HealthInsurance
Nitheesha Daka,Shiwani kulkarni,Siddharth Menon,Bhuwaneshwari Iyer
13/02/2020
#install.packages("tidyverse")
#install.packages("funModeling")
#install.packages("Hmisc")library(funModeling) ## Warning: package 'funModeling' was built under R version 3.6.2## Loading required package: Hmisc## Warning: package 'Hmisc' was built under R version 3.6.2## Loading required package: lattice## Loading required package: survival## Warning: package 'survival' was built under R version 3.6.2## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
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## Examples and tutorials at livebook.datascienceheroes.com
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## x dplyr::src() masks Hmisc::src()
## x dplyr::summarize() masks Hmisc::summarize()library(Hmisc)- In you data set, how many covariates do you have? What are they? How many observations do you have? How did you collect them?
We are using Insurance Dataset for our project to predict insurance cost based on factors like Age, Smoking habits, BMI, region. In the dataset below, we have 6 covariates and 1338 observations. We got this dataset from Kaggle.
R Markdown
setwd("C:/Users/bhuvi iyer/Desktop/MSIS/Spring2020/DAM/GroupProject")
getwd()## [1] "C:/Users/bhuvi iyer/Desktop/MSIS/Spring2020/DAM/GroupProject"Insurance <- read.csv("insurance.csv",h=T)head(Insurance,50)## age sex bmi children smoker region charges
## 1 19 female 27.900 0 yes southwest 16884.924
## 2 18 male 33.770 1 no southeast 1725.552
## 3 28 male 33.000 3 no southeast 4449.462
## 4 33 male 22.705 0 no northwest 21984.471
## 5 32 male 28.880 0 no northwest 3866.855
## 6 31 female 25.740 0 no southeast 3756.622
## 7 46 female 33.440 1 no southeast 8240.590
## 8 37 female 27.740 3 no northwest 7281.506
## 9 37 male 29.830 2 no northeast 6406.411
## 10 60 female 25.840 0 no northwest 28923.137
## 11 25 male 26.220 0 no northeast 2721.321
## 12 62 female 26.290 0 yes southeast 27808.725
## 13 23 male 34.400 0 no southwest 1826.843
## 14 56 female 39.820 0 no southeast 11090.718
## 15 27 male 42.130 0 yes southeast 39611.758
## 16 19 male 24.600 1 no southwest 1837.237
## 17 52 female 30.780 1 no northeast 10797.336
## 18 23 male 23.845 0 no northeast 2395.172
## 19 56 male 40.300 0 no southwest 10602.385
## 20 30 male 35.300 0 yes southwest 36837.467
## 21 60 female 36.005 0 no northeast 13228.847
## 22 30 female 32.400 1 no southwest 4149.736
## 23 18 male 34.100 0 no southeast 1137.011
## 24 34 female 31.920 1 yes northeast 37701.877
## 25 37 male 28.025 2 no northwest 6203.902
## 26 59 female 27.720 3 no southeast 14001.134
## 27 63 female 23.085 0 no northeast 14451.835
## 28 55 female 32.775 2 no northwest 12268.632
## 29 23 male 17.385 1 no northwest 2775.192
## 30 31 male 36.300 2 yes southwest 38711.000
## 31 22 male 35.600 0 yes southwest 35585.576
## 32 18 female 26.315 0 no northeast 2198.190
## 33 19 female 28.600 5 no southwest 4687.797
## 34 63 male 28.310 0 no northwest 13770.098
## 35 28 male 36.400 1 yes southwest 51194.559
## 36 19 male 20.425 0 no northwest 1625.434
## 37 62 female 32.965 3 no northwest 15612.193
## 38 26 male 20.800 0 no southwest 2302.300
## 39 35 male 36.670 1 yes northeast 39774.276
## 40 60 male 39.900 0 yes southwest 48173.361
## 41 24 female 26.600 0 no northeast 3046.062
## 42 31 female 36.630 2 no southeast 4949.759
## 43 41 male 21.780 1 no southeast 6272.477
## 44 37 female 30.800 2 no southeast 6313.759
## 45 38 male 37.050 1 no northeast 6079.672
## 46 55 male 37.300 0 no southwest 20630.284
## 47 18 female 38.665 2 no northeast 3393.356
## 48 28 female 34.770 0 no northwest 3556.922
## 49 60 female 24.530 0 no southeast 12629.897
## 50 36 male 35.200 1 yes southeast 38709.176is.null(Insurance[1:6])## [1] FALSEIncluding Plots
You can also embed plots, for example:
EDA
Analyzing Variables
We can see from the output the data types of all the covariates and the response variable.
df_status(Insurance)## variable q_zeros p_zeros q_na p_na q_inf p_inf type unique
## 1 age 0 0.0 0 0 0 0 integer 47
## 2 sex 0 0.0 0 0 0 0 factor 2
## 3 bmi 0 0.0 0 0 0 0 numeric 548
## 4 children 574 42.9 0 0 0 0 integer 6
## 5 smoker 0 0.0 0 0 0 0 factor 2
## 6 region 0 0.0 0 0 0 0 factor 4
## 7 charges 0 0.0 0 0 0 0 numeric 1337glimpse(Insurance)## Observations: 1,338
## Variables: 7
## $ age <int> 19, 18, 28, 33, 32, 31, 46, 37, 37, 60, 25, 62, 23, 5...
## $ sex <fct> female, male, male, male, male, female, female, femal...
## $ bmi <dbl> 27.900, 33.770, 33.000, 22.705, 28.880, 25.740, 33.44...
## $ children <int> 0, 1, 3, 0, 0, 0, 1, 3, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0,...
## $ smoker <fct> yes, no, no, no, no, no, no, no, no, no, no, yes, no,...
## $ region <fct> southwest, southeast, southeast, northwest, northwest...
## $ charges <dbl> 16884.924, 1725.552, 4449.462, 21984.471, 3866.855, 3...Analyzing variables
freq(Insurance$age)
## var frequency percentage cumulative_perc
## 1 18 69 5.16 5.16
## 2 19 68 5.08 10.24
## 3 20 29 2.17 12.41
## 4 45 29 2.17 14.58
## 5 46 29 2.17 16.75
## 6 47 29 2.17 18.92
## 7 48 29 2.17 21.09
## 8 50 29 2.17 23.26
## 9 51 29 2.17 25.43
## 10 52 29 2.17 27.60
## 11 21 28 2.09 29.69
## 12 22 28 2.09 31.78
## 13 23 28 2.09 33.87
## 14 24 28 2.09 35.96
## 15 25 28 2.09 38.05
## 16 26 28 2.09 40.14
## 17 27 28 2.09 42.23
## 18 28 28 2.09 44.32
## 19 49 28 2.09 46.41
## 20 53 28 2.09 48.50
## 21 54 28 2.09 50.59
## 22 29 27 2.02 52.61
## 23 30 27 2.02 54.63
## 24 31 27 2.02 56.65
## 25 40 27 2.02 58.67
## 26 41 27 2.02 60.69
## 27 42 27 2.02 62.71
## 28 43 27 2.02 64.73
## 29 44 27 2.02 66.75
## 30 32 26 1.94 68.69
## 31 33 26 1.94 70.63
## 32 34 26 1.94 72.57
## 33 55 26 1.94 74.51
## 34 56 26 1.94 76.45
## 35 57 26 1.94 78.39
## 36 35 25 1.87 80.26
## 37 36 25 1.87 82.13
## 38 37 25 1.87 84.00
## 39 38 25 1.87 85.87
## 40 39 25 1.87 87.74
## 41 58 25 1.87 89.61
## 42 59 25 1.87 91.48
## 43 60 23 1.72 93.20
## 44 61 23 1.72 94.92
## 45 62 23 1.72 96.64
## 46 63 23 1.72 98.36
## 47 64 22 1.64 100.00freq(Insurance$sex)
## var frequency percentage cumulative_perc
## 1 male 676 50.52 50.52
## 2 female 662 49.48 100.00freq(Insurance$bmi)## Warning in freq_logic(data = data, input = input, plot, na.rm, path_out =
## path_out): Skipping plot for variable 'var' (more than 100 categories)## var frequency percentage cumulative_perc
## 1 32.3 13 0.97 0.97
## 2 28.31 9 0.67 1.64
## 3 28.88 8 0.60 2.24
## 4 30.495 8 0.60 2.84
## 5 30.8 8 0.60 3.44
## 6 30.875 8 0.60 4.04
## 7 31.35 8 0.60 4.64
## 8 34.1 8 0.60 5.24
## 9 24.32 7 0.52 5.76
## 10 25.46 7 0.52 6.28
## 11 25.8 7 0.52 6.80
## 12 27.36 7 0.52 7.32
## 13 27.645 7 0.52 7.84
## 14 30.59 7 0.52 8.36
## 15 32.11 7 0.52 8.88
## 16 32.775 7 0.52 9.40
## 17 33.33 7 0.52 9.92
## 18 34.8 7 0.52 10.44
## 19 35.2 7 0.52 10.96
## 20 38.06 7 0.52 11.48
## 21 19.95 6 0.45 11.93
## 22 25.175 6 0.45 12.38
## 23 26.41 6 0.45 12.83
## 24 26.6 6 0.45 13.28
## 25 27.5 6 0.45 13.73
## 26 27.74 6 0.45 14.18
## 27 28.595 6 0.45 14.63
## 28 29.83 6 0.45 15.08
## 29 29.92 6 0.45 15.53
## 30 30.115 6 0.45 15.98
## 31 30.2 6 0.45 16.43
## 32 31.73 6 0.45 16.88
## 33 33 6 0.45 17.33
## 34 33.63 6 0.45 17.78
## 35 35.53 6 0.45 18.23
## 36 37.1 6 0.45 18.68
## 37 22.515 5 0.37 19.05
## 38 23.18 5 0.37 19.42
## 39 23.21 5 0.37 19.79
## 40 23.655 5 0.37 20.16
## 41 25.08 5 0.37 20.53
## 42 25.3 5 0.37 20.90
## 43 25.84 5 0.37 21.27
## 44 26.03 5 0.37 21.64
## 45 26.315 5 0.37 22.01
## 46 26.695 5 0.37 22.38
## 47 27.6 5 0.37 22.75
## 48 27.835 5 0.37 23.12
## 49 28.025 5 0.37 23.49
## 50 28.5 5 0.37 23.86
## 51 28.7 5 0.37 24.23
## 52 28.785 5 0.37 24.60
## 53 28.9 5 0.37 24.97
## 54 28.975 5 0.37 25.34
## 55 29.64 5 0.37 25.71
## 56 29.7 5 0.37 26.08
## 57 30.4 5 0.37 26.45
## 58 30.78 5 0.37 26.82
## 59 31.825 5 0.37 27.19
## 60 31.92 5 0.37 27.56
## 61 32.395 5 0.37 27.93
## 62 33.155 5 0.37 28.30
## 63 33.345 5 0.37 28.67
## 64 33.66 5 0.37 29.04
## 65 34.2 5 0.37 29.41
## 66 36.85 5 0.37 29.78
## 67 20.235 4 0.30 30.08
## 68 21.755 4 0.30 30.38
## 69 21.85 4 0.30 30.68
## 70 22.135 4 0.30 30.98
## 71 22.61 4 0.30 31.28
## 72 22.895 4 0.30 31.58
## 73 24.13 4 0.30 31.88
## 74 24.605 4 0.30 32.18
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## 77 25.6 4 0.30 33.08
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## 81 26.4 4 0.30 34.28
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## 84 27.265 4 0.30 35.18
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## 87 27.83 4 0.30 36.08
## 88 27.93 4 0.30 36.38
## 89 28.12 4 0.30 36.68
## 90 28.215 4 0.30 36.98
## 91 29.26 4 0.30 37.28
## 92 29.6 4 0.30 37.58
## 93 29.735 4 0.30 37.88
## 94 29.8 4 0.30 38.18
## 95 29.81 4 0.30 38.48
## 96 30.02 4 0.30 38.78
## 97 30.21 4 0.30 39.08
## 98 30.5 4 0.30 39.38
## 99 31.065 4 0.30 39.68
## 100 31.13 4 0.30 39.98
## 101 31.16 4 0.30 40.28
## 102 31.79 4 0.30 40.58
## 103 32.68 4 0.30 40.88
## 104 32.965 4 0.30 41.18
## 105 33.1 4 0.30 41.48
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## 111 34.21 4 0.30 43.28
