R Markdown
library(e1071)
data(iris)
set.seed(1234)
rndSample<-sample(1:nrow(iris),100)
str(rndSample)
## int [1:100] 28 80 101 111 137 133 144 132 98 103 ...
tr<-iris[rndSample,]
ts<-iris[-rndSample,]
s<-svm(Species~.,tr)
ps<-predict(s,ts)
cm<-table(ps,ts$Species)
precision<-100*(1-sum(diag(cm))/sum(cm))
precision
## [1] 4
s2<-svm(Species~.,tr,cost=10,kernel="polynomial",degree=3)
ps2<-predict(s2,ts)
(cm <- table(ps, ts$Species))
##
## ps setosa versicolor virginica
## setosa 18 0 0
## versicolor 0 17 1
## virginica 0 1 13
precision <- 100*(1-sum(diag(cm))/sum(cm)) #the error rate
#try different numbers for cost and degree and see which gives lowest error
s2 <- svm(Species ~., tr, cost=30, kernel = "polynomial", degree = 1)
ps2 <- predict (s2, ts)
cm2 <- table (ps2, ts$Species)
#the error rate
100*(1-sum(diag(cm2))/sum(cm2))
## [1] 0
data(Boston, package='MASS')
set.seed(1234)
sp<-sample(1:nrow(Boston), 354)
tr<-Boston[sp, ]
ts<-Boston[-sp, ]
s1<-svm(medv ~., tr)
ps1<-predict(s1, ts)
mean(abs(ps1-ts$medv))
## [1] 2.158999
s2<-svm(medv~., tr, kernel="radial", cost=15, epsilon=.1, gamma=.04)
ps2<-predict(s2,ts)
mean(abs(ps2-ts$medv))
## [1] 1.904667
library(readr)
letterdata <- read_csv("C:/Users/alviy/Downloads/letterdata.csv")
## Rows: 20000 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): letter
## dbl (16): xbox, ybox, width, height, onpix, xbar, ybar, x2bar, y2bar, xybar,...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
View(letterdata)
library(kernlab)
str(letterdata)
## spc_tbl_ [20,000 × 17] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ letter: chr [1:20000] "T" "I" "D" "N" ...
## $ xbox : num [1:20000] 2 5 4 7 2 4 4 1 2 11 ...
## $ ybox : num [1:20000] 8 12 11 11 1 11 2 1 2 15 ...
## $ width : num [1:20000] 3 3 6 6 3 5 5 3 4 13 ...
## $ height: num [1:20000] 5 7 8 6 1 8 4 2 4 9 ...
## $ onpix : num [1:20000] 1 2 6 3 1 3 4 1 2 7 ...
## $ xbar : num [1:20000] 8 10 10 5 8 8 8 8 10 13 ...
## $ ybar : num [1:20000] 13 5 6 9 6 8 7 2 6 2 ...
## $ x2bar : num [1:20000] 0 5 2 4 6 6 6 2 2 6 ...
## $ y2bar : num [1:20000] 6 4 6 6 6 9 6 2 6 2 ...
## $ xybar : num [1:20000] 6 13 10 4 6 5 7 8 12 12 ...
## $ x2ybar: num [1:20000] 10 3 3 4 5 6 6 2 4 1 ...
## $ xy2bar: num [1:20000] 8 9 7 10 9 6 6 8 8 9 ...
## $ xedge : num [1:20000] 0 2 3 6 1 0 2 1 1 8 ...
## $ xedgey: num [1:20000] 8 8 7 10 7 8 8 6 6 1 ...
## $ yedge : num [1:20000] 0 4 3 2 5 9 7 2 1 1 ...
## $ yedgex: num [1:20000] 8 10 9 8 10 7 10 7 7 8 ...
## - attr(*, "spec")=
## .. cols(
## .. letter = col_character(),
## .. xbox = col_double(),
## .. ybox = col_double(),
## .. width = col_double(),
## .. height = col_double(),
## .. onpix = col_double(),
## .. xbar = col_double(),
## .. ybar = col_double(),
## .. x2bar = col_double(),
## .. y2bar = col_double(),
## .. xybar = col_double(),
## .. x2ybar = col_double(),
## .. xy2bar = col_double(),
## .. xedge = col_double(),
## .. xedgey = col_double(),
## .. yedge = col_double(),
## .. yedgex = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
letters <- letterdata
letters$letter <- as.factor(letters$letter)
str(letters)
## spc_tbl_ [20,000 × 17] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ letter: Factor w/ 26 levels "A","B","C","D",..: 20 9 4 14 7 19 2 1 10 13 ...
