data("cars")
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
glimpse(cars)
## Rows: 50
## Columns: 2
## $ speed <dbl> 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13…
## $ dist <dbl> 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34…
plot(cars)
car_model<-lm(dist~speed,data=cars)
summary(car_model)
##
## Call:
## lm(formula = dist ~ speed, data = cars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.069 -9.525 -2.272 9.215 43.201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.5791 6.7584 -2.601 0.0123 *
## speed 3.9324 0.4155 9.464 1.49e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438
## F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12
coef(car_model)
## (Intercept) speed
## -17.579095 3.932409
abline(car_model,col='red')
fitted(car_model)
## 1 2 3 4 5 6 7 8
## -1.849460 -1.849460 9.947766 9.947766 13.880175 17.812584 21.744993 21.744993
## 9 10 11 12 13 14 15 16
## 21.744993 25.677401 25.677401 29.609810 29.609810 29.609810 29.609810 33.542219
## 17 18 19 20 21 22 23 24
## 33.542219 33.542219 33.542219 37.474628 37.474628 37.474628 37.474628 41.407036
## 25 26 27 28 29 30 31 32
## 41.407036 41.407036 45.339445 45.339445 49.271854 49.271854 49.271854 53.204263
## 33 34 35 36 37 38 39 40
## 53.204263 53.204263 53.204263 57.136672 57.136672 57.136672 61.069080 61.069080
## 41 42 43 44 45 46 47 48
## 61.069080 61.069080 61.069080 68.933898 72.866307 76.798715 76.798715 76.798715
## 49 50
## 76.798715 80.731124
residuals(car_model)
## 1 2 3 4 5 6 7
## 3.849460 11.849460 -5.947766 12.052234 2.119825 -7.812584 -3.744993
## 8 9 10 11 12 13 14
## 4.255007 12.255007 -8.677401 2.322599 -15.609810 -9.609810 -5.609810
## 15 16 17 18 19 20 21
## -1.609810 -7.542219 0.457781 0.457781 12.457781 -11.474628 -1.474628
## 22 23 24 25 26 27 28
## 22.525372 42.525372 -21.407036 -15.407036 12.592964 -13.339445 -5.339445
## 29 30 31 32 33 34 35
## -17.271854 -9.271854 0.728146 -11.204263 2.795737 22.795737 30.795737
## 36 37 38 39 40 41 42
## -21.136672 -11.136672 10.863328 -29.069080 -13.069080 -9.069080 -5.069080
## 43 44 45 46 47 48 49
## 2.930920 -2.933898 -18.866307 -6.798715 15.201285 16.201285 43.201285
## 50
## 4.268876
nx1<-data.frame(speed=c(21.5))
predict(car_model,nx1)
## 1
## 66.96769
nx<-data.frame(speed=c(21.5,25.0,25.5,26.0,26.5,27.0,28.0))
plot(nx$speed,predict(car_model,nx),col='red',cex=2,pch=20)
abline(car_model)
library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
library(mlbench)
library(dplyr)
data(Sonar)
glimpse(Sonar)
## Rows: 208
## Columns: 61
## $ V1 <dbl> 0.0200, 0.0453, 0.0262, 0.0100, 0.0762, 0.0286, 0.0317, 0.0519, …
## $ V2 <dbl> 0.0371, 0.0523, 0.0582, 0.0171, 0.0666, 0.0453, 0.0956, 0.0548, …
## $ V3 <dbl> 0.0428, 0.0843, 0.1099, 0.0623, 0.0481, 0.0277, 0.1321, 0.0842, …
## $ V4 <dbl> 0.0207, 0.0689, 0.1083, 0.0205, 0.0394, 0.0174, 0.1408, 0.0319, …
## $ V5 <dbl> 0.0954, 0.1183, 0.0974, 0.0205, 0.0590, 0.0384, 0.1674, 0.1158, …
## $ V6 <dbl> 0.0986, 0.2583, 0.2280, 0.0368, 0.0649, 0.0990, 0.1710, 0.0922, …
## $ V7 <dbl> 0.1539, 0.2156, 0.2431, 0.1098, 0.1209, 0.1201, 0.0731, 0.1027, …
## $ V8