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## 113 34.43 4 0.30 43.88
## 114 35.3 4 0.30 44.18
## 115 35.625 4 0.30 44.48
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## 117 35.86 4 0.30 45.08
## 118 35.97 4 0.30 45.38
## 119 36.08 4 0.30 45.68
## 120 36.3 4 0.30 45.98
## 121 36.67 4 0.30 46.28
## 122 36.955 4 0.30 46.58
## 123 37.29 4 0.30 46.88
## 124 42.13 4 0.30 47.18
## 125 17.29 3 0.22 47.40
## 126 18.335 3 0.22 47.62
## 127 19.8 3 0.22 47.84
## 128 21.47 3 0.22 48.06
## 129 21.66 3 0.22 48.28
## 130 22.42 3 0.22 48.50
## 131 22.705 3 0.22 48.72
## 132 22.99 3 0.22 48.94
## 133 23.37 3 0.22 49.16
## 134 23.75 3 0.22 49.38
## 135 23.845 3 0.22 49.60
## 136 23.98 3 0.22 49.82
## 137 24.035 3 0.22 50.04
## 138 24.225 3 0.22 50.26
## 139 24.3 3 0.22 50.48
## 140 24.42 3 0.22 50.70
## 141 24.51 3 0.22 50.92
## 142 24.6 3 0.22 51.14
## 143 25.27 3 0.22 51.36
## 144 25.365 3 0.22 51.58
## 145 25.555 3 0.22 51.80
## 146 25.745 3 0.22 52.02
## 147 25.9 3 0.22 52.24
## 148 25.935 3 0.22 52.46
## 149 26.98 3 0.22 52.68
## 150 27.7 3 0.22 52.90
## 151 27.94 3 0.22 53.12
## 152 28 3 0.22 53.34
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## 154 28.6 3 0.22 53.78
## 155 28.69 3 0.22 54.00
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## 172 33.25 3 0.22 57.74
## 173 33.4 3 0.22 57.96
## 174 33.535 3 0.22 58.18
## 175 33.7 3 0.22 58.40
## 176 33.88 3 0.22 58.62
## 177 34.32 3 0.22 58.84
## 178 34.77 3 0.22 59.06
## 179 34.96 3 0.22 59.28
## 180 35.75 3 0.22 59.50
## 181 36.1 3 0.22 59.72
## 182 36.19 3 0.22 59.94
## 183 36.48 3 0.22 60.16
## 184 36.63 3 0.22 60.38
## 185 36.765 3 0.22 60.60
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## 401 26.07 1 0.07 88.30
## 402 26.2 1 0.07 88.37
## 403 26.29 1 0.07 88.44
## 404 26.505 1 0.07 88.51
## 405 26.9 1 0.07 88.58
## 406 27 1 0.07 88.65
## 407 27.06 1 0.07 88.72
## 408 27.075 1 0.07 88.79
## 409 27.28 1 0.07 88.86
## 410 27.3 1 0.07 88.93
## 411 27.61 1 0.07 89.00
## 412 27.8 1 0.07 89.07
## 413 27.9 1 0.07 89.14
## 414 28.16 1 0.07 89.21
## 415 28.2 1 0.07 89.28
## 416 28.38 1 0.07 89.35
## 417 28.49 1 0.07 89.42
## 418 28.8 1 0.07 89.49
## 419 28.82 1 0.07 89.56
## 420 29.04 1 0.07 89.63
## 421 29.1 1 0.07 89.70
## 422 29.165 1 0.07 89.77
## 423 29.2 1 0.07 89.84
## 424 29.4 1 0.07 89.91
## 425 29.45 1 0.07 89.98
## 426 29.5 1 0.07 90.05
## 427 29.545 1 0.07 90.12
## 428 30.36 1 0.07 90.19
## 429 30.97 1 0.07 90.26
## 430 31.1 1 0.07 90.33
## 431 31.2 1 0.07 90.40
## 432 31.24 1 0.07 90.47
## 433 31.3 1 0.07 90.54
## 434 31.8 1 0.07 90.61
## 435 32 1 0.07 90.68
## 436 32.1 1 0.07 90.75
## 437 32.12 1 0.07 90.82
## 438 32.4 1 0.07 90.89
## 439 32.45 1 0.07 90.96
## 440 32.5 1 0.07 91.03
## 441 32.585 1 0.07 91.10
## 442 32.78 1 0.07 91.17
## 443 32.87 1 0.07 91.24
## 444 33.06 1 0.07 91.31
## 445 33.2 1 0.07 91.38
## 446 33.5 1 0.07 91.45
## 447 33.55 1 0.07 91.52
## 448 33.8 1 0.07 91.59
## 449 34.01 1 0.07 91.66
## 450 34.295 1 0.07 91.73
## 451 34.3 1 0.07 91.80
## 452 34.5 1 0.07 91.87
## 453 34.675 1 0.07 91.94
## 454 34.87 1 0.07 92.01
## 455 34.9 1 0.07 92.08
## 456 35.09 1 0.07 92.15
## 457 35.1 1 0.07 92.22
## 458 35.15 1 0.07 92.29
## 459 35.4 1 0.07 92.36
## 460 35.42 1 0.07 92.43
## 461 35.435 1 0.07 92.50
## 462 35.5 1 0.07 92.57
## 463 35.6 1 0.07 92.64
## 464 35.64 1 0.07 92.71
## 465 35.7 1 0.07 92.78
## 466 35.9 1 0.07 92.85
## 467 36.005 1 0.07 92.92
## 468 36.195 1 0.07 92.99
## 469 36.29 1 0.07 93.06
## 470 36.4 1 0.07 93.13
## 471 36.52 1 0.07 93.20
## 472 36.6 1 0.07 93.27
## 473 36.7 1 0.07 93.34
## 474 36.96 1 0.07 93.41
## 475 37.145 1 0.07 93.48
## 476 37.3 1 0.07 93.55
## 477 37.525 1 0.07 93.62
## 478 37.7 1 0.07 93.69
## 479 37.715 1 0.07 93.76
## 480 37.8 1 0.07 93.83
## 481 37.9 1 0.07 93.90
## 482 37.905 1 0.07 93.97
## 483 38.19 1 0.07 94.04
## 484 38.285 1 0.07 94.11
## 485 38.665 1 0.07 94.18
## 486 38.9 1 0.07 94.25
## 487 38.95 1 0.07 94.32
## 488 39.1 1 0.07 94.39
## 489 39.14 1 0.07 94.46
## 490 39.2 1 0.07 94.53
## 491 39.27 1 0.07 94.60
## 492 39.33 1 0.07 94.67
## 493 39.4 1 0.07 94.74
## 494 39.425 1 0.07 94.81
## 495 39.52 1 0.07 94.88
## 496 39.615 1 0.07 94.95
## 497 39.71 1 0.07 95.02
## 498 39.8 1 0.07 95.09
## 499 39.9 1 0.07 95.16
## 500 39.93 1 0.07 95.23
## 501 39.995 1 0.07 95.30
## 502 40.3 1 0.07 95.37
## 503 40.375 1 0.07 95.44
## 504 40.47 1 0.07 95.51
## 505 40.48 1 0.07 95.58
## 506 40.5 1 0.07 95.65
## 507 40.66 1 0.07 95.72
## 508 40.81 1 0.07 95.79
## 509 40.92 1 0.07 95.86
## 510 40.945 1 0.07 95.93
## 511 41.1 1 0.07 96.00
## 512 41.42 1 0.07 96.07
## 513 41.69 1 0.07 96.14
## 514 41.895 1 0.07 96.21
## 515 42.24 1 0.07 96.28
## 516 42.35 1 0.07 96.35
## 517 42.46 1 0.07 96.42
## 518 42.655 1 0.07 96.49
## 519 42.68 1 0.07 96.56
## 520 42.75 1 0.07 96.63
## 521 42.94 1 0.07 96.70
## 522 43.01 1 0.07 96.77
## 523 43.12 1 0.07 96.84
## 524 43.34 1 0.07 96.91
## 525 43.4 1 0.07 96.98
## 526 43.7 1 0.07 97.05
## 527 44 1 0.07 97.12
## 528 44.7 1 0.07 97.19
## 529 44.745 1 0.07 97.26
## 530 44.77 1 0.07 97.33
## 531 44.88 1 0.07 97.40
## 532 45.32 1 0.07 97.47
## 533 45.43 1 0.07 97.54
## 534 45.54 1 0.07 97.61
## 535 45.9 1 0.07 97.68
## 536 46.09 1 0.07 97.75
## 537 46.2 1 0.07 97.82
## 538 46.7 1 0.07 97.89
## 539 46.75 1 0.07 97.96
## 540 47.41 1 0.07 98.03
## 541 47.52 1 0.07 98.10
## 542 47.6 1 0.07 98.17
## 543 47.74 1 0.07 98.24
## 544 48.07 1 0.07 98.31
## 545 49.06 1 0.07 98.38
## 546 50.38 1 0.07 98.45
## 547 52.58 1 0.07 98.52
## 548 53.13 1 0.07 100.00freq(Insurance$children)
## var frequency percentage cumulative_perc
## 1 0 574 42.90 42.90
## 2 1 324 24.22 67.12
## 3 2 240 17.94 85.06
## 4 3 157 11.73 96.79
## 5 4 25 1.87 98.66
## 6 5 18 1.35 100.00freq(Insurance$smoker)
## var frequency percentage cumulative_perc
## 1 no 1064 79.52 79.52
## 2 yes 274 20.48 100.00freq(Insurance$region)
## var frequency percentage cumulative_perc
## 1 southeast 364 27.20 27.20
## 2 northwest 325 24.29 51.49
## 3 southwest 325 24.29 75.78
## 4 northeast 324 24.22 100.00plot_num(Insurance)
Check if the data has missing values
library(Hmisc)
describe(Insurance)## Insurance
##
## 7 Variables 1338 Observations
## ---------------------------------------------------------------------------
## age
## n missing distinct Info Mean Gmd .05 .10
## 1338 0 47 0.999 39.21 16.21 18 19
## .25 .50 .75 .90 .95
## 27 39 51 59 62
##
## lowest : 18 19 20 21 22, highest: 60 61 62 63 64
## ---------------------------------------------------------------------------
## sex
## n missing distinct
## 1338 0 2
##
## Value female male
## Frequency 662 676
## Proportion 0.495 0.505
## ---------------------------------------------------------------------------
## bmi
## n missing distinct Info Mean Gmd .05 .10
## 1338 0 548 1 30.66 6.893 21.26 22.99
## .25 .50 .75 .90 .95
## 26.30 30.40 34.69 38.62 41.11
##
## lowest : 15.960 16.815 17.195 17.290 17.385, highest: 48.070 49.060 50.380 52.580 53.130
## ---------------------------------------------------------------------------
## children
## n missing distinct Info Mean Gmd
## 1338 0 6 0.899 1.095 1.275
##
## lowest : 0 1 2 3 4, highest: 1 2 3 4 5
##
## Value 0 1 2 3 4 5
## Frequency 574 324 240 157 25 18
## Proportion 0.429 0.242 0.179 0.117 0.019 0.013
## ---------------------------------------------------------------------------
## smoker
## n missing distinct
## 1338 0 2
##
## Value no yes
## Frequency 1064 274
## Proportion 0.795 0.205
## ---------------------------------------------------------------------------
## region
## n missing distinct
## 1338 0 4
##
## Value northeast northwest southeast southwest
## Frequency 324 325 364 325
## Proportion 0.242 0.243 0.272 0.243
## ---------------------------------------------------------------------------
## charges
## n missing distinct Info Mean Gmd .05 .10
## 1338 0 1337 1 13270 12301 1758 2347
## .25 .50 .75 .90 .95
## 4740 9382 16640 34832 41182
##
## lowest : 1121.874 1131.507 1135.941 1136.399 1137.011
## highest: 55135.402 58571.074 60021.399 62592.873 63770.428
## ---------------------------------------------------------------------------pairs(Insurance, pch=20)
plot(Insurance$charges, Insurance$age, pch=2,col="red")
plot(Insurance$sex, Insurance$charges, pch=2,col="green")
plot(Insurance$bmi, Insurance$charges, pch=2,col="blue")
plot(Insurance$children, Insurance$charges, pch=2,col="pink")
plot(Insurance$smoker, Insurance$charges, pch=2,col="purple")
plot(Insurance$region, Insurance$charges, pch=2,col="yellow")
library("ggplot2")
r <- ggplot(data=Insurance, aes(x=age, y=charges))
r + geom_point(aes(colour=smoker))
- What kind of models are you using? What techniques are you using, for example, indicator variables, polynomial regression, transformation and so on?