## $ xbox : num [1:20000] 2 5 4 7 2 4 4 1 2 11 ...
## $ ybox : num [1:20000] 8 12 11 11 1 11 2 1 2 15 ...
## $ width : num [1:20000] 3 3 6 6 3 5 5 3 4 13 ...
## $ height: num [1:20000] 5 7 8 6 1 8 4 2 4 9 ...
## $ onpix : num [1:20000] 1 2 6 3 1 3 4 1 2 7 ...
## $ xbar : num [1:20000] 8 10 10 5 8 8 8 8 10 13 ...
## $ ybar : num [1:20000] 13 5 6 9 6 8 7 2 6 2 ...
## $ x2bar : num [1:20000] 0 5 2 4 6 6 6 2 2 6 ...
## $ y2bar : num [1:20000] 6 4 6 6 6 9 6 2 6 2 ...
## $ xybar : num [1:20000] 6 13 10 4 6 5 7 8 12 12 ...
## $ x2ybar: num [1:20000] 10 3 3 4 5 6 6 2 4 1 ...
## $ xy2bar: num [1:20000] 8 9 7 10 9 6 6 8 8 9 ...
## $ xedge : num [1:20000] 0 2 3 6 1 0 2 1 1 8 ...
## $ xedgey: num [1:20000] 8 8 7 10 7 8 8 6 6 1 ...
## $ yedge : num [1:20000] 0 4 3 2 5 9 7 2 1 1 ...
## $ yedgex: num [1:20000] 8 10 9 8 10 7 10 7 7 8 ...
## - attr(*, "spec")=
## .. cols(
## .. letter = col_character(),
## .. xbox = col_double(),
## .. ybox = col_double(),
## .. width = col_double(),
## .. height = col_double(),
## .. onpix = col_double(),
## .. xbar = col_double(),
## .. ybar = col_double(),
## .. x2bar = col_double(),
## .. y2bar = col_double(),
## .. xybar = col_double(),
## .. x2ybar = col_double(),
## .. xy2bar = col_double(),
## .. xedge = col_double(),
## .. xedgey = col_double(),
## .. yedge = col_double(),
## .. yedgex = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
letters_train <- letters[1:16000, ]
letters_test <- letters[16001:20000, ]
letter_classifier <- ksvm(letter~., data=letters_train, kernel="vanilladot") #~., means predict response against all the variables
## Setting default kernel parameters
letter_predictions<-predict(letter_classifier, letters_test)
head(letter_predictions)
## [1] U N V X N H
## Levels: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
table(letter_predictions, letters_test$letter)
##
## letter_predictions A B C D E F G H I J K L M N O
## A 144 0 0 0 0 0 0 0 0 1 0 0 1 2 2
## B 0 121 0 5 2 0 1 2 0 0 1 0 1 0 0
## C 0 0 120 0 4 0 10 2 2 0 1 3 0 0 2
## D 2 2 0 156 0 1 3 10 4 3 4 3 0 5 5
## E 0 0 5 0 127 3 1 1 0 0 3 4 0 0 0
## F 0 0 0 0 0 138 2 2 6 0 0 0 0 0 0
## G 1 1 2 1 9 2 123 2 0 0 1 2 1 0 1
## H 0 0 0 1 0 1 0 102 0 2 3 2 3 4 20
## I 0 1 0 0 0 1 0 0 141 8 0 0 0 0 0
## J 0 1 0 0 0 1 0 2 5 128 0 0 0 0 1
## K 1 1 9 0 0 0 2 5 0 0 118 0 0 2 0
## L 0 0 0 0 2 0 1 1 0 0 0 133 0 0 0
## M 0 0 1 1 0 0 1 1 0 0 0 0 135 4 0
## N 0 0 0 0 0 1 0 1 0 0 0 0 0 145 0
## O 1 0 2 1 0 0 1 2 0 1 0 0 0 1 99
## P 0 0 0 1 0 2 1 0 0 0 0 0 0 0 2
## Q 0 0 0 0 0 0 8 2 0 0 0 3 0 0 3
## R 0 7 0 0 1 0 3 8 0 0 13 0 0 1 1
## S 1 1 0 0 1 0 3 0 1 1 0 1 0 0 0
## T 0 0 0 0 3 2 0 0 0 0 1 0 0 0 0
## U 1 0 3 1 0 0 0 2 0 0 0 0 0 0 1
## V 0 0 0 0 0 1 3 4 0 0 0 0 1 2 1
## W 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0
## X 0 1 0 0 2 0 0 1 3 0 1 6 0 0 1
## Y 3 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## Z 2 0 0 0 1 0 0 0 3 4 0 0 0 0 0
##
## letter_predictions P Q R S T U V W X Y Z
## A 0 5 0 1 1 1 0 1 0 0 1
## B 2 2 3 5 0 0 2 0 1 0 0
## C 0 0 0 0 0 0 0 0 0 0 0
## D 3 1 4 0 0 0 0 0 3 3 1
## E 0 2 0 10 0 0 0 0 2 0 3
## F 16 0 0 3 0 0 1 0 1 2 0
## G 2 8 2 4 3 0 0 0 1 0 0
## H 0 2 3 0 3 0 2 0 0 1 0
## I 1 0 0 3 0 0 0 0 5 1 1
## J 1 3 0 2 0 0 0 0 1 0 6
## K 1 0 7 0 1 3 0 0 5 0 0
## L 0 1 0 5 0 0 0 0 0 0 1
## M 0 0 0 0 0 3 0 8 0 0 0
## N 0 0 3 0 0 1 0 2 0 0 0
## O 3 3 0 0 0 3 0 0 0 0 0
## P 130 0 0 0 0 0 0 0 0 1 0
## Q 1 124 0 5 0 0 0 0 0 2 0
## R 1 0 138 0 1 0 1 0 0 0 0
## S 0 14 0 101 3 0 0 0 2 0 10
## T 0 0 0 3 133 1 0 0 0 2 2
## U 0 0 0 0 0 152 0 0 1 1 0
## V 0 3 1 0 0 0 126 1 0 4 0
## W 0 0 0 0 0 4 4 127 0 0 0
## X 0 0 0 1 0 0 0 0 137 1 1
## Y 7 0 0 0 3 0 0 0 0 127 0
## Z 0 0 0 18 3 0 0 0 0 0 132
#diagonal values indicate the total number of records where the predicted letter matches the true value
agreement<-letter_predictions==letters_test$letter
table(agreement)
## agreement
## FALSE TRUE
## 643 3357
prop.table(table(agreement))
## agreement
## FALSE TRUE
## 0.16075 0.83925
letter_classifier_rbf<-ksvm(letter~.,data=letters_train, kernel="rbfdot")
letter_predictions_rbf<-predict(letter_classifier_rbf, letters_test)
library(readxl)
AgeHeight <- read_excel("C:/Users/alviy/Downloads/AgeHeight.xlsx")
#AgeHeight <- read_excel("AgeHeight.xlsx",sheet="Hoja2")#Rename sheet
View(AgeHeight)
lmHeight=lm(height~age, data=AgeHeight)
summary(lmHeight)
##
## Call:
## lm(formula = height ~ age, data = AgeHeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27238 -0.24248 -0.02762 0.16014 0.47238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.9283 0.5084 127.71 < 2e-16 ***
## age 0.6350 0.0214 29.66 4.43e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.256 on 10 degrees of freedom
## Multiple R-squared: 0.9888, Adjusted R-squared: 0.9876
## F-statistic: 880 on 1 and 10 DF, p-value: 4.428e-11
lmHeight2=lm(height~age+no_siblings, data=AgeHeight)
summary(lmHeight2)
##
## Call:
## lm(formula = height ~ age + no_siblings, data = AgeHeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26297 -0.22462 -0.02021 0.16102 0.49752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.90554 0.53526 121.260 8.96e-16 ***
## age 0.63751 0.02340 27.249 5.85e-10 ***
## no_siblings -0.01772 0.04735 -0.374 0.717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2677 on 9 degrees of freedom
## Multiple R-squared: 0.9889, Adjusted R-squared: 0.9865
## F-statistic: 402.2 on 2 and 9 DF, p-value: 1.576e-09
library(readr)
insurance <- read.csv("C:/Users/alviy/Downloads/insurance.csv", stringsAsFactors=TRUE)
View(insurance)
str(insurance)
