" "HRD" 13909
1.01 "E" "VVS2" "HRD" 11531
1.01 "E" "VS1" "HRD" 10692
1.01 "F" "VVS1" "HRD" 11811
1.01 "F" "VS1" "HRD" 10272
1.01 "G" "VVS2" "HRD" 9993
1.01 "G" "VS2" "HRD" 9293
1.01 "H" "VVS2" "HRD" 9433
1.01 "H" "VS1" "HRD" 9153
1.01 "I" "VVS1" "HRD" 8873
1.01 "I" "VS1" "HRD" 8175
1.02 "F" "VVS2" "HRD" 10796
1.06 "H" "VVS2" "HRD" 9890
1.02 "H" "VS2" "HRD" 8959
1.09 "I" "VVS2" "HRD" 9107
Explanation / Answer
Copy the data into Excel and save it in .csv format.
> data1=read.csv(file.choose(),header=T) #importing the dataset into R
> attach(data1) #attaching the dataset
> names(data1)
[1] "wt" "color" "clarity" "cert" "price"
> logprice=log(price) #log-transformed price
> model1=lm(logprice~wt)
> model2=lm(price~wt)
> newdata=data.frame(wt=0.75)
> predict(model1,newdata=newdata,interval="predict",conf.level=0.9)
fit lwr upr
1 8.576049 8.167775 8.984323
> predict(model2,newdata=newdata,interval="predict",conf.level=0.9)
fit lwr upr
1 6400.805 4197.495 8604.116
90% Prediction Interval for log-transformed price : (8.1678, 8.9843)
90% Prediction Interval for price : (4197.495, 8604.116)
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