Model for regression
model_Insurance <- lm(Insurance$charges ~ Insurance$age + Insurance$sex + Insurance$bmi + Insurance$children + Insurance$smoker + Insurance$region , data=Insurance)
summary(model_Insurance)##
## Call:
## lm(formula = Insurance$charges ~ Insurance$age + Insurance$sex +
## Insurance$bmi + Insurance$children + Insurance$smoker + Insurance$region,
## data = Insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11304.9 -2848.1 -982.1 1393.9 29992.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11938.5 987.8 -12.086 < 2e-16 ***
## Insurance$age 256.9 11.9 21.587 < 2e-16 ***
## Insurance$sexmale -131.3 332.9 -0.394 0.693348
## Insurance$bmi 339.2 28.6 11.860 < 2e-16 ***
## Insurance$children 475.5 137.8 3.451 0.000577 ***
## Insurance$smokeryes 23848.5 413.1 57.723 < 2e-16 ***
## Insurance$regionnorthwest -353.0 476.3 -0.741 0.458769
## Insurance$regionsoutheast -1035.0 478.7 -2.162 0.030782 *
## Insurance$regionsouthwest -960.0 477.9 -2.009 0.044765 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.8 on 8 and 1329 DF, p-value: < 2.2e-16model_Insurance$coefficients## (Intercept) Insurance$age
## -11938.5386 256.8564
## Insurance$sexmale Insurance$bmi
## -131.3144 339.1935
## Insurance$children Insurance$smokeryes
## 475.5005 23848.5345
## Insurance$regionnorthwest Insurance$regionsoutheast
## -352.9639 -1035.0220
## Insurance$regionsouthwest
## -960.0510model_Insurance$residuals## 1 2 3 4 5
## -8408.789028 -1723.050534 -2257.526491 18229.640447 -1725.638186
## 6 7 8 9 10
## 36.795801 -2419.371625 -766.405007 -2096.563220 17038.499402
## 11 12 13 14 15
## -523.887432 -7908.738569 -2719.203986 -3826.360639 7642.756424
## 16 17 18 19 20
## 1167.210725 -1536.530603 469.260476 -4421.162996 6339.616896
## 21 22 23 24 25
## -2456.655923 -2122.733451 -1948.025129 5756.209264 -1333.864087
## 26 27 28 29 30
## 991.225456 2378.142640 -1635.031196 2917.934140 6666.099000
## 31 32 33 34 35
## 7040.818681 587.438349 627.680370 408.397853 20361.808397
## 36 37 38 39 40
## 2239.953597 -629.411865 1598.714926 6091.897866 8409.530434
## 41 42 43 44 45
## -202.497751 -3414.884899 983.107766 -1614.524880 -4653.634962
## 46 47 48 49 50
## 6881.172228 -3357.435394 -3137.309478 1871.660756 6303.577639
## 51 52 53 54 55
## -2557.511804 -1880.729163 -9552.380783 6073.656844 -1081.034345
## 56 57 58 59 60
## 7687.213127 -1097.593872 7239.443597 -9479.817165 -4066.878542
## 61 62 63 64 65
## -1075.587350 -2131.125258 17297.049593 -39.316510 -9587.132547
## 66 67 68 69 70
## -41.157940 -2748.041064 -863.435693 -3656.000462 -9832.853881
## 71 72 73 74 75
## -9627.353912 -1137.752147 69.091201 -1179.250557 -789.823304
## 76 77 78 79 80
## -2397.303717 -1040.095336 -2808.182125 -4458.875651 -2850.095827
## 81 82 83 84 85
## -1046.197389 -4670.727510 7534.706217 -4890.889019 6627.955706
## 86 87 88 89 90
## -10602.534732 6811.827225 361.747887 -906.449544 95.540908
## 91 92 93 94 95
## -3788.198161 734.445614 -8292.912063 -3582.907676 8334.547275
## 96 97 98 99 100
## -3687.491715 -739.993476 -3780.265609 -10516.898248 -11304.906666
## 101 102 103 104 105
## -2164.907021 -626.613569 18445.160075 -7176.189389 -633.993938
## 106 107 108 109 110
## -8983.862090 241.243242 -1801.743052 -953.904733 8227.624046
## 111 112 113 114 115
## -2504.748892 -372.198485 -2274.180488 -2813.737291 -2148.587255
## 116 117 118 119 120
## 17219.230537 -7052.298896 -9168.594179 -226.957483 596.296631
## 121 122 123 124 125
## -4066.516804 1096.218567 -416.279644 5366.918066 -2595.984858
## 126 127 128 129 130
## -1118.011002 -8348.310410 -3509.237930 5980.978159 -3369.246400
## 131 132 133 134 135
## 609.136239 2410.835954 -2679.275192 507.021880 -505.060887
## 136 137 138 139 140
## -35.974004 -2155.421539 278.467135 14179.278643 -2796.482518
## 141 142 143 144 145
## 22156.923409 -2613.758983 -10036.876010 12094.940178 -9543.381003
## 146 147 148 149 150
## -3934.400337 5709.235123 -3521.775204 -3533.701023 -116.442399
## 151 152 153 154 155
## -102.178385 -1508.640509 -3972.363625 -10660.167483 -369.891999
## 156 157 158 159 160
## -5335.087163 -10132.192816 -9423.110897 6449.363160 9013.870929
## 161 162 163 164 165
## -10018.838739 8151.816472 -4297.348418 -1227.645722 -2106.415574
## 166 167 168 169 170
## -1067.655258 -2335.567993 -2471.563946 -1139.820679 2123.682491
## 171 172 173 174 175
## -3738.037446 -1716.938992 3727.707470 -3124.768502 -2328.018146
## 176 177 178 179 180
## 8904.961615 -1274.312783 -784.192501 -847.215549 -2726.744018
## 181 182 183 184 185
## -438.209368 -3002.357924 2231.024645 -548.798246 -1826.225608
## 186 187 188 189 190
## 7090.815378 -822.396963 -1389.029361 -2254.089638 -2076.918734
## 191 192 193 194 195
## -714.094550 -351.241608 90.280276 453.842322 -2059.500269
## 196 197 198 199 200
## -1193.818509 -2594.638460 -720.080102 2713.639159 -2939.229817
## 201 202 203 204 205
## -1349.594118 -1892.098151 1739.815316 7085.702959 797.602695
## 206 207 208 209 210
## -1187.111580 738.942010 -10144.787839 -188.763467 -6054.738103
## 211 212 213 214 215
## -1796.037638 -2063.321077 -822.047144 -298.914221 -1571.999104
## 216 217 218 219 220
## -3795.827106 11.210925 818.120688 -935.896418 24018.095946
## 221 222 223 224 225
## -2728.375351 -2388.145941 -1809.635361 7276.781501 -10373.811461
## 226 227 228 229 230
## -1953.432048 -4307.310331 8087.631778 -2440.281678 -364.005653
## 231 232 233 234 235
## -3805.428880 954.067076 3708.460395 405.886608 -149.021652
## 236 237 238 239 240
## -10192.841847 899.271965 -4367.104618 -8813.661802 -4429.336516
## 241 242 243 244 245
## 7304.711192 832.805952 24365.739646 -3447.513723 -7978.006979
## 246 247 248 249 250
## 12846.464831 -2698.819971 -3236.221322 2417.083503 -1642.053902
## 251 252 253 254 255
## -10388.296755 8300.379519 7092.038168 -1348.536872 5680.830856
## 256 257 258 259 260
## 828.627950 6704.434406 -5004.617433 659.832355 6617.248356
## 261 262 263 264 265
## 1290.406089 -8506.286207 -9941.061566 7378.522967 5486.967121
## 266 267 268 269 270
## 7800.728330 -11029.922585 -1040.027739 -1806.721782 -473.887125
## 271 272 273 274 275
## -236.715338 6643.972554 -4360.709666 -943.359055 -820.202125
## 276 277 278 279 280
## -391.415949 2402.769850 1155.817889 -854.819695 1940.506641
## 281 282 283 284 285
## -9866.303728 7714.369625 -1251.214661 -1773.129238 -1414.856517
## 286 287 288 289 290
## -473.237712 -7699.958746 1472.092712 7886.322717 15359.956882
## 291 292 293 294 295
## -2450.431654 14369.631712 8549.296262 -296.082663 -2.264079
## 296 297 298 299 300
## 1352.949191 -8796.713978 -9931.637428 6266.725959 -1059.514732
## 301 302 303 304 305
## -1201.514538 -9745.663372 -2819.035752 -2013.340305 -2936.367855
## 306 307 308 309 310
## 12154.929310 15605.461762 -2361.919605 -2709.200922 -2655.188245
## 311 312 313 314 315
## -390.985566 1377.616565 6708.742422 -3520.155136 6303.132064
## 316 317 318 319 320
## -2842.090229 -2508.461015 -2482.390294 -965.985511 -4621.230831
## 321 322 323 324 325
## -462.464969 17976.240605 5492.735027 -4892.934567 -778.901235
## 326 327 328 329 330
## -3647.888496 1252.147404 6451.470351 8599.039186 -3630.461153
## 331 332 333 334 335
## 8122.275325 -9668.958530 -516.967644 -550.721578 6971.300684
## 336 337 338 339 340
## -1288.273785 1105.232937 615.109286 5866.148670 -487.135870
## 341 342 343 344 345
## 16327.517957 -332.764700 399.472277 -2600.694246 -4603.549051
## 346 347 348 349 350
## -926.558049 -3558.552206 -3196.987987 -1419.399943 -263.169994
## 351 352 353 354 355
## 1618.793326 304.503528 -648.556674 4043.599129 9498.858626
## 356 357 358 359 360
## 16455.820760 -6080.104446 -1573.743391 -5181.136864 2905.824479
## 361 362 363 364 365
## -2254.266988 -2029.899292 -9346.207616 672.177444 2384.141532
## 366 367 368 369 370
## -1784.950545 -1397.602353 94.847290 -2572.873334 -809.676035
## 371 372 373 374 375
## 2884.713134 1786.742708 -2931.470280 6477.857505 -1946.041175
## 376 377 378 379 380
## -9033.326946 -10136.490311 7599.417320 667.091272 13034.239262
## 381 382 383 384 385
## -10879.757584 5989.760030 8565.880546 -5821.139483 611.660888
## 386 387 388 389 390
## -2256.762576 -3313.200685 20309.999107 1120.889223 -928.505954
## 391 392 393 394 395
## -3508.150202 -3146.708491 -2436.630130 -2335.184155 -2372.798282
## 396 397 398 399 400
## 1399.445047 -2718.987031 13775.608361 1945.175862 -2965.199544
## 401 402 403 404 405
## 2076.327444 -7477.427245 -636.146935 -2276.134626 1408.009545
## 406 407 408 409 410
## -3990.337396 436.606035 885.545948 1406.595013 -1701.554553
## 411 412 413 414 415
## 3234.784768 -10955.945906 -10916.049607 1204.364846 -2376.516617
## 416 417 418 419 420
## -3289.891165 -2677.201115 -10205.284808 -2673.967366 -7939.952455
## 421 422 423 424 425
## 8214.920872 8023.734092 5479.830555 -2000.088524 -1525.514384
## 426 427 428 429 430
## 711.909438 -990.542528 4746.281975 3532.972555 12423.150732
## 431 432 433 434 435
## 20005.285244 1934.497278 -912.643782 -219.996920 -1470.877395
## 436 437 438 439 440
## -1043.880152 -2088.798403 -1262.414857 -6025.231888 -1700.335939
## 441 442 443 444 445
## -2493.118862 6290.186696 -4957.853901 13244.088015 -9230.614188
## 446 447 448 449 450
## -2542.165611 -664.222582 661.256148 -1504.846761 -4766.107266
## 451 452 453 454 455
## -1417.355230 89.128378 897.838651 -1030.695909 -7161.812083
## 456 457 458 459 460
## 6986.544362 -445.860946 -852.238937 -4184.700578 -2237.909081
## 461 462 463 464 465
## -3082.079790 -9638.369030 -2628.806937 54.332624 635.387192
## 466 467 468 469 470
## -9160.507051 501.548751 -1871.599158 19310.803768 1904.572537
## 471 472 473 474 475
## -2414.658363 -696.214775 -345.181048 9434.668726 -9246.833973
## 476 477 478 479 480
## -8303.358529 7537.280985 -3547.965013 -3254.082684 -2022.674573
## 481 482 483 484 485
## -3647.615731 -3850.531925 -661.379991 -4194.658375 -2797.009089
## 486 487 488 489 490
## -2214.029639 2187.625654 -331.282890 13798.779338 -1773.359009
## 491 492 493 494 495
## -1392.371755 13311.442564 1004.625614 -4785.280465 -8889.781957
## 496 497 498 499 500
## -573.924575 911.723043 -1186.517146 798.121206 -2852.027671
## 501 502 503 504 505
## 6261.979357 -966.807121 -9973.399240 6663.808273 -1100.963229
## 506 507 508 509 510
## -2183.104475 -1693.969737 1099.083318 246.780843 -21.794646
## 511 512 513 514 515
## -1918.104247 -2749.083782 726.788526 -905.548761 -9828.543646
## 516 517 518 519 520
## -2614.215814 23239.615292 -2016.961437 -1841.115378 -2507.532623
## 521 522 523 524 525
## 15471.963319 -6250.799374 -2798.576532 -4187.133076 7395.693026
## 526 527 528 529 530
## 8340.906922 20143.983131 433.248940 -5250.832985 518.574661
## 531 532 533 534 535
## 8525.325303 -705.686864 -148.810477 10540.484385 -3233.367380
## 536 537 538 539 540
## -1604.958793 -4226.419047 -1286.360039 -598.611010 16203.815600
## 541 542 543 544 545
## -3953.931291 -841.139306 -1633.907950 22944.049421 -1462.960536
## 546 547 548 549 550
## -9920.198313 -3872.598314 -6224.567843 -968.484993 8272.670368
## 551 552 553 554 555
## -208.645654 -1085.784569 2803.188162 -1590.980530 9378.860972
## 556 557 558 559 560
## 661.794770 -3229.079315 -3296.869149 6441.727174 -2862.567570
## 561 562 563 564 565
## 1952.038269 -2092.613325 -1756.595927 -6340.403805 -694.489740
## 566 567 568 569 570
## -804.041540 -5330.364562 -2178.499355 -1332.241603 7236.816185
## 571 572 573 574 575
## -1173.194861 -2554.433050 -5555.515961 14655.274534 -2061.857050
## 576 577 578 579 580
## 400.846194 15.082534 25301.456425 -1321.239249 764.446724
## 581 582 583 584 585
## 717.954662 -1193.818509 -6916.811752 13882.971131 2371.144739
## 586 587 588 589 590
## -787.596187 2246.998013 12931.193269 -2274.497948 -1695.497307
## 591 592 593 594 595
## 6.752966 1665.121133 -975.874667 -9831.752376 -5372.999511
## 596 597 598 599 600
## -2967.667659 -1124.521084 -2953.414788 -2582.125910 18727.708597
## 601 602 603 604 605
## -3299.624964 -2233.106399 1003.574449 -2052.124436 -8570.885536
## 606 607 608 609 610
## -2409.048122 22.842113 -9056.399561 -789.471204 6944.607172
## 611 612 613 614 615
## -988.608921 -3045.341105 -1723.137274 2087.283336 -1476.880394
## 616 617 618 619 620
## 7122.473463 -486.538922 -9732.398392 7453.916036 -3098.942951
## 621 622 623 624 625
## -2142.615638 6391.431392 1794.477186 6840.892231 -365.777377
## 626 627 628 629 630
## -250.072645 -1650.793132 1077.675636 -3391.163758 6913.161904
## 631 632 633 634 635
## -3218.020978 -1095.201725 -3160.147305 316.570330 -4619.904706
## 636 637 638 639 640
## -2911.819520 1331.211584 13991.036792 -10604.855565 -1649.179186
## 641 642 643 644 645
## -5539.417866 -455.294231 -1958.265698 -2434.277006 7938.275359
## 646 647 648 649 650
## -1984.991924 -840.165013 563.116128 -508.347838 -1709.688719
## 651 652 653 654 655
## -5239.290139 -3967.676367 -1634.013807 -3321.166695 -1876.042741
## 656 657 658 659 660
## -9096.680715 -5226.654577 -2650.552278 13345.756480 26.438889
## 661 662 663 664 665
## -7172.359391 11915.826078 -2305.974177 -1799.391609 -8073.923877
## 666 667 668 669 670
## 6911.243749 -1062.954011 6103.979550 7147.153969 -1387.314973
## 671 672 673 674 675
## -1898.072257 -2135.968262 -1816.268279 -1894.009959 8186.129903
## 676 677 678 679 680
## 836.807150 -3936.724341 7233.211235 -2661.890126 1048.819056
## 681 682 683 684 685
## 3712.408526 2506.266120 6343.331633 423.717159 2437.772497
## 686 687 688 689 690
## -208.257049 -800.898187 -5871.605098 18412.858191 6093.093868
## 691 692 693 694 695
## -500.349959 -3728.463208 -1815.753641 587.611679 -2737.965682
## 696 697 698 699 700
## -4816.006474 15604.684610 6397.208977 -2424.192380 -3704.651196
## 701 702 703 704 705
## -2227.546205 -6539.794583 -5070.553921 -489.875266 -1346.782676
## 706 707 708 709 710
## -2313.097780 7516.055660 -1056.664159 -1680.983306 -1248.509918
## 711 712 713 714 715
## -2206.109473 1302.348610 -1801.633748 -4809.979883 1525.767055
## 716 717 718 719 720
## -37.197035 1127.867570 1399.355146 -3349.262238 -1717.181460
## 721 722 723 724 725
## -5077.060827 -3159.923795 -2601.667095 -2594.566029 -457.308102
## 726 727 728 729 730
## 7679.759009 -1553.898264 -10555.766868 -4129.986881 -3489.795980
## 731 732 733 734 735
## -10081.238868 1747.689790 -667.260483 -666.926053 -563.324729
## 736 737 738 739 740
## -2979.822426 7018.723456 846.083820 6313.614067 13325.622338
## 741 742 743 744 745
## 12.284974 -9319.774748 6294.156924 -260.471238 -550.890002
## 746 747 748 749 750
## -1331.266702 5925.412443 1790.675003 -3303.216877 -2179.250666
## 751 752 753 754 755
## -9794.123136 -892.938637 -2662.581637 2186.239540 9724.648529
## 756 757 758 759 760
## -1189.428558 746.843449 -9321.555600 -4329.622545 7993.710273
## 761 762 763 764 765
## -2466.853696 -2875.947294 -9921.657387 -623.665480 -15.125323
## 766 767 768 769 770
## -1301.517530 -2411.029739 -1150.845939 -2687.166103 1907.409730
## 771 772 773 774 775
## 11631.568691 428.516581 1060.291497 -8484.703505 -3397.969823
## 776 777 778 779 780
## -2166.126739 -2771.689908 -5541.874400 -3018.338517 -1116.666590
## 781 782 783 784 785
## -9967.927095 -4326.161442 -3284.926766 -9109.738466 -1038.772901
## 786 787 788 789 790
## -499.365072 -3135.254845 -3556.518868 767.155318 357.759436
## 791 792 793 794 795
## -5559.898484 40.300909 1157.106766 -10250.371422 -2294.459603
## 796 797 798 799 800
## -9717.110653 -6284.785400 711.037384 -1378.241194 -10760.715872
## 801 802 803 804 805
## -123.269142 -1352.188163 1699.485963 8966.765857 21.036321
## 806 807 808 809 810
## -3683.389080 15969.089970 -2857.886538 -610.323453 -282.022664
## 811 812 813 814 815
## -1375.542656 -5815.232092 2170.888297 718.821216 -3187.079705
## 816 817 818 819 820
## -956.663076 752.749351 -3290.774946 -9917.868306 23050.566983
## 821 822 823 824 825
## -2989.033869 2431.952644 -587.063231 -1171.272929 1285.855691
## 826 827 828 829 830
## -177.015988 6952.289820 -10233.279630 5420.739002 636.036079
## 831 832 833 834 835
## -985.593598 -453.719457 780.192163 -2395.780382 -3393.577203
## 836 837 838 839 840
## -3674.551138 -2499.285553 -390.264938 440.682108 -874.557595
## 841 842 843 844 845
## -1386.683884 861.185832 7168.578676 -8093.229963 -1815.183067
## 846 847 848 849 850
## 7715.772862 -2404.300071 -7928.832661 763.031817 -2219.715747
## 851 852 853 854 855
## 5416.095688 -1032.750312 6334.733111 1047.985778 -9903.614227
## 856 857 858 859 860
## -403.319710 6539.390813 -10213.878856 13362.607647 -176.798214
## 861 862 863 864 865
## 8563.271499 -634.778166 -1891.761821 1415.070313 97.185226
## 866 867 868 869 870
## -1736.874528 -3025.618146 -5333.032636 1507.597736 1199.930196
## 871 872 873 874 875
## -3633.898721 -787.262898 -148.553678 -1851.116731 821.434327
## 876 877 878 879 880
## -464.199748 16785.345455 -2437.727863 -1463.243536 -1250.351448
## 881 882 883 884 885
## -2408.305650 -451.655309 1622.358727 7251.823463 -77.382353
## 886 887 888 889 890
## -9531.735296 -9029.186769 -1865.737893 -4336.480247 -2155.438950
## 891 892 893 894 895
## -7784.071479 -781.634539 470.011891 7227.551300 -1191.737817
## 896 897 898 899 900
## -4630.276896 -10906.898443 620.521335 -3671.208762 1891.630019
## 901 902 903 904 905
## 535.809903 8638.721969 -621.737029 -3854.580555 -1773.892807
## 906 907 908 909 910
## -1083.560061 -2497.468754 -2139.415121 -2908.378372 -10017.201214
## 911 912 913 914 915
## -667.047238 6567.982465 1038.415846 -579.417464 -92.790865
## 916 917 918 919 920
## -2246.843224 -9946.749076 3966.322929 707.017671 -2850.493406
## 921 922 923 924 925
## 1944.781370 -825.206950 -2232.873077 -4138.101842 366.227644
## 926 927 928 929 930
## 12717.865263 2043.759964 2996.814510 -2763.544475 -3215.789162
## 931 932 933 934 935
## -6904.497423 -2379.797969 182.787881 -3285.333209 -4003.349792
## 936 937 938 939 940
## 650.072793 21839.917811 645.436337 954.377133 -1020.290512
## 941 942 943 944 945
## 1730.654481 -6428.618723 -4097.895553 1501.853051 -3381.338775
## 946 947 948 949 950
## -2429.862359 -3692.095609 5689.001691 -2607.864914 -8807.128636
## 951 952 953 954 955
## 2744.801519 8117.160213 -997.295745 5683.592484 -10066.150370
## 956 957 958 959 960
## -4852.187872 6462.958490 9305.658227 5877.012951 15648.906434
## 961 962 963 964 965
## -3771.309583 17.928895 -1148.824697 -81.769549 12111.935461
## 966 967 968 969 970
## -881.367550 -9919.311409 -439.979823 272.201529 -2465.631377
## 971 972 973 974 975
## -144.803890 206.401223 2304.901836 -3959.678002 -3265.000508
## 976 977 978 979 980
## -10854.587900 -5038.686599 -1033.473399 -4907.873051 -1532.899398
## 981 982 983 984 985
## 14605.357654 586.816128 -9792.845628 10948.400707 -744.527846
## 986 987 988 989 990
## -5.151592 -1853.271965 19220.651891 -3905.969805 -10462.907295
## 991 992 993 994 995
## 2407.703475 -1069.591042 -1495.318284 -1235.698590 -10297.293448
## 996 997 998 999 1000
## 586.386809 -2693.284585 -1819.699850 -3721.803025 -806.724066
## 1001 1002 1003 1004 1005
## -10518.700772 6398.031991 87.110363 11892.855038 1640.522546
## 1006 1007 1008 1009 1010
## -2306.239062 -1559.663078 -9579.590355 19464.169123 -956.826392
## 1011 1012 1013 1014 1015
## 1104.917903 -10799.710328 20678.285291 -2572.488184 -840.155149
## 1016 1017 1018 1019 1020
## 757.419106 1299.120256 -2343.166802 -2658.164888 20880.626438
## 1021 1022 1023 1024 1025
## -3821.334836 7121.493561 6681.629722 1806.995556 -6376.574006
## 1026 1027 1028 1029 1030
## -2211.310331 -9159.799848 21762.497532 -1708.420244 2497.177729
## 1031 1032 1033 1034 1035
## -10194.262523 7482.120127 -1103.302459 -9968.930429 -3313.594219
## 1036 1037 1038 1039 1040
## 1894.873462 7565.047572 5790.745206 -1126.058561 19837.095174
## 1041 1042 1043 1044 1045
## -9818.046193 1320.857863 6151.857369 116.874593 -3093.554722
## 1046 1047 1048 1049 1050
## -10050.114620 -288.208199 9796.606551 1351.823359 5841.944394
## 1051 1052 1053 1054 1055
## -3997.436209 1067.505163 -1821.722905 -9115.856737 1427.367808
## 1056 1057 1058 1059 1060
## -486.784030 -955.683164 8561.368241 -4104.762218 -3280.887792
## 1061 1062 1063 1064 1065
## -1935.678026 65.720851 8642.144017 -1401.555248 573.267751
## 1066 1067 1068 1069 1070
## 99.026839 -3845.569812 -6658.428127 2768.290275 -1263.605127
## 1071 1072 1073 1074 1075
## 6574.957829 -803.579873 -1663.130511 -581.961291 3512.331102
## 1076 1077 1078 1079 1080
## -1195.235393 -1952.003062 -51.071365 5990.861162 -759.294109
## 1081 1082 1083 1084 1085
## 12026.874709 -1259.134123 1275.767994 -2273.096688 91.463210
## 1086 1087 1088 1089 1090
## -10528.825650 -1089.026522 -1562.929187 -7171.340768 1726.859860
## 1091 1092 1093 1094 1095
## 6584.761888 -1020.162835 -1804.439750 6388.195188 -1977.706627
## 1096 1097 1098 1099 1100
## -659.404221 6822.323226 -2325.895399 11154.976524 -2225.413121
## 1101 1102 1103 1104 1105
## -11037.851636 -457.496166 -4556.243267 -2667.610068 13838.858615
## 1106 1107 1108 1109 1110
## -1154.154302 -1456.664148 97.977205 -1395.577393 1822.612204
## 1111 1112 1113 1114 1115
## -1850.748558 6996.904827 -9217.797749 59.317087 244.621179
## 1116 1117 1118 1119 1120
## -1771.688779 -1670.051609 6703.186430 6461.163798 2085.831364
## 1121 1122 1123 1124 1125
## 6657.957474 -4261.368146 7561.851314 12443.235993 8110.486739
## 1126 1127 1128 1129 1130
## 1857.188649 -1024.443726 -3294.369650 7054.106487 3438.217632
## 1131 1132 1133 1134 1135
## 1064.414713 -6731.770203 4475.348869 2706.897822 13432.652093
## 1136 1137 1138 1139 1140
## -430.349902 265.091170 1249.254536 -1927.632121 9441.035008
## 1141 1142 1143 1144 1145
## -3739.317212 -2162.212110 18302.674817 -2494.964544 -2089.466342
## 1146 1147 1148 1149 1150
## -2188.171324 15235.272344 -1411.110814 1926.604740 -3344.828648
## 1151 1152 1153 1154 