## 'data.frame': 1338 obs. of 7 variables:
## $ age : int 19 18 28 33 32 31 46 37 37 60 ...
## $ sex : Factor w/ 2 levels "female","male": 1 2 2 2 2 1 1 1 2 1 ...
## $ bmi : num 27.9 33.8 33 22.7 28.9 ...
## $ children: int 0 1 3 0 0 0 1 3 2 0 ...
## $ smoker : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
## $ region : Factor w/ 4 levels "northeast","northwest",..: 4 3 3 2 2 3 3 2 1 2 ...
## $ charges : num 16885 1726 4449 21984 3867 ...
summary(insurance)
## age sex bmi children smoker
## Min. :18.00 female:662 Min. :15.96 Min. :0.000 no :1064
## 1st Qu.:27.00 male :676 1st Qu.:26.30 1st Qu.:0.000 yes: 274
## Median :39.00 Median :30.40 Median :1.000
## Mean :39.21 Mean :30.66 Mean :1.095
## 3rd Qu.:51.00 3rd Qu.:34.69 3rd Qu.:2.000
## Max. :64.00 Max. :53.13 Max. :5.000
## region charges
## northeast:324 Min. : 1122
## northwest:325 1st Qu.: 4740
## southeast:364 Median : 9382
## southwest:325 Mean :13270
## 3rd Qu.:16640
## Max. :63770
hist(insurance$charges)
table(insurance$charges)
##
## 1121.8739 1131.5066 1135.9407 1136.3994 1137.011 1137.4697
## 1 1 1 1 1 1
## 1141.4451 1146.7966 1149.3959 1163.4627 1241.565 1242.26
## 1 1 1 1 1 1
## 1242.816 1252.407 1253.936 1256.299 1261.442 1261.859
## 1 1 1 1 1 1
## 1263.249 1391.5287 1515.3449 1526.312 1532.4697 1534.3045
## 1 1 1 1 1 1
## 1607.5101 1615.7667 1621.3402 1621.8827 1622.1885 1625.43375
## 1 1 1 1 1 1
## 1627.28245 1628.4709 1629.8335 1631.6683 1631.8212 1632.03625
## 1 1 1 1 1 1
## 1632.56445 1633.0444 1633.9618 1634.5734 1635.73365 1639.5631
## 1 1 1 1 1 2
## 1646.4297 1664.9996 1674.6323 1682.597 1694.7964 1702.4553
## 1 1 1 1 1 1
## 1704.5681 1704.70015 1705.6245 1708.0014 1708.92575 1711.0268
## 1 1 1 1 1 1
## 1712.227 1719.4363 1720.3537 1725.5523 1727.54 1727.785
## 1 1 1 1 1 1
## 1728.897 1731.677 1737.376 1743.214 1744.465 1748.774
## 1 1 1 1 1 1
## 1759.338 1769.53165 1815.8759 1824.2854 1826.843 1832.094
## 1 1 1 1 1 1
## 1837.237 1837.2819 1842.519 1875.344 1877.9294 1880.07
## 1 1 1 1 1 1
## 1880.487 1906.35825 1909.52745 1917.3184 1964.78 1967.0227
## 1 1 1 1 1 1
## 1969.614 1972.95 1977.815 1980.07 1981.5819 1984.4533
## 1 1 1 1 1 1
## 1986.9334 2007.945 2020.177 2020.5523 2026.9741 2045.68525
## 1 1 1 1 1 1
## 2055.3249 2102.2647 2103.08 2104.1134 2117.33885 2128.43105
## 1 1 1 1 1 1
## 2130.6759 2134.9015 2136.88225 2137.6536 2138.0707 2150.469
## 1 1 1 1 1 1
## 2154.361 2155.6815 2156.7518 2166.732 2196.4732 2198.18985
## 1 1 1 1 1 1
## 2200.83085 2201.0971 2203.47185 2203.73595 2205.9808 2207.69745
## 1 1 1 1 1 1
## 2211.13075 2217.46915 2217.6012 2219.4451 2221.56445 2250.8352
## 1 1 1 1 1 1
## 2254.7967 2257.47525 2261.5688 2302.3 2304.0022 2322.6218
## 1 1 1 1 1 1
## 2331.519 2352.96845 2362.22905 2395.17155 2396.0959 2404.7338
## 1 1 1 1 1 1
## 2416.955 2438.0552 2457.21115 2457.502 2459.7201 2464.6188
## 1 1 1 1 1 1
## 2473.3341 2480.9791 2483.736 2494.022 2497.0383 2498.4144
## 1 1 1 1 1 1
## 2523.1695 2527.81865 2534.39375 2566.4707 2585.269 2585.85065
## 1 1 1 1 1 1
## 2597.779 2632.992 2639.0429 2643.2685 2680.9493 2689.4954
## 1 1 1 1 1 1
## 2690.1138 2699.56835 2709.1119 2709.24395 2710.82855 2719.27975
## 1 1 1 1 1 1
## 2721.3208 2727.3951 2730.10785 2731.9122 2741.948 2755.02095
## 1 1 1 1 1 1
## 2775.19215 2789.0574 2801.2588 2803.69785 2842.76075 2850.68375
## 1 1 1 1 1 1
## 2855.43755 2866.091 2867.1196 2897.3235 2899.48935 2902.9065
## 1 1 1 1 1 1
## 2904.088 2913.569 2927.0647 2974.126 3021.80915 3044.2133
## 1 1 1 1 1 1
## 3046.062 3056.3881 3062.50825 3070.8087 3077.0955 3161.454
## 1 1 1 1 1 1
## 3167.45585 3171.6149 3172.018 3176.2877 3176.8159 3180.5101
## 1 1 1 1 1 1
## 3201.24515 3206.49135 3208.787 3213.62205 3227.1211 3238.4357
## 1 1 1 1 1 1
## 3260.199 3268.84665 3277.161 3279.86855 3292.52985 3309.7926
## 1 1 1 1 1 1
## 3353.284 