1155
## -760.397431 -2744.103959 6550.847840 -3691.726099 -398.103086
## 1156 1157 1158 1159 1160
## 985.376804 8875.813747 11996.374872 -1114.796121 -5271.823657
## 1161 1162 1163 1164 1165
## -3230.877655 -5745.273592 10715.973980 -54.388213 -1164.121295
## 1166 1167 1168 1169 1170
## -684.873988 -4246.675532 684.072295 -3409.470012 -3143.522899
## 1171 1172 1173 1174 1175
## -8979.246988 -9523.634435 -4532.369857 -1755.682704 -2434.604374
## 1176 1177 1178 1179 1180
## 209.968219 -9686.138279 -648.179708 -2895.647942 -9467.194438
## 1181 1182 1183 1184 1185
## -5691.324496 -1172.730335 -1167.388890 -699.017382 -8593.553963
## 1186 1187 1188 1189 1190
## 172.741614 7392.230572 -873.636246 -10230.395943 10620.154208
## 1191 1192 1193 1194 1195
## -2411.710735 7278.245834 -1403.641296 -3772.411762 1083.884414
## 1196 1197 1198 1199 1200
## 15349.760643 6687.660558 -3106.338338 -1890.358192 168.555445
## 1201 1202 1203 1204 1205
## -82.302291 -5305.282912 -2064.199816 -2497.210141 -7954.636112
## 1206 1207 1208 1209 1210
## 2015.849270 21899.739522 6069.952253 -10260.406812 -2837.026547
## 1211 1212 1213 1214 1215
## -2398.746032 14132.995558 1866.410441 -1897.244860 -1764.539531
## 1216 1217 1218 1219 1220
## 7060.464466 -260.689733 -3885.368114 6684.670769 -1605.410890
## 1221 1222 1223 1224 1225
## 1031.950665 3.467556 123.129982 1830.469666 -198.569743
## 1226 1227 1228 1229 1230
## -4689.226076 2295.317376 -4083.293317 -2363.285665 -1168.817173
## 1231 1232 1233 1234 1235
## 22115.563048 -3314.153284 1128.611827 1574.547011 -459.971443
## 1236 1237 1238 1239 1240
## -2092.924617 2859.512561 47.841585 423.785842 -4975.133234
## 1241 1242 1243 1244 1245
## 8040.376660 8907.605145 2292.395591 -2277.497595 -1687.916470
## 1246 1247 1248 1249 1250
## 833.391407 298.078310 -1261.472424 -3522.575243 5726.866422
## 1251 1252 1253 1254 1255
## -9412.953088 2675.167847 -8982.891949 6612.786825 -746.839095
## 1256 1257 1258 1259 1260
## -4270.796131 -3139.488799 -125.309582 14140.115257 917.276190
## 1261 1262 1263 1264 1265
## 1303.120427 -3944.490618 -777.234247 -1425.870400 -2537.916949
## 1266 1267 1268 1269 1270
## -8315.188177 -869.440157 5773.774646 -1653.192489 -667.653547
## 1271 1272 1273 1274 1275
## -2942.165005 -2805.183436 5504.662314 -978.676253 -9557.158178
## 1276 1277 1278 1279 1280
## 1309.536982 -1281.834169 -1656.774499 -9959.900250 21.213050
## 1281 1282 1283 1284 1285
## -2377.181405 -9421.586201 -9596.881117 -459.665618 8128.788969
## 1286 1287 1288 1289 1290
## 151.777015 2614.530992 -136.401118 8073.585172 -3165.951600
## 1291 1292 1293 1294 1295
## 1593.989190 7291.901156 1353.556423 -249.718930 564.114544
## 1296 1297 1298 1299 1300
## 1919.800352 293.935364 179.004109 -1055.530708 914.024319
## 1301 1302 1303 1304 1305
## 29992.764417 7468.252170 2155.243374 6536.692415 -10604.126479
## 1306 1307 1308 1309 1310
## -128.815569 -10654.902651 -9612.764284 6285.656913 -2498.275824
## 1311 1312 1313 1314 1315
## -825.616399 -668.113352 -6193.852764 7846.346397 -9946.969973
## 1316 1317 1318 1319 1320
## 8640.702763 2762.610725 -8376.424851 7205.225543 -401.071245
## 1321 1322 1323 1324 1325
## -2078.253016 -8657.211658 -3009.754976 7589.194765 -572.320208
## 1326 1327 1328 1329 1330
## -1829.900386 -2948.695751 -1278.374252 19258.624204 -4045.288805
## 1331 1332 1333 1334 1335
## 1280.073545 6457.769439 -5634.704776 -1750.775386 -1305.950009
## 1336 1337 1338
## -2519.298986 761.360061 -7944.262968obtain estimate and standard errors
summary(model_Insurance)$coef## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11938.5386 987.81918 -12.0857530 5.579044e-32
## Insurance$age 256.8564 11.89885 21.5866552 7.783217e-89
## Insurance$sexmale -131.3144 332.94544 -0.3944020 6.933475e-01
## Insurance$bmi 339.1935 28.59947 11.8601306 6.498194e-31
## Insurance$children 475.5005 137.80409 3.4505546 5.769682e-04
## Insurance$smokeryes 23848.5345 413.15335 57.7232020 0.000000e+00
## Insurance$regionnorthwest -352.9639 476.27579 -0.7410914 4.587689e-01
## Insurance$regionsoutheast -1035.0220 478.69221 -2.1621870 3.078174e-02
## Insurance$regionsouthwest -960.0510 477.93302 -2.0087563 4.476493e-02cor(Insurance$children,Insurance$charges)## [1] 0.06799823model_Insurance_new <- lm(Insurance$charges ~ Insurance$age + Insurance$sex + Insurance$bmi + Insurance$smoker + Insurance$region , data=Insurance)
summary(model_Insurance_new)##
## Call:
## lm(formula = Insurance$charges ~ Insurance$age + Insurance$sex +
## Insurance$bmi + Insurance$smoker + Insurance$region, data = Insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11852.6 -3010.9 -987.8 1515.8 29467.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11556.96 985.63 -11.725 <2e-16 ***
## Insurance$age 258.54 11.94 21.658 <2e-16 ***
## Insurance$sexmale -111.57 334.26 -0.334 0.7386
## Insurance$bmi 340.46 28.71 11.857 <2e-16 ***
## Insurance$smokeryes 23862.91 414.82 57.526 <2e-16 ***
## Insurance$regionnorthwest -304.10 478.01 -0.636 0.5248
## Insurance$regionsoutheast -1039.20 480.65 -2.162 0.0308 *
## Insurance$regionsouthwest -916.44 479.72 -1.910 0.0563 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6087 on 1330 degrees of freedom
## Multiple R-squared: 0.7487, Adjusted R-squared: 0.7474
## F-statistic: 566 on 7 and 1330 DF, p-value: < 2.2e-16model_Insurance$fitted.values## 1 2 3 4 5 6
## 25293.71303 3448.60283 6706.98849 3754.83016 5592.49339 3719.82580
## 7 8 9 10 11 12
## 10659.96123 8047.91061 8502.97392 11884.63752 3245.20823 35717.46367
## 13 14 15 16 17 18
## 4546.04699 14917.07844 31969.00128 670.02628 12333.86680 1925.91107
## 19 20 21 22 23 24
## 15023.54800 30497.85010 15685.50287 6272.46945 3085.03613 31945.66754
## 25 26 27 28 29 30
## 7537.76584 13009.90834 12073.69251 13903.66345 -142.74199 32044.90100
## 31 32 33 34 35 36
## 28544.75732 1610.75150 4060.11663 13361.70005 30832.75074 -614.51985
## 37 38 39 40 41 42
## 16241.60522 703.58507 33682.37843 39763.83057 3248.55975 8364.64360
## 43 44 45 46 47 48
## 5289.36943 7928.28388 10733.30646 13749.11128 6750.79174 6694.23178
## 49 50 51 52 53 54
## 10758.23594 32405.59836 4768.64255 5460.55786 33120.65278 31668.91886
## 55 56 57 58 59 60
## 9140.71345 39809.28132 14704.96262 27063.72360 32724.60736 10056.40219
## 61 62 63 64 65 66
## 9681.80475 6635.78766 12869.56858 4172.95816 24298.87635 1784.37194
## 67 68 69 70 71 72
## 16983.11306 7252.81354 9576.10456 27495.99808 26205.13341 7937.21015
## 73 74 75 76 77 78
## 11672.63480 13125.87646 8516.67730 13753.96462 4987.50844 4340.65183
## 79 80 81 82 83 84
## 7213.89660 9421.12018 5487.41054 12606.01866 29630.45758 15924.55072
## 85 86 87 88 89 90
## 33208.56329 31701.08878 36767.11218 10711.42811 8933.11614 10987.03629
## 91 92 93 94 95 96
## 5815.17226 10207.68644 38477.84876 9311.91298 38956.50773 7454.37552
## 97 98 99 100 101 102
## 12845.31348 14006.54981 32929.54675 27125.60567 8351.03402 4271.70297
## 103 104 105 106 107 108
## 2899.68662 38118.38119 5637.84694 26544.24184 2090.27576 5679.04730
## 109 110 111 112 113 114
## 3821.02433 38827.90805 13330.00259 12253.55648 6920.93949 5218.47109
## 115 116 117 118 119 120
## 13636.90421 13040.76502 18433.62430 28276.37378 8828.28678 6090.13467
## 121 122 123 124 125 126
## 11806.85380 609.40593 2673.75489 34189.57643 12710.99371 4503.41015
## 127 128 129 130 131 132
## 25429.39041 13143.77593 26753.20814 9451.65140 12206.30871 11205.52265
## 133 134 135 136 137 138
## 13842.84319 1125.54257 2962.27204 2191.65550 3416.86354 1767.21812
## 139 140 141 142 143 144
## 13143.45522 4963.21452 5218.98137 6104.30808 29009.37101 6062.93582
## 145 146 147 148 149 150
## 30289.37010 9072.65704 35011.31593 13399.38290 14493.39572 1958.96140
## 151 152 153 154 155 156
## 5227.39408 9298.27551 10306.70717 30624.91378 7447.08140 12283.78796
## 157 158 159 160 161 162
## 31355.86862 24941.29115 30500.89354 10735.51245 31367.54474 27997.66703
## 163 164 165 166 167 168
## 14747.90042 6379.77972 7134.56217 11474.74111 7166.19799 8600.36140
## 169 170 171 172 173 174
## 3859.10043 2704.22246 17143.42775 9833.61899 -2032.91107 8370.81550
## 175 176 177 178 179 180
## 5183.45570 39919.48839 7730.17543 11220.28850 9670.49455 11265.03247
## 181 182 183 184 185 186
## 12174.08842 4634.17912 1774.39786 7968.27615 9557.65271 36662.52167
## 187 188 189 190 191 192
## 4804.37376 6714.68036 9030.05064 6999.83463 13271.69985 5235.10761
## 193 194 195 196 197 198
## 2047.37332 11590.49968 3196.96997 2833.38161 8244.35346 9236.90910
## 199 200 201 202 203 204
## 6930.61334 17840.74652 3480.27002 10763.24985 11272.39333 30048.19524
## 205 206 207 208 209 210
## 6349.50231 5524.84678 11004.35699 31128.88144 14069.71247 12664.84780
## 211 212 213 214 215 216
## 3776.10764 10226.03733 4359.75014 5301.69692 10092.02510 11167.59911
## 217 218 219 220 221 222
## 10344.43007 1665.61531 4328.87322 1063.67189 7740.84635 12953.03044
## 223 224 225 226 227 228
## 7063.15936 27502.83350 29889.35306 13940.60025 6996.80573 16139.70546
## 229 230 231 232 233 234
## 9798.45733 9589.26205 11249.07193 13047.21962 -1980.67539 11927.94139
## 235 236 237 238 239 240
## 6859.21355 29637.10765 716.49474 8830.30972 26166.34210 11582.00792
## 241 242 243 244 245 246
## 31206.91711 4521.26870 10794.39492 10644.38072 37501.17258 11630.01368
## 247 248 249 250 251 252
## 15347.52337 5223.15472 -584.98950 5682.61215 23217.75186 39004.92548
## 253 254 255 256 257 258
## 37168.71173 5609.28087 35416.33089 12218.70440 37216.74929 10405.59793
## 259 260 261 262 263 264
## 10860.26749 27133.04344 10546.75391 25591.55381 34810.89837 28840.88248
## 265 266 267 268 269 270
## 14976.03054 38350.39617 28209.44459 15630.65979 9247.77478 9756.36773
## 271 272 273 274 275 276
## 1956.15164 36212.86545 11626.41217 10561.02151 3343.37163 10107.25695
## 277 278 279 280 281 282
## 400.92800 994.65111 13783.61080 7914.62476 32197.87053 40834.80872
## 283 284 285 286 287 288
## 5488.34121 13652.23329 11040.77652 8215.34751 17132.88405 12784.10009
## 289 290 291 292 293 294
## 40010.46863 10632.86416 5622.44965 5908.17580 33562.93934 2452.83446
## 295 296 297 298 299 300
## 3908.39108 351.61891 25094.55998 31910.31433 32479.62914 10309.00993
## 301 302 303 304 305 306
## 7948.25704 34619.04827 15084.54265 6362.80230 15582.57485 7287.42419
## 307 308 309 310 311 312
## 4572.20937 6512.94830 14653.79527 10404.34465 8835.45957 359.75943
## 313 314 315 316 317 318
## 35415.77288 11644.56354 28535.74094 12564.85973 11343.72597 12917.45554
## 319 320 321 322 323 324
## 8387.18006 9288.83848 5357.21827 6695.42274 29998.90497 16459.23512
## 325 326 327 328 329 330
## 3644.99223 10248.09445 2309.74150 36309.03185 39328.99081 12775.02615
## 331 332 333 334 335 336
## 40395.28783 34062.58093 13946.00304 12209.10073 12173.27584 15111.07679
## 337 338 339 340 341 342
## 11037.34566 13322.55721 36052.94833 8719.77467 2627.70221 13684.86450
## 343 344 345 346 347 348
## 12817.62222 16582.54460 15580.75535 7110.85745 8448.55171 11531.44554
## 349 350 351 352 353 354
## 6897.43674 1898.90364 10211.81387 8627.58047 4202.75967 8361.27997
## 355 356 357 358 359 360
## 4634.17912 8147.22761 15024.21955 11194.07409 7018.41876 -1298.31438
## 361 362 363 364 365 366
## 12297.51599 6780.96929 23190.71362 1925.60156 796.36857 11563.29775
## 367 368 369 370 371 372
## 14827.86735 7922.21386 10689.14218 4291.54404 10530.32497 10242.54399
## 373 374 375 376 377 378
## 10570.88773 29607.36150 3337.56987 27067.29485 31796.42041 30526.82918
## 379 380 381 382 383 384
## 15788.61658 13966.74547 25886.33703 36313.93212 12215.60837 11668.05708
## 385 386 387 388 389 390
## 7690.87476 3518.62158 15169.61219 9974.64383 2055.92668 5546.58585
## 391 392 393 394 395 396
## 14245.02095 5284.77919 11400.69068 11625.32365 11783.80328 6127.26140
## 397 398 399 400 401 402
## 11240.99003 2810.88935 13043.25614 4596.86784 7188.46956 15561.34705
## 403 404 405 406 407 408
## 15328.81629 12545.59463 1852.18946 15387.23760 3748.49187 7654.12505
## 409 410 411 412 413 414
## 5245.93379 5776.00825 -1613.44457 30550.75556 25371.69366 3875.73115
## 415 416 417 418 419 420
## 4511.41812 10635.61777 11818.15212 28813.54681 17092.24777 36890.42165
## 421 422 423 424 425 426
## 38674.34033 38575.37431 33645.50170 4727.48362 10493.84438 9076.95646
## 427 428 429 430 431 432
## 7545.61288 2577.45284 -365.51671 6381.60167 3077.67009 2971.91237
## 433 434 435 436 437 438
## 6882.36678 12858.19192 5714.46744 14963.70305 4343.59510 7189.26086
## 439 440 441 442 443 444
## 18617.76639 4597.65944 7231.38706 30789.18530 6107.24980 15043.80965
## 445 446 447 448 449 450
## 35339.94324 9887.24961 13395.22218 10792.76535 7415.79076 9528.43627
## 451 452 453 454 455 456
## 8929.62223 3943.11232 1071.77535 2800.22756 11848.20078 14810.45604
## 457 458 459 460 461 462
## 12327.83055 12693.01399 14786.11258 9920.57908 13463.55849 31782.40103
## 463 464 465 466 467 468
## 17859.13099 11111.08503 996.64906 28682.47525 12723.14425 14514.97696
## 469 470 471 472 473 474
## 3978.12463 296.52456 4911.69666 2899.68662 2089.64605 11444.11570
## 475 476 477 478 479 480
## 34629.13097 37172.02243 27610.24750 6082.35876 4788.38718 3846.95997
## 481 482 483 484 485 486
## 19202.80448 13155.23382 2283.56849 14074.72637 12360.03809 6561.05299
## 487 488 489 490 491 492
## 10287.72565 1585.21889 35086.35627 12235.33841 3141.14575 11201.64870
## 493 494 495 496 497 498
## 1191.84759 17359.32946 26831.88796 2540.94727 4019.92396 9214.48515
## 499 500 501 502 503 504
## 7412.97899 16322.88767 29935.71964 7804.17582 32191.51414 25884.53223
## 505 506 507 508 509 510
## 7075.34793 8979.96772 4337.23824 1978.01218 2797.43246 11477.07465
## 511 512 513 514 515 516
## 13681.10515 5247.49818 8634.53827 2161.84776 30910.70365 13976.97081
## 517 518 519 520 521 522
## 4484.67346 10430.42449 7081.88038 6365.29187 10184.61194 10244.97717
## 523 524 525 526 527 528
## 12664.88138 9584.74978 30849.90024 3141.72793 3915.69706 9427.77606
## 529 530 531 532 533 534
## 13593.74173 1189.42674 40150.19240 14749.16356 13074.69648 8674.22115
## 535 536 537 538 539 540
## 17064.48258 7672.08554 10198.79705 10111.44604 8831.70851 11142.22647
## 541 542 543 544 545 546
## 10150.37929 3897.52741 15521.11195 40826.37859 11694.46044 33727.43891
## 547 548 549 550 551 552
## 7141.44496 17762.98884 4182.10704 37590.53463 13599.20465 5058.70927
## 553 554 555 556 557 558
## 10153.92984 12778.63723 8500.03971 3185.87923 11563.66892 7232.04905
## 559 560 561 562 563 564
## 33541.69878 4508.99727 7241.80023 13016.54652 4250.61793 15399.13411
## 565 566 567 568 569 570
## 3495.74854 2932.47259 11703.92191 9435.22246 12885.14560 38465.20616
## 571 572 573 574 575 576
## 4934.48686 4773.87815 10309.15276 16964.72653 15285.91410 11822.05211
## 577 578 579 580 581 582
## 1649.91707 33269.61805 11045.76925 2442.04463 12196.03774 2833.38161
## 583 584 585 586 587 588
## 13273.08245 3743.26838 -1128.32874 5567.19849 1614.21164 31012.68283
## 589 590 591 592 593 594
## 15910.13585 7672.32841 11835.68903 6762.94817 3542.34537 25190.85688
## 595 596 597 598 599 600
## 11082.16391 11791.65341 8764.83028 8548.26029 10023.62691 14744.26329
## 601 602 603 604 605 606
## 4932.66936 11407.24205 10066.96055 18137.25194 26039.86944 11692.61012
## 607 608 609 610 611 612
## 3535.77814 34735.17801 5224.56540 32296.83483 9536.30022 9616.88510
## 613 614 615 616 617 618
## 3930.83472 4665.75466 3356.95039 35847.37924 12144.65397 33038.94539
## 619 620 621 622 623 624
## 26985.93986 13812.58695 5801.96164 33790.81461 7387.69281 27776.94842
## 625 626 627 628 629 630
## 12495.39153 3986.53735 8399.38433 10249.03923 14757.11576 36070.29660
## 631 632 633 634 635 636
## 13303.86698 3073.01672 6526.81700 6856.78962 14011.25071 17322.75162
## 637 638 639 640 641 642
## 1377.90032 10924.00947 30754.17847 14598.33459 12205.66087 33242.75282
## 643 644 645 646 647 648
## 15102.13055 6900.89841 10867.87011 12126.12812 6963.73381 7689.16817
## 649 650 651 652 653 654
## 2220.57484 14140.64207 15040.17834 14547.38737 9914.63651 11848.69869
## 655 656 657 658 659 660
## 14120.57374 33764.09971 8636.97858 6709.26473 13046.50381 14367.95926
## 661 662 663 664 665 666
## 13607.98309 10276.61103 7454.52678 2935.79101 35111.83798 35649.18665
## 667 668 669 670 671 672
## 9766.41001 33899.35270 38563.05388 7887.55087 6735.65456 6079.56366
## 673 674 675 676 677 678
## 6215.99928 8079.33076 38014.85520 6385.97910 16422.52524 38897.31527
## 679 680 681 682 683 684
## 15025.43713 9107.96414 -1127.13953 -1264.00612 33760.55837 9439.75464
## 685 686 687 688 689 690
## 2328.24950 11452.63395 8530.54394 11310.35420 7823.72178 28713.37383
## 691 692 693 694 695 696
## 2604.46336 11796.64821 4177.98269 1765.35677 6315.96468 8017.25162
## 697 698 699 700 701 702
## 13581.79775 33876.43652 13400.43813 7205.26350 4248.09851 16081.49013
## 703 704 705 706 707 708
## 14574.86422 5875.21317 10277.71723 7688.13578 36884.35074 11321.10626
## 709 710 711 712 713 714
## 7794.21436 6717.51652 3933.64947 8804.87199 10112.47290 6794.43318
## 715 716 717 718 719 720
## 931.73495 12184.16803 8439.12333 11713.24965 14197.39654 13948.79506
## 721 722 723 724 725 726
## 14952.74123 14424.46480 15581.02510 3857.81503 10563.44235 33252.67049
## 727 728 729 730 731 732
## 8218.58421 27213.48432 6347.58808 10271.15018 29443.23767 8317.72321
## 733 734 735 736 737 738
## 4902.18748 10114.17640 14570.54673 12563.71573 33400.29564 2638.24718
## 739 740 741 742 743 744
## 29875.48763 31259.83353 8592.19868 27566.27025 36960.26103 4018.31604
## 745 746 747 748 749 750
## 9378.09990 11241.62655 5812.43640 -163.39255 11860.12388 5241.75892
## 751 752 753 754 755 756
## 29333.36614 2799.29689 16873.11759 9647.54276 7403.77755 6220.69811
## 757 758 759 760 761 762
## 7238.97155 32386.97630 9758.35024 28314.08803 6392.61190 5292.90229
## 763 764 765 766 767 768
## 28962.53339 3694.47418 9110.19357 13144.14128 10473.79374 8201.48794
## 769 770 771 772 773 774
## 17006.19710 5025.83252 16309.71889 10722.26342 11736.91812 26233.20970
## 775 776 777 778 779 780
## 10659.71082 12726.61844 9758.38691 12990.27835 8952.71832 10986.47679
## 781 782 783 784 785 786
## 28227.14309 5472.95804 12671.08807 33630.00247 5389.28730 6913.54307
## 787 788 789 790 791 792
## 15876.42229 5473.83727 4442.42353 13100.20136 11222.12348 1212.10609
## 793 794 795 796 797 798
## 1574.80543 31446.18942 9503.95140 28027.85265 10550.95120 4008.48667
## 799 800 801 802 803 804
## 13226.38219 28665.24292 7169.99134 15666.03446 403.59404 29825.91974
## 805 806 807 808 809 810
## 1794.83958 11415.24693 12507.64502 4994.76879 1741.83005 3591.81526
## 811 812 813 814 815 816
## 10790.46266 12176.22569 8842.82360 3710.06663 8771.38540 2834.59248
## 817 818 819 820 821 822
## 2090.01140 6888.37095 33319.17406 32084.83511 10434.95187 248.99666
## 823 824 825 826 827 828
## 2208.94593 9390.47683 11237.74911 16246.10074 36861.57628 31006.90738
## 829 830 831 832 833 834
## 34176.66820 5481.45842 14379.34960 5720.08506 3939.54439 14139.71448
## 835 836 837 838 839 840
## 8771.03500 10834.88144 6901.51855 12047.98384 5961.60924 13496.73709
## 841 842 843 844 845 846
## 2912.99588 11462.75017 28852.43252 35627.14286 11887.23812 37293.18264
## 847 848 849 850 851 852
## 12277.00107 10366.88786 2211.09418 12821.34800 31854.05551 15152.37031
## 853 854 855 856 857 858
## 35776.93159 10681.69372 34010.52678 2278.66371 34434.77409 26031.86456
## 859 860 861 862 863 864
## 4855.55374 11142.24421 37550.23950 7785.87017 14161.45047 4042.97614
## 865 866 867 868 869 870
## 8685.28377 8337.23553 4167.06325 16909.16264 11622.00571 3191.72180
## 871 872 873 874 875 876
## 12091.71672 4179.62810 6115.44108 8700.14273 8069.70517 3154.31355
## 877 878 879 880 881 882
## 9355.01484 9091.51646 7745.47854 7562.30345 5851.36965 3240.71271
## 883 884 885 886 887 888
## 963.49192 39003.28904 4955.36340 29251.43000 36247.62402 7137.91369
## 889 890 891 892 893 894
## 6019.07725 14100.57165 37115.05463 8025.44814 9952.90476 36975.10230
## 895 896 897 898 899 900
## 14746.74272 17694.15990 30704.95299 1601.04312 5305.78216 225.70883
## 901 902 903 904 905 906
## 8153.04895 40034.83683 5283.02338 11980.36505 14418.48181 5647.75151
## 907 908 909 910 911 912
## 7344.38890 9773.13572 18078.44737 27513.50721 3306.09014 27164.70424
## 913 914 915 916 917 918
## 13344.29320 8206.41046 5350.29882 4720.17732 31721.07123 31103.05159
## 919 920 921 922 923 924
## 12334.90333 8095.72031 11506.34063 14287.72695 7721.13508 8458.51269
## 925 926 927 928 929 930
## 5884.20736 12615.46758 869.80904 9035.51149 16234.34888 9505.54406
## 931 932 933 934 935 936
## 9831.56212 8618.09597 9914.18212 10633.47521 8676.74199 11583.75521
## 937 938 939 940 941 942
## 10268.74501 8320.35941 1349.62507 10507.93471 -608.78058 15978.18382
## 943 944 945 946 947 948
## 6315.36470 126.61785 16364.21348 14103.99236 10852.18961 33358.28331
## 949 950 951 952 953 954
## 8966.64136 28740.58664 8790.07113 39345.73379 5524.47870 33314.95352
## 955 956 957 958 959 960
## 30075.78402 8727.92197 35536.56151 3304.22879 35157.20845 12820.01258
## 961 962 963 964 965 966
## 6501.41743 3335.35510 15623.49970 9582.34260 14355.16191 5627.71155
## 967 968 969 970 971 972
## 33886.69446 7958.00517 3007.66702 11062.45918 10847.44629 4785.97518
## 973 974 975 976 977 978
## 222.91681 5719.01600 5587.62231 26993.34995 12842.84710 3936.37990
## 979 980 981 982 983 984
## 14612.54110 6421.93620 10911.75598 3913.52312 28992.78963 5848.01123
## 985 986 987 988 989 990
## 5659.58770 7629.78159 10263.31882 9119.53696 8424.79605 25034.79809
## 991 992 993 994 995 996
## 971.20653 8214.45369 11613.74228 6720.16589 26717.78800 7400.08844
## 997 998 999 1000 1001 1002
## 10111.80659 15707.66835 10273.55312 6074.54222 27880.46687 28074.80901
## 1003 1004 1005 