3353.4703 3366.6697 3378.91 3385.39915 3392.3652
## 1 1 1 1 1 1
## 3392.9768 3393.35635 3410.324 3443.064 3471.4096 3481.868
## 1 1 1 1 1 1
## 3484.331 3490.5491 3500.6123 3537.703 3554.203 3556.9223
## 1 1 1 1 1 1
## 3558.62025 3561.8889 3577.999 3579.8287 3591.48 3594.17085
## 1 1 1 1 1 1
## 3597.596 3645.0894 3659.346 3693.428 3704.3545 3732.6251
## 1 1 1 1 1 1
## 3736.4647 3756.6216 3757.8448 3761.292 3766.8838 3847.674
## 1 1 1 1 1 1
## 3857.75925 3861.20965 3866.8552 3875.7341 3877.30425 3906.127
## 1 1 1 1 1 1
## 3925.7582 3935.1799 3943.5954 3947.4131 3956.07145 3972.9247
## 1 1 1 1 1 1
## 3981.9768 3987.926 3989.841 3994.1778 4005.4225 4032.2407
## 1 1 1 1 1 1
## 4040.55825 4058.1161 4058.71245 4074.4537 4076.497 4133.64165
## 1 1 1 1 1 1
## 4134.08245 4137.5227 4149.736 4151.0287 4185.0979 4189.1131
## 1 1 1 1 1 1
## 4234.927 4237.12655 4239.89265 4243.59005 4260.744 4266.1658
## 1 1 1 1 1 1
## 4296.2712 4320.41085 4337.7352 4340.4409 4347.02335 4349.462
## 1 1 1 1 1 1
## 4350.5144 4357.04365 4391.652 4399.731 4402.233 4415.1588
## 1 1 1 1 1 1
## 4428.88785 4433.3877 4433.9159 4435.0942 4438.2634 4441.21315
## 1 1 1 1 1 1
## 4449.462 4454.40265 4462.7218 4463.2051 4466.6214 4500.33925
## 1 1 1 1 1 1
## 4504.6624 4518.82625 4527.18295 4529.477 4536.259 4544.2348
## 1 1 1 1 1 1
## 4561.1885 4562.8421 4564.19145 4571.41305 4618.0799 4646.759
## 1 1 1 1 1 1
## 4661.28635 4667.60765 4670.64 4673.3922 4686.3887 4687.797
## 1 1 1 1 1 1
## 4718.20355 4719.52405 4719.73655 4738.2682 4746.344 4747.0529
## 1 1 1 1 1 1
## 4751.07 4753.6368 4762.329 4766.022 4779.6023 4795.6568
## 1 1 1 1 1 1
## 4827.90495 4830.63 4837.5823 4846.92015 4877.98105 4883.866
## 1 1 1 1 1 1
## 4889.0368 4889.9995 4894.7533 4906.40965 4915.05985 4922.9159
## 1 1 1 1 1 1
## 4931.647 4934.705 4949.7587 4992.3764 5002.7827 5003.853
## 1 1 1 1 1 1
## 5012.471 5028.1466 5031.26955 5080.096 5116.5004 5124.1887
## 1 1 1 1 1 1
## 5125.2157 5138.2567 5148.5526 5152.134 5209.57885 5227.98875
## 1 1 1 1 1 1
## 5240.765 5245.2269 5246.047 5253.524 5257.50795 5261.46945
## 1 1 1 1 1 1
## 5266.3656 5267.81815 5272.1758 5312.16985 5325.651 5327.40025
## 1 1 1 1 1 1
## 5354.07465 5373.36425 5375.038 5377.4578 5383.536 5385.3379
## 1 1 1 1 1 1
## 5397.6167 5400.9805 5415.6612 5425.02335 5428.7277 5438.7491
## 1 1 1 1 1 1
## 5458.04645 5469.0066 5472.449 5478.0368 5484.4673 5488.262
## 1 1 1 1 1 1
## 5584.3057 5594.8455 5615.369 5630.45785 5649.715 5662.225
## 1 1 1 1 1 1
## 5693.4305 5699.8375 5708.867 5709.1644 5729.0053 5757.41345
## 1 1 1 1 1 1
## 5836.5204 5846.9176 5855.9025 5910.944 5920.1041 5926.846
## 1 1 1 1 1 1
## 5934.3798 5966.8874 5969.723 5972.378 5974.3847 5976.8311
## 1 1 1 1 1 1
## 5979.731 5989.52365 6059.173 6067.12675 6079.6715 6082.405
## 1 1 1 1 1 1
## 6112.35295 6113.23105 6117.4945 6123.5688 6128.79745 6184.2994
## 1 1 1 1 1 1
## 6185.3208 6186.127 6196.448 6198.7518 6203.90175 6238.298
## 1 1 1 1 1 1
## 6250.435 6272.4772 6282.235 6289.7549 6311.952 6313.759
## 1 1 1 1 1 1
## 6334.34355 6338.0756 6356.2707 6358.77645 6360.9936 6373.55735
## 1 1 1 1 1 1
## 6389.37785 6393.60345 6402.29135 6406.4107 6414.178 6435.6237
## 1 1 1 1 1 1
## 6455.86265 6457.8434 6474.013 6496.886 6500.2359 6548.19505
## 1 1 1 1 1 1
## 6551.7501 6555.07035 6571.02435 6571.544 6593.5083 6600.20595
## 1 1 1 1 1 1
## 6600.361 6610.1097 6640.54485 6652.5288 6653.7886 6664.68595
## 1 1 1 1 1 1
## 6666.243 6686.4313 6710.1919 6746.7425 6748.5912 6753.038
## 1 1 1 1 1 1
## 6770.1925 6775.961 6781.3542 6796.86325 6799.458 6837.3687
## 1 1 1 1 1 1
## 6849.026 6858.4796 6875.961 6877.9801 6933.24225 6940.90985
## 1 1 1 1 1 1
## 6948.7008 6985.50695 6986.697 7045.499 7046.7222 7050.0213
## 1 1 1 1 1 1
## 7050.642 7077.1894 7133.9025 7144.86265 7147.105 7147.4728
## 1 1 1 1 1 1
## 7151.092 