1006 1007 1008
## 1885.83964 9339.32722 6987.01855 6739.62676 5997.92648 34494.81121
## 1009 1010 1011 1012 1013 1014
## 3777.30541 10914.54799 7164.12610 29567.44803 15901.99687 11337.73718
## 1015 1016 1017 1018 1019 1020
## 6223.69115 11367.57329 1410.12369 6331.09280 15153.45574 5138.32408
## 1021 1022 1023 1024 1025 1026
## 12619.92784 28474.09624 35529.50848 -95.96876 14946.43581 4231.48733
## 1027 1028 1029 1030 1031 1032
## 25610.69455 -167.11524 11558.85224 4380.80237 31871.54597 36941.68287
## 1033 1034 1035 1036 1037 1038
## 5240.82516 23716.80278 16263.66542 10199.60454 29919.40173 33934.77284
## 1039 1040 1041 1042 1043 1044
## 3376.89376 2656.56447 30052.90094 383.84229 27323.95978 3044.57941
## 1045 1046 1047 1048 1049 1050
## 14487.62027 31930.93462 7613.25640 34704.79165 2242.34749 33885.66961
## 1051 1052 1053 1054 1055 1056
## 12020.57166 13327.05274 11109.74961 34425.34574 1926.10249 11081.28558
## 1057 1058 1059 1060 1061 1062
## 9233.20616 9367.93513 6585.74132 7743.60959 3917.25993 11488.50275
## 1063 1064 1065 1066 1067 1068
## 40328.10358 7949.75030 5135.59925 6946.47216 12823.75491 12415.84158
## 1069 1070 1071 1072 1073 1074
## 11581.56413 12192.45413 33296.74647 14778.03542 3572.65796 12678.61249
## 1075 1076 1077 1078 1079 1080
## 9691.95455 5758.07749 10503.35006 2153.33607 28681.28604 15920.82851
## 1081 1082 1083 1084 1085 1086
## -142.82613 5713.53677 4580.13451 6349.59369 14928.29684 29552.08565
## 1087 1088 1089 1090 1091 1092
## 11885.37677 12916.15679 16920.25137 8850.22714 35091.31921 12306.70153
## 1093 1094 1095 1096 1097 1098
## 5395.91975 27519.35281 13277.04963 5220.59272 37818.87417 4000.52770
## 1099 1100 1101 1102 1103 1104
## 11890.58964 5452.53422 27814.15569 11710.91717 8027.65287 14030.89327
## 1105 1106 1107 1108 1109 1110
## 6581.74603 11493.08590 10444.82290 10395.96860 4299.66539 6782.74930
## 1111 1112 1113 1114 1115 1116
## 13363.15356 34952.33927 33398.73125 5252.85276 2151.47472 12579.17508
## 1117 1118 1119 1120 1121 1122
## 10892.45421 29421.38727 31821.58570 3607.59914 27508.31553 12608.53245
## 1123 1124 1125 1126 1127 1128
## 39099.59109 6460.25542 32793.71276 12397.41955 11239.07973 9130.89005
## 1129 1130 1131 1132 1133 1134
## 7304.25788 -1709.32063 7517.88759 10425.19820 16233.67147 7284.13983
## 1135 1136 1137 1138 1139 1140
## 6240.68364 11515.93670 7358.42683 1927.03316 5631.98662 27457.69807
## 1141 1142 1143 1144 1145 1146
## 12787.34451 10116.72911 8815.31896 8833.04014 11719.86334 13477.28057
## 1147 1148 1149 1150 1151 1152
## 37355.55705 3672.67961 8865.35526 9324.55965 2964.13338 14979.94316
## 1153 1154 1155 1156 1157 1158
## 34390.43756 9322.18395 11413.27779 6242.83885 30846.93245 2429.69898
## 1159 1160 1161 1162 1163 1164
## 3574.51622 9261.66466 10958.13085 10869.46229 8247.19794 2255.21906
## 1165 1166 1167 1168 1169 1170
## 8317.67520 5912.86274 15229.17683 3845.40471 8080.11001 9255.87585
## 1171 1172 1173 1174 1175 1176
## 26157.92939 32002.23444 15625.99276 8213.52610 6868.52027 1944.39278
## 1177 1178 1179 1180 1181 1182
## 33573.80098 7145.06571 5795.13729 28817.56334 13342.09825 4023.41408
## 1183 1184 1185 1186 1187 1188
## 3800.38089 10146.39978 26921.79206 8431.08179 30073.11318 14718.43345
## 1189 1190 1191 1192 1193 1194
## 32001.73824 2506.52324 7739.11099 6447.22601 14422.80235 12443.60301
## 1195 1196 1197 1198 1199 1200
## 3050.19804 3488.94302 26619.89024 8806.17584 8283.96164 4766.14955
## 1201 1202 1203 1204 1205 1206
## 6281.05409 14038.51216 4119.52472 12461.27014 26178.08731 3100.65113
## 1207 1208 1209 1210 1211 1212
## 15010.86851 32345.52175 30557.27026 15184.19855 7772.11028 9430.02062
## 1213 1214 1215 1216 1217 1218
## -163.95514 12704.08386 5720.61098 5829.59318 5676.35093 7943.48421
## 1219 1220 1221 1222 1223 1224
## 34976.93123 9142.57479 3686.25288 6590.04074 8319.53702 24295.20510
## 1225 1226 1227 1228 1229 1230
## 7057.04934 9484.88288 4345.22747 11245.30552 12957.51136 13107.07312
## 1231 1232 1233 1234 1235 1236
## 37905.83592 23481.48931 11351.09712 9770.97199 8975.73014 4792.49297
## 1237 1238 1239 1240 1241 1242
## 11590.34184 12176.50927 6561.72111 8213.56893 39229.47734 40670.05726
## 1243 1244 1245 1246 1247 1248
## 2003.87561 5449.11249 2823.85717 4781.97759 8803.71969 7320.64542
## 1249 1250 1251 1252 1253 1254
## 5156.53704 31880.66128 28061.37479 -1433.60285 25215.73895 9216.03491
## 1255 1256 1257 1258 1259 1260
## 5161.99789 10744.80913 14576.22695 11431.24413 15923.46529 9280.49601
## 1261 1262 1263 1264 1265 1266
## 3241.11437 7221.65162 7547.42675 8763.61840 12908.82950 35241.70258
## 1267 1268 1269 1270 1271 1272
## 11573.91016 28480.27870 3533.67949 9282.95355 6234.69486 5826.99259
## 1273 1274 1275 1276 1277 1278
## 8973.66784 5725.72915 26600.49958 9649.79302 4023.78217 6013.81815
## 1279 1280 1281 1282 1283 1284
## 32421.94400 4167.90005 10660.86211 33957.28475 23880.34052 2180.01932
## 1285 1286 1287 1288 1289 1290
## 39275.09103 8382.89478 1118.09411 5608.85012 30270.98083 10313.42440
## 1291 1292 1293 1294 1295 1296
## 5539.91331 27536.75284 161.78848 9551.61248 11367.01071 44.97965
## 1297 1298 1299 1300 1301 1302
## 1414.99039 4161.43679 6317.00016 1796.80423 32600.10867 39249.91108
## 1303 1304 1305 1306 1307 1308
## 1053.54363 31293.03178 31863.50443 2593.43437 26770.20715 31085.24308
## 1309 1310 1311 1312 1313 1314
## 27614.99609 9374.23682 7766.52625 5239.52640 10730.11176 28551.22960
## 1315 1316 1317 1318 1319 1320
## 28712.84542 2631.62863 -1030.93372 9539.88755 12291.49363 7602.77210
## 1321 1322 1323 1324 1325 1326
## 7503.27637 36758.54471 15991.10068 36307.18154 4812.21286 14973.23704
## 1327 1328 1329 1330 1331 1332
## 9998.71705 10656.27895 3137.12004 14370.49480 11349.09206 4338.16789
## 1333 1334 1335 1336 1337 1338
## 17046.38978 12351.32369 3511.93081 4149.13249 1246.58494 37085.62327observations_for_pred=data.frame(age = 33, sex= "female",bmi=22.705,chilrdren="0",smoker="no",region="northwest")
observations_for_pred## age sex bmi chilrdren smoker region
## 1 33 female 22.705 0 no northwestpredict(model_Insurance,observations_for_pred,interval="prediction", level=0.95, type="response")## Warning: 'newdata' had 1 row but variables found have 1338 rows## fit lwr upr
## 1 25293.71303 1.334593e+04 37241.493
## 2 3448.60283 -8.476283e+03 15373.488
## 3 6706.98849 -5.222575e+03 18636.552
## 4 3754.83016 -8.171799e+03 15681.459
## 5 5592.49339 -6.328943e+03 17513.930
## 6 3719.82580 -8.205887e+03 15645.539
## 7 10659.96123 -1.255782e+03 22575.704
## 8 8047.91061 -3.878934e+03 19974.756
## 9 8502.97392 -3.416500e+03 20422.448
## 10 11884.63752 -4.687777e+01 23816.153
## 11 3245.20823 -8.679862e+03 15170.279
## 12 35717.46367 2.376323e+04 47671.695
## 13 4546.04699 -7.382381e+03 16474.474
## 14 14917.07844 2.987898e+03 26846.259
## 15 31969.00128 2.002435e+04 43913.648
## 16 670.02628 -1.125923e+04 12599.286
## 17 12333.86680 4.142316e+02 24253.502
## 18 1925.91107 -1.000267e+04 13854.495
## 19 15023.54800 3.086631e+03 26960.465
## 20 30497.85010 1.855640e+04 42439.298
## 21 15685.50287 3.751601e+03 27619.405
## 22 6272.46945 -5.646255e+03 18191.194
## 23 3085.03613 -8.842962e+03 15013.034
## 24 31945.66754 2.000972e+04 43881.615
## 25 7537.76584 -4.381124e+03 19456.656
## 26 13009.90834 1.069809e+03 24950.007
## 27 12073.69251 1.353518e+02 24012.033
## 28 13903.66345 1.979507e+03 25827.820
## 29 -142.74199 -1.208187e+04 11796.384
## 30 32044.90100 2.010449e+04 43985.313
## 31 28544.75732 1.659801e+04 40491.500
## 32 1610.75150 -1.031888e+04 13540.387
## 33 4060.11663 -7.913452e+03 16033.685
## 34 13361.70005 1.426993e+03 25296.407
## 35 30832.75074 1.889274e+04 42772.763
## 36 -614.51985 -1.255208e+04 11323.039
## 37 16241.60522 4.303856e+03 28179.354
## 38 703.58507 -1.123202e+04 12639.189
## 39 33682.37843 2.174339e+04 45621.366
## 40 39763.83057 2.780731e+04 51720.353
## 41 3248.55975 -8.676160e+03 15173.279
## 42 8364.64360 -3.556772e+03 20286.059
## 43 5289.36943 -6.644626e+03 17223.364
## 44 7928.28388 -3.990290e+03 19846.858
## 45 10733.30646 -1.191011e+03 22657.624
## 46 13749.11128 1.818542e+03 25679.681
## 47 6750.79174 -5.194346e+03 18695.930
## 48 6694.23178 -5.233387e+03 18621.851
## 49 10758.23594 -1.181786e+03 22698.258
## 50 32405.59836 2.047794e+04 44333.258
## 51 4768.64255 -7.168666e+03 16705.951
## 52 5460.55786 -6.469531e+03 17390.646
## 53 33120.65278 2.118496e+04 45056.342
## 54 31668.91886 1.973798e+04 43599.854
## 55 9140.71345 -2.785679e+03 21067.106
## 56 39809.28132 2.786062e+04 51757.943
## 57 14704.96262 2.778372e+03 26631.554
## 58 27063.72360 1.512453e+04 39002.919
## 59 32724.60736 2.077455e+04 44674.660
## 60 10056.40219 -1.872043e+03 21984.847
## 61 9681.80475 -2.247258e+03 21610.867
## 62 6635.78766 -5.310831e+03 18582.407
## 63 12869.56858 9.342868e+02 24804.850
## 64 4172.95816 -7.746483e+03 16092.399
## 65 24298.87635 1.234869e+04 36249.059
## 66 1784.37194 -1.014444e+04 13713.184
## 67 16983.11306 5.047688e+03 28918.538
## 68 7252.81354 -4.665006e+03 19170.633
## 69 9576.10456 -2.343126e+03 21495.335
## 70 27495.99808 1.554420e+04 39447.799
## 71 26205.13341 1.426130e+04 38148.963
## 72 7937.21015 -4.029171e+03 19903.592
## 73 11672.63480 -2.584708e+02 23603.740
## 74 13125.87646 1.201809e+03 25049.944
## 75 8516.67730 -3.404015e+03 20437.369
## 76 13753.96462 1.823953e+03 25683.976
## 77 4987.50844 -6.930924e+03 16905.941
## 78 4340.65183 -7.585527e+03 16266.831
## 79 7213.89660 -4.730224e+03 19158.017
## 80 9421.12018 -2.500493e+03 21342.734
## 81 5487.41054 -6.431333e+03 17406.154
## 82 12606.01866 6.750569e+02 24536.980
## 83 29630.45758 1.769428e+04 41566.631
## 84 15924.55072 3.964669e+03 27884.432
## 85 33208.56329 2.126819e+04 45148.936
## 86 31701.08878 1.975984e+04 43642.334
## 87 36767.11218 2.481988e+04 48714.341
## 88 10711.42811 -1.216350e+03 22639.207
## 89 8933.11614 -2.987702e+03 20853.935
## 90 10987.03629 -9.390892e+02 22913.162
## 91 5815.17226 -6.117039e+03 17747.384
## 92 10207.68644 -1.715108e+03 22130.480
## 93 38477.84876 2.652685e+04 50428.847
## 94 9311.91298 -2.610880e+03 21234.706
## 95 38956.50773 2.700570e+04 50907.314
## 96 7454.37552 -4.466658e+03 19375.409
## 97 12845.31348 9.148310e+02 24775.796
## 98 14006.54981 2.079941e+03 25933.158
## 99 32929.54675 2.097405e+04 44885.043
## 100 27125.60567 1.517238e+04 39078.831
## 101 8351.03402 -3.568729e+03 20270.797
## 102 4271.70297 -7.651655e+03 16195.061
## 103 2899.68662 -9.030319e+03 14829.693
## 104 38118.38119 2.616388e+04 50072.885
## 105 5637.84694 -6.279524e+03 17555.218
## 106 26544.24184 1.460432e+04 38484.164
## 107 2090.27576 -9.835331e+03 14015.882
## 108 5679.04730 -6.244034e+03 17602.129
## 109 3821.02433 -8.102858e+03 15744.906
## 110 38827.90805 2.688259e+04 50773.231
## 111 13330.00259 1.406970e+03 25253.035
## 112 12253.55648 3.303289e+02 24176.784
## 113 6920.93949 -4.999453e+03 18841.332
## 114 5218.47109 -6.716137e+03 17153.079
## 115 13636.90421 1.705120e+03 25568.688
## 116 13040.76502 1.109993e+03 24971.537
## 117 18433.62430 6.478747e+03 30388.501
## 118 28276.37378 1.634139e+04 40211.360
## 119 8828.28678 -3.097338e+03 20753.911
## 120 6090.13467 -5.832066e+03 18012.336
## 121 11806.85380 -1.165764e+02 23730.284
## 122 609.40593 -1.132308e+04 12541.892
## 123 2673.75489 -9.253988e+03 14601.498
## 124 34189.57643 2.225729e+04 46121.861
## 125 12710.99371 7.810750e+02 24640.912
## 126 4503.41015 -7.419758e+03 16426.579
## 127 25429.39041 1.348171e+04 37377.067
## 128 13143.77593 1.215072e+03 25072.480
## 129 26753.20814 1.479984e+04 38706.579
## 130 9451.65140 -2.468733e+03 21372.036
## 131 12206.30871 2.767960e+02 24135.821
## 132 11205.52265 -7.326190e+02 23143.664
## 133 13842.84319 1.918059e+03 25767.628
## 134 1125.54257 -1.080461e+04 13055.698
## 135 2962.27204 -8.965329e+03 14889.873
## 136 2191.65550 -9.735056e+03 14118.367
## 137 3416.86354 -8.514643e+03 15348.370
## 138 1767.21812 -1.016095e+04 13695.382
## 139 13143.45522 1.211984e+03 25074.926
## 140 4963.21452 -6.968707e+03 16895.136
## 141 5218.98137 -6.707266e+03 17145.229
## 142 6104.30808 -5.817952e+03 18026.568
## 143 29009.37101 1.707091e+04 40947.832
## 144 6062.93582 -5.858081e+03 17983.952
## 145 30289.37010 1.834510e+04 42233.636
## 146 9072.65704 -2.861862e+03 21007.176
## 147 35011.31593 2.306783e+04 46954.799
## 148 13399.38290 1.479454e+03 25319.312
## 149 14493.39572 2.565655e+03 26421.137
## 150 1958.96140 -9.966884e+03 13884.807
## 151 5227.39408 -6.692915e+03 17147.703
## 152 9298.27551 -2.624680e+03 21221.231
## 153 10306.70717 -1.632386e+03 22245.800
## 154 30624.91378 1.868355e+04 42566.273
## 155 7447.08140 -4.470576e+03 19364.739
## 156 12283.78796 3.498354e+02 24217.741
## 157 31355.86862 1.941103e+04 43300.708
## 158 24941.29115 1.299655e+04 36886.031
## 159 30500.89354 1.856804e+04 42433.745
## 160 10735.51245 -1.197976e+03 22669.000
## 161 31367.54474 1.942762e+04 43307.473
## 162 27997.66703 1.605164e+04 39943.690
## 163 14747.90042 2.818261e+03 26677.540
## 164 6379.77972 -5.539859e+03 18299.418
## 165 7134.56217 -4.785981e+03 19055.106
## 166 11474.74111 -4.696144e+02 23419.097
## 167 7166.19799 -4.813327e+03 19145.723
## 168 8600.36140 -3.330223e+03 20530.946
## 169 3859.10043 -8.067990e+03 15786.191
## 170 2704.22246 -9.241234e+03 14649.679
## 171 17143.42775 5.205467e+03 29081.388
## 172 9833.61899 -2.089201e+03 21756.439
## 173 -2032.91107 -1.398293e+04 9917.105
## 174 8370.81550 -3.548304e+03 20289.935
## 175 5183.45570 -6.744630e+03 17111.541
## 176 39919.48839 2.796141e+04 51877.565
## 177 7730.17543 -4.188723e+03 19649.074
## 178 11220.28850 -7.016778e+02 23142.255
## 179 9670.49455 -2.248755e+03 21589.744
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## 182 4634.17912 -7.298754e+03 16567.113
## 183 1774.39786 -1.017136e+04 13720.160
## 184 7968.27615 -3.952690e+03 19889.242
## 185 9557.65271 -2.361858e+03 21477.163
## 186 36662.52167 2.469892e+04 48626.127
## 187 4804.37376 -7.118593e+03 16727.340
## 188 6714.68036 -5.214593e+03 18643.954
## 189 9030.05064 -2.886122e+03 20946.224
## 190 6999.83463 -4.922545e+03 18922.214
## 191 13271.69985 1.340504e+03 25202.896
## 192 5235.10761 -6.686668e+03 17156.883
## 193 2047.37332 -9.881830e+03 13976.577
## 194 11590.49968 -3.325629e+02 23513.562
## 195 3196.96997 -8.731174e+03 15125.114
## 196 2833.38161 -9.096257e+03 14763.020
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## 199 6930.61334 -5.009249e+03 18870.476
## 200 17840.74652 5.896395e+03 29785.098
## 201 3480.27002 -8.450539e+03 15411.079
## 202 10763.24985 -1.153413e+03 22679.913
## 203 11272.39333 -6.614883e+02 23206.275
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## 205 6349.50231 -5.582349e+03 18281.354
## 206 5524.84678 -6.394289e+03 17443.982
## 207 11004.35699 -9.324426e+02 22941.157
## 208 31128.88144 1.919467e+04 43063.093
## 209 14069.71247 2.137550e+03 26001.875
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## 213 4359.75014 -7.564150e+03 16283.650
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## 221 7740.84635 -4.177363e+03 19659.056
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## 223 7063.15936 -4.864989e+03 18991.308
## 224 27502.83350 1.555468e+04 39450.982
## 225 29889.35306 1.794776e+04 41830.945
## 226 13940.60025 2.008975e+03 25872.226
## 227 6996.80573 -4.927251e+03 18920.863
## 228 16139.70546 4.205253e+03 28074.158
## 229 9798.45733 -2.118503e+03 21715.418
## 230 9589.26205 -2.333887e+03 21512.411
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## 232 13047.21962 1.107307e+03 24987.132
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## 235 6859.21355 -5.062633e+03 18781.060
## 236 29637.10765 1.768869e+04 41585.526
## 237 716.49474 -1.121504e+04 12648.025
## 238 8830.30972 -3.092219e+03 20752.838
## 239 26166.34210 1.422171e+04 38110.971
## 240 11582.00792 -3.357780e+02 23499.794
## 241 31206.91711 1.925436e+04 43159.476
## 242 4521.26870 -7.401344e+03 16443.881
## 243 10794.39492 -1.128985e+03 22717.775
## 244 10644.38072 -1.284618e+03 22573.380
## 245 37501.17258 2.554979e+04 49452.558
## 246 11630.01368 -2.958922e+02 23555.920
## 247 15347.52337 3.417456e+03 27277.591
## 248 5223.15472 -6.701021e+03 17147.331
## 249 -584.98950 -1.252123e+04 11351.254
## 250 5682.61215 -6.236316e+03 17601.541
## 251 23217.75186 1.125840e+04 35177.107
## 252 39004.92548 2.705510e+04 50954.748
## 253 37168.71173 2.523372e+04 49103.701
## 254 5609.28087 -6.321289e+03 17539.851
## 255 35416.33089 2.347772e+04 47354.946
## 256 12218.70440 2.834527e+02 24153.956
## 257 37216.74929 2.527081e+04 49162.684
## 258 10405.59793 -1.519093e+03 22330.289
## 259 10860.26749 -1.087660e+03 22808.195
## 260 27133.04344 1.518673e+04 39079.361
## 261 10546.75391 -1.385354e+03 22478.862
## 262 25591.55381 1.365001e+04 37533.093
## 263 34810.89837 2.286076e+04 46761.037
## 264 28840.88248 1.688635e+04 40795.411
## 265 14976.03054 3.043469e+03 26908.592
## 266 38350.39617 2.640171e+04 50299.079
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## 271 1956.15164 -9.969990e+03 13882.294
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## 274 10561.02151 -1.359110e+03 22481.153
## 275 3343.37163 -8.581402e+03 15268.145
## 276 10107.25695 -1.813766e+03 22028.280
## 277 400.92800 -1.153539e+04 12337.246
## 278 994.65111 -1.093509e+04 12924.390
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## 1283 23880.34052 1.192911e+04 35831.567
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## 1285 39275.09103 2.732852e+04 51221.663
## 1286 8382.89478 -3.540899e+03 20306.689
## 1287 1118.09411 -1.082002e+04 13056.207
## 1288 5608.85012 -6.309627e+03 17527.327
## 1289 30270.98083 1.831647e+04 42225.497
## 1290 10313.42440 -1.602114e+03 22228.963
## 1291 5539.91331 -6.389823e+03 17469.650
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## 1293 161.78848 -1.177533e+04 12098.907
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## 1296 44.97965 -1.188802e+04 11977.982
## 1297 1414.99039 -1.051533e+04 13345.312
## 1298 4161.43679 -7.764431e+03 16087.305
## 1299 6317.00016 -5.602860e+03 18236.860
## 1300 1796.80423 -1.012899e+04 13722.599
## 1301 32600.10867 2.066670e+04 44533.519
## 1302 39249.91108 2.729582e+04 51204.004
## 1303 1053.54363 -1.087746e+04 12984.550
## 1304 31293.03178 1.935473e+04 43231.336
## 1305 31863.50443 1.992653e+04 43800.475
## 1306 2593.43437 -9.332340e+03 14519.209
## 1307 26770.20715 1.482579e+04 38714.627
## 1308 31085.24308 1.912733e+04 43043.159
## 1309 27614.99609 1.567176e+04 39558.229
## 1310 9374.23682 -2.544375e+03 21292.849
## 1311 7766.52625 -4.151559e+03 19684.611
## 1312 5239.52640 -6.681209e+03 17160.262
## 1313 10730.11176 -1.206667e+03 22666.890
## 1314 28551.22960 1.660050e+04 40501.955
## 1315 28712.84542 1.676234e+04 40663.352
## 1316 2631.62863 -9.295057e+03 14558.314
## 1317 -1030.93372 -1.296970e+04 10907.833
## 1318 9539.88755 -2.443349e+03 21523.124
## 1319 12291.49363 3.339531e+02 24249.034
## 1320 7602.77210 -4.316147e+03 19521.691
## 1321 7503.27637 -4.425641e+03 19432.194
## 1322 36758.54471 2.480897e+04 48708.119
## 1323 15991.10068 4.057917e+03 27924.284
## 1324 36307.18154 2.436704e+04 48247.326
## 1325 4812.21286 -7.106974e+03 16731.400
## 1326 14973.23704 3.040694e+03 26905.780
## 1327 9998.71705 -1.922632e+03 21920.066
## 1328 10656.27895 -1.264325e+03 22576.883
## 1329 3137.12004 -8.790597e+03 15064.837
## 1330 14370.49480 2.442192e+03 26298.798
## 1331 11349.09206 -5.843261e+02 23282.510
## 1332 4338.16789 -7.589339e+03 16265.675
## 1333 17046.38978 5.092596e+03 29000.184
## 1334 12351.32369 4.223226e+02 24280.325
## 1335 3511.93081 -8.419586e+03 15443.447
## 1336 4149.13249 -7.781718e+03 16079.983
## 1337 1246.58494 -1.068217e+04 13175.341
## 1338 37085.62327 2.513494e+04 49036.304We will use Multiple linear regression since the model seems to be fitting in the linear regression model, based on further analysis we might use polynomial regression.
4.What are the potential problems/issues in your model? For example, skewness, nonnormality, nonlinearity, multicollinearity, heteroscedasticity, dummy variables, outliers and/or the data simply has very weak signal?
hist(model_Insurance$residuals)
The histogram shows that the residual value is less hence linear model is appropriate for this data.
library(psych)## Warning: package 'psych' was built under R version 3.6.2##
## Attaching package: 'psych'## The following object is masked from 'package:Hmisc':
##
## describe## The following objects are masked from 'package:ggplot2':
##
## %+%, alphasumm <- describe(Insurance)
summ## vars n mean sd median trimmed mad min
## age 1 1338 39.21 14.05 39.00 39.01 17.79 18.00
## sex* 2 1338 1.51 0.50 2.00 1.51 0.00 1.00
## bmi 3 1338 30.66 6.10 30.40 30.50 6.20 15.96
## children 4 1338 1.09 1.21 1.00 0.94 1.48 0.00
## smoker* 5 1338 1.20 0.40 1.00 1.13 0.00 1.00
## region* 6 1338 2.52 1.10 3.00 2.52 1.48 1.00
## charges 7 1338 13270.42 12110.01 9382.03 11076.02 7440.81 1121.87
## max range skew kurtosis se
## age 64.00 46.00 0.06 -1.25 0.38
## sex* 2.00 1.00 -0.02 -2.00 0.01
## bmi 53.13 37.17 0.28 -0.06 0.17
## children 5.00 5.00 0.94 0.19 0.03
## smoker* 2.00 1.00 1.46 0.14 0.01
## region* 4.00 3.00 -0.04 -1.33 0.03
## charges 63770.43 62648.55 1.51 1.59 331.07There are outliers such as cases where a male that is under age is obese which is linearly correlated to charge. In the near future we may come across more issues related to regression but we can always change and model in different ways to adapt to such problems.
5.What kind of remedies are you proposing to use to solve the potential issues?
The outliers present are not due to incorrect measurement but due to variance in different cases so we will not drop the outlier data but instead can come up with alternate methods like transformation as a remedy.