7152.6714 7153.5539 7160.094 7160.3303 7162.0122
## 1 1 1 1 1 1
## 7173.35995 7196.867 7201.70085 7209.4918 7222.78625 7228.21565
## 1 1 1 1 1 1
## 7243.8136 7256.7231 7261.741 7265.7025 7281.5056 7323.734819
## 1 1 1 1 1 1
## 7325.0482 7337.748 7345.084 7345.7266 7348.142 7358.17565
## 1 1 1 1 1 1
## 7371.772 7418.522 7419.4779 7421.19455 7441.053 7441.501
## 1 1 1 1 1 1
## 7443.64305 7445.918 7448.40395 7512.267 7518.02535 7526.70645
## 1 1 1 1 1 1
## 7537.1639 7623.518 7624.63 7626.993 7633.7206 7639.41745
## 1 1 1 1 1 1
## 7640.3092 7650.77375 7682.67 7726.854 7727.2532 7729.64575
## 1 1 1 1 1 1
## 7731.4271 7731.85785 7740.337 7742.1098 7749.1564 7789.635
## 1 1 1 1 1 1
## 7804.1605 7935.29115 7954.517 7985.815 7986.47525 8017.06115
## 1 1 1 1 1 1
## 8023.13545 8026.6666 8027.968 8059.6791 8062.764 8068.185
## 1 1 1 1 1 1
## 8083.9198 8116.26885 8116.68 8124.4084 8125.7845 8162.71625
## 1 1 1 1 1 1
## 8211.1002 8219.2039 8232.6388 8233.0975 8240.5896 8252.2843
## 1 1 1 1 1 1
## 8269.044 8277.523 8280.6227 8283.6807 8302.53565 8310.83915
## 1 1 1 1 1 1
## 8334.45755 8334.5896 8342.90875 8347.1643 8410.04685 8413.46305
## 1 1 1 1 1 1
## 8428.0693 8442.667 8444.474 8457.818 8515.7587 8516.829
## 1 1 1 1 1 1
## 8520.026 8522.003 8527.532 8534.6718 8538.28845 8539.671
## 1 1 1 1 1 1
## 8547.6913 8551.347 8556.907 8569.8618 8582.3023 8596.8278
## 1 1 1 1 1 1
## 8601.3293 8603.8234 8604.48365 8605.3615 8606.2174 8615.3
## 1 1 1 1 1 1
## 8627.5411 8671.19125 8688.85885 8703.456 8733.22925 8765.249
## 1 1 1 1 1 1
## 8782.469 8798.593 8823.279 8823.98575 8825.086 8827.2099
## 1 1 1 1 1 1
## 8835.26495 8871.1517 8891.1395 8930.93455 8932.084 8944.1151
## 1 1 1 1 1 1
## 8964.06055 8965.79575 8968.33 8978.1851 8988.15875 9048.0273
## 1 1 1 1 1 1
## 9058.7303 9095.06825 9101.798 9140.951 9144.565 9174.13565
## 1 1 1 1 1 1
## 9182.17 9193.8385 9222.4026 9225.2564 9249.4952 9264.797
## 1 1 1 1 1 1
## 9282.4806 9283.562 9288.0267 9290.1395 9301.89355 9304.7019
## 1 1 1 1 1 1
## 9361.3268 9377.9047 9386.1613 9391.346 9411.005 9414.92
## 1 1 1 1 1 1
## 9432.9253 9447.25035 9447.3824 9487.6442 9500.57305 9504.3103
## 1 1 1 1 1 1
## 9541.69555 9549.5651 9563.029 9566.9909 9583.8933 9617.66245
## 1 1 1 1 1 1
## 9620.3307 9625.92 9630.397 9634.538 9644.2525 9704.66805
## 1 1 1 1 1 1
## 9715.841 9722.7695 9724.53 9748.9106 9778.3472 9788.8659
## 1 1 1 1 1 1
## 9800.8882 9850.432 9855.1314 9861.025 9863.4718 9866.30485
## 1 1 1 1 1 1
## 9869.8102 9872.701 9875.6804 9877.6077 9880.068 9910.35985
## 1 1 1 1 1 1
## 9957.7216 9964.06 9991.03765 10043.249 10065.413 10072.05505
## 1 1 1 1 1 1
## 10085.846 10096.97 10106.13425 10107.2206 10115.00885 10118.424
## 1 1 1 1 1 1
## 10141.1362 10156.7832 10197.7722 10214.636 10226.2842 10231.4999
## 1 1 1 1 1 1
## 10264.4421 10269.46 10325.206 10338.9316 10355.641 10370.91255
## 1 1 1 1 1 1
## 10381.4787 10407.08585 10422.91665 10435.06525 10436.096 10450.552
## 1 1 1 1 1 1
## 10461.9794 10493.9458 10560.4917 10564.8845 10577.087 10579.711
## 1 1 1 1 1 1
## 10594.2257 10594.50155 10600.5483 10601.412 10601.63225 10602.385
## 1 1 1 1 1 1
## 10702.6424 10704.47 10713.644 10736.87075 10791.96 10795.93733
## 1 1 1 1 1 1
## 10796.35025 10797.3362 10806.839 10807.4863 10825.2537 10848.1343
## 1 1 1 1 1 1
## 10923.9332 10928.849 10942.13205 10959.33 10959.6947 10965.446
## 1 1 1 1 1 1
## 10976.24575 10977.2063 10982.5013 11013.7119 11015.1747 11033.6617
## 1 1 1 1 1 1
## 11070.535 11073.176 11082.5772 11085.5868 11090.7178 11093.6229
## 1 1 1 1 1 1
## 11150.78 11163.568 11165.41765 11187.6567 11244.3769 11253.421
## 1 1 1 1 1 1
## 11264.541 11272.33139 11286.5387 11289.10925 11299.343 11305.93455
## 1 1 1 1 1 1
## 11326.71487 11345.519 11353.2276 11356.6609 11362.755 11363.2832
## 1 1 1 1 1 1
## 11365.952 11381.3254 11394.06555 11396.9002 11411.685 11436.73815
## 1 1 1 1 1 1
## 11454.0215 11455.28 11482.63485 11488.31695 11512.405 11520.09985
## 1 1 1 1 1 1
## 11534.87265 11538.421 11552.904 11554.2236 11566.30055 11576.13
## 1 1 1 1 1 1
## 11657.7189 11658.11505 11658.37915 11674.13 11729.6795 11735.87905
## 1 1 1 1 1 1
## 11737.84884 11741.726 11743.299 11743.9341 11763.0009 11830.6072
## 1 1 1 1 1 1
## 11833.7823 11837.16 11840.77505 11842.442 11842.62375 11848.141
## 1 1 1 1 1 1
## 11856.4115 11879.10405 11881.358 11881.9696 11884.04858 11931.12525
## 1 1 1 1 1 1
## 11938.25595 11944.59435 11945.1327 11946.6259 11987.1682 12029.2867
## 1 1 1 1 1 1
## 12032.326 12044.342 12094.478 12096.6512 12105.32 12124.9924
## 1 1 1 1 1 1
## 12129.61415 12142.5786 12146.971 12222.8983 12224.35085 12231.6136
## 1 1 1 1 1 1
## 12233.828 12235.8392 12244.531 12265.5069 12268.63225 12269.68865
## 1 1 1 1 1 1
## 12323.936 12333.828 12347.172 12363.547 12404.8791 12430.95335
## 1 1 1 1 1 1
## 12475.3513 12479.70895 12485.8009 12495.29085 12523.6048 12557.6053
## 1 1 1 1 1 1
## 12574.049 12592.5345 12609.88702 12622.1795 12629.1656 12629.8967
## 1 1 1 1 1 1
## 12638.195 12643.3778 12644.589 12646.207 12648.7034 12730.9996
## 1 1 1 1 1 1
## 12741.16745 12797.20962 12815.44495 12829.4551 12890.05765 12913.9924
## 1 1 1 1 1 1
## 12925.886 12928.7911 12949.1554 12950.0712 12957.118 12979.358
## 1 1 1 1 1 1
## 12981.3457 12982.8747 13012.20865 13019.16105 13041.921 13047.33235
## 1 1 1 1 1 1
## 13063.883 13112.6048 13126.67745 13129.60345 13143.33665 13143.86485
## 1 1 1 1 1 1
## 13204.28565 13217.0945 13224.05705 13224.693 13228.84695 13352.0998
## 1 1 1 1 1 1
## 13390.559 13393.756 13405.3903 13415.0381 13429.0354 13430.265
## 1 1 1 1 1 1
## 13451.122 13457.9608 13462.52 13470.8044 13470.86 13555.0049
## 1 1 1 1 1 1
## 13607.36875 13616.3586 13635.6379 13725.47184 13747.87235 13770.0979
## 1 1 1 1 1 1
## 13822.803 13831.1152 13844.506 13844.7972 13880.949 13887.204
## 1 1 1 1 1 1
## 13887.9685 13919.8229 13937.6665 13974.45555 13981.85035 14001.1338
## 1 1 1 1 1 1
## 14001.2867 14007.222 14043.4767 14119.62 14133.03775 14210.53595
## 1 1 1 1 1 1
## 14235.072 14254.6082 14256.1928 14283.4594 14313.8463 14319.031
## 1 1 1 1 1 1
## 14349.8544 14358.36437 14382.70905 14394.39815 14394.5579 14410.9321
## 1 1 1 1 1 1
## 14418.2804 14426.07385 14449.8544 14451.83515 14455.64405 14474.675
## 1 1 1 1 1 1
## 14478.33015 14571.8908 14590.63205 14692.66935 14711.7438 14901.5167
## 1 1 1 1 1 1
## 14988.432 15006.57945 15019.76005 15161.5344 15170.069 15230.32405
## 1 1 1 1 1 1
## 15359.1045 15518.18025 15555.18875 15612.19335 15817.9857 15820.699
## 1 1 1 1 1 1
## 15828.82173 16069.08475 16085.1275 16115.3045 16138.76205 16232.847
## 1 1 1 1 1 1
## 16297.846 16420.49455 16450.8947 16455.70785 16577.7795 16586.49771
## 1 1 1 1 1 1
## 16657.71745 16776.30405 16796.41194 16884.924 17043.3414 17081.08
## 1 1 1 1 1 1
## 17085.2676 17128.42608 17178.6824 17179.522 17352.6803 17361.7661
## 1 1 1 1 1 1
## 17468.9839 17496.306 17560.37975 17626.23951 17663.1442 17748.5062
## 1 1 1 1 1 1
## 17878.90068 17904.52705 17929.30337 17942.106 18033.9679 18157.876
## 1 1 1 1 1 1
## 18218.16139 18223.4512 18246.4955 18259.216 18310.742 18328.2381
## 1 1 1 1 1 1
## 18608.262 18648.4217 18765.87545 18767.7377 18804.7524 18806.14547
## 1 1 1 1 1 1
## 18838.70366 18903.49141 18955.22017 18963.17192 18972.495 19023.26
## 1 1 1 1 1 1
## 19040.876 19107.7796 19144.57652 19199.944 19214.70553 19350.3689
## 1 1 1 1 1 1
## 19361.9988 19442.3535 19444.2658 19496.71917 19515.5416 19521.9682
## 1 1 1 1 1 1
## 19539.243 19594.80965 19673.33573 19719.6947 19749.38338 19798.05455
## 1 1 1 1 1 1
## 19933.458 19964.7463 20009.63365 20149.3229 20167.33603 20177.67113
## 1 1 1 1 1 1
## 20234.85475 20277.80751 20296.86345 20420.60465 20462.99766 20630.28351
## 1 1 1 1 1 1
## 20709.02034 20745.9891 20773.62775 20781.48892 20878.78443 20984.0936
## 1 1 1 1 1 1
## 21082.16 21098.55405 21195.818 21223.6758 21232.18226 21259.37795
## 1 1 1 1 1 1
## 21344.8467 21348.706 21472.4788 21595.38229 21659.9301 21677.28345
## 1 1 1 1 1 1
## 21771.3423 21774.32215 21797.0004 21880.82 21978.6769 21984.47061
## 1 1 1 1 1 1
## 22144.032 22192.43711 22218.1149 22331.5668 22395.74424 22412.6485
## 1 1 1 1 1 1
## 22462.04375 22478.6 22493.65964 23045.56616 23065.4207 23082.95533
## 1 1 1 1 1 1
## 23241.47453 23244.7902 23288.9284 23306.547 23401.30575 23563.01618
## 1 1 1 1 1 1
## 23568.272 23807.2406 23887.6627 23967.38305 24059.68019 24106.91255
## 1 1 1 1 1 1
## 24180.9335 24227.33724 24393.6224 24476.47851 24513.09126 24520.264
## 1 1 1 1 1 1
## 24535.69855 24603.04837 24667.419 24671.66334 24869.8368 24873.3849
## 1 1 1 1 1 1
## 24915.04626 24915.22085 25081.76784 25309.489 25333.33284 25382.297
## 1 1 1 1 1 1
## 25517.11363 25656.57526 25678.77845 25992.82104 26018.95052 26109.32905
## 1 1 1 1 1 1
## 26125.67477 26140.3603 26236.57997 26392.26029 26467.09737 26926.5144
## 1 1 1 1 1 1
## 27000.98473 27037.9141 27117.99378 27218.43725 27322.73386 27346.04207
## 1 1 1 1 1 1
## 27375.90478 27533.9129 27724.28875 27808.7251 27941.28758 28101.33305
## 1 1 1 1 1 1
## 28287.89766 28340.18885 28468.91901 28476.73499 28868.6639 28923.13692
## 1 1 1 1 1 1
## 28950.4692 29141.3603 29186.48236 29330.98315 29523.1656 30063.58055
## 1 1 1 1 1 1
## 30166.61817 30184.9367 30259.99556 30284.64294 30942.1918 31620.00106
## 1 1 1 1 1 1
## 32108.66282 32548.3405 32734.1863 32787.45859 33307.5508 33471.97189
## 1 1 1 1 1 1
## 33475.81715 33732.6867 33750.2918 33900.653 33907.548 34166.273
## 1 1 1 1 1 1
## 34254.05335 34303.1672 34439.8559 34472.841 34617.84065 34672.1472
## 1 1 1 1 1 1
## 34779.615 34806.4677 34828.654 34838.873 35069.37452 35147.52848
## 1 1 1 1 1 1
## 35160.13457 35491.64 35585.576 35595.5898 36021.0112 36085.219
## 1 1 1 1 1 1
## 36124.5737 36149.4835 36189.1017 36197.699 36219.40545 36307.7983
## 1 1 1 1 1 1
## 36397.576 36580.28216 36837.467 36898.73308 36910.60803 36950.2567
## 1 1 1 1 1 1
## 37079.372 37133.8982 37165.1638 37270.1512 37465.34375 37484.4493
## 1 1 1 1 1 1
## 37607.5277 37701.8768 37742.5757 37829.7242 38126.2465 38245.59327
## 1 1 1 1 1 1
## 38282.7495 38344.566 38415.474 38511.6283 38709.176 38711
## 1 1 1 1 1 1
## 38746.3551 38792.6856 38998.546 39047.285 39125.33225 39241.442
## 1 1 1 1 1 1
## 39556.4945 39597.4072 39611.7577 39722.7462 39725.51805 39727.614
## 1 1 1 1 1 1
## 39774.2763 39836.519 39871.7043 39983.42595 40003.33225 40103.89
## 1 1 1 1 1 1
## 40182.246 40273.6455 40419.0191 40720.55105 40904.1995 40932.4295
## 1 1 1 1 1 1
## 40941.2854 40974.1649 41034.2214 41097.16175 41661.602 41676.0811
## 1 1 1 1 1 1
## 41919.097 41949.2441 41999.52 42111.6647 42112.2356 42124.5153
## 1 1 1 1 1 1
## 42211.1382 42303.69215 42560.4304 42760.5022 42856.838 42969.8527
## 1 1 1 1 1 1
## 42983.4585 43254.41795 43578.9394 43753.33705 43813.8661 43896.3763
## 1 1 1 1 1 1
## 43921.1837 43943.8761 44202.6536 44260.7499 44400.4064 44423.803
## 1 1 1 1 1 1
## 44501.3982 44585.45587 44641.1974 45008.9555 45702.02235 45710.20785
## 1 1 1 1 1 1
## 45863.205 46113.511 46130.5265 46151.1245 46200.9851 46255.1125
## 1 1 1 1 1 1
## 46599.1084 46661.4424 46718.16325 46889.2612 47055.5321 47269.854
## 1 1 1 1 1 1
## 47291.055 47305.305 47403.88 47462.894 47496.49445 47896.79135
## 1 1 1 1 1 1
## 47928.03 48173.361 48517.56315 48549.17835 48673.5588 48675.5177
## 1 1 1 1 1 1
## 48824.45 48885.13561 48970.2476 49577.6624 51194.55914 52590.82939
## 1 1 1 1 1 1
## 55135.40209 58571.07448 60021.39897 62592.87309 63770.42801
## 1 1 1 1 1
table(insurance$smoker)
##
## no yes
## 1064 274
table(insurance$sex)
##
## female male
## 662 676
cor(insurance[c('age','bmi','children','charges')])
## age bmi children charges
## age 1.0000000 0.1092719 0.04246900 0.29900819
## bmi 0.1092719 1.0000000 0.01275890 0.19834097
## children 0.0424690 0.0127589 1.00000000 0.06799823
## charges 0.2990082 0.1983410 0.06799823 1.00000000
pairs(insurance[c('age','bmi','children','charges')])
library(psych)
## Warning: package 'psych' was built under R version 4.3.3
##
## Attaching package: 'psych'
##
## The following object is masked from 'package:kernlab':
##
## alpha
pairs.panels(insurance[c('age','bmi','children','charges')])
#Building model:
#m<-lm(dv~iv,data=mydata)
#Making predictions:
#p<-predict(m,test)
ins_model<-lm(charges~age+children+bmi+sex+smoker+region,data=insurance)
ins_model
##
## Call:
## lm(formula = charges ~ age + children + bmi + sex + smoker +
## region, data = insurance)
##
## Coefficients:
## (Intercept) age children bmi
## -11938.5 256.9 475.5 339.2
## sexmale smokeryes regionnorthwest regionsoutheast
## -131.3 23848.5 -353.0 -1035.0
## regionsouthwest
## -960.1
#period character(.) can be used to specify all features excluding those already specified in formula
#eg: ins_model<-lm(charges~.,data=insurance)
summary(ins_model)
##
## Call:
## lm(formula = charges ~ age + children + bmi + sex + smoker +
## 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 ***
## age 256.9 11.9 21.587 < 2e-16 ***
## children 475.5 137.8 3.451 0.000577 ***
## bmi 339.2 28.6 11.860 < 2e-16 ***
## sexmale -131.3 332.9 -0.394 0.693348
## smokeryes 23848.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -353.0 476.3 -0.741 0.458769
## regionsoutheast -1035.0 478.7 -2.162 0.030782 *
## 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-16
insurance$age2<-insurance$age^2
ins_model<-lm(charges~age+children+bmi+sex+smoker+region+age2,data=insurance)
ins_model
##
## Call:
## lm(formula = charges ~ age + children + bmi + sex + smoker +
## region + age2, data = insurance)
##
## Coefficients:
## (Intercept) age children bmi
## -6596.665 -54.575 642.024 335.211
## sexmale smokeryes regionnorthwest regionsoutheast
## -138.428 23859.745 -367.812 -1031.503
## regionsouthwest age2
## -957.546 3.927
insurance$bmi30<-ifelse(insurance$bmi>=30,1,0)
ins_model<-lm(charges~age+children+bmi+sex+smoker+region+age2+bmi30,data=insurance)
ins_model
##
## Call:
## lm(formula = charges ~ age + children + bmi + sex + smoker +
## region + age2 + bmi30, data = insurance)
##
## Coefficients:
## (Intercept) age children bmi
## -2943.176 -28.533 630.402 153.905
## sexmale smokeryes regionnorthwest regionsoutheast
## -166.295 23857.543 -400.518 -888.533
## regionsouthwest age2 bmi30
## -947.681 3.603 2727.552
ins_model2<-lm(charges~age+age2+children+bmi+sex+bmi30*smoker+region,data=insurance)
ins_model2
##
## Call:
## lm(formula = charges ~ age + age2 + children + bmi + sex + bmi30 *
## smoker + region, data = insurance)
##
## Coefficients:
## (Intercept) age age2 children
## 134.251 -32.685 3.732 678.561
## bmi sexmale bmi30 smokeryes
## 120.020 -496.824 -1000.140 13404.687
## regionnorthwest regionsoutheast regionsouthwest bmi30:smokeryes
## -279.204 -828.547 -1222.644 19810.753
insurance$pred<-predict(ins_model2,insurance)
cor(insurance$pred,insurance$charges)
## [1] 0.9308031
plot(insurance$pred,insurance$charges)
#abline(a=0,b=1,col="red",lwd=3,lty=2)
predict(ins_model2,data.frame(age=30,age2=30^2,children=2,bmi=30,sex='male',bmi30=1,smoker='no',region='northeast'))
## 1
## 5972.859
predict(ins_model2,data.frame(age=30,age2=30^2,children=2,bmi=30,sex='female',bmi30=1,smoker='no',region='northeast'))
## 1
## 6469.683
predict(ins_model2,data.frame(age=30,age2=30^2,children=0,bmi=30,sex='male',bmi30=1,smoker='no',region='northeast'))
## 1
## 4615.736
6469.683-4615.736
## [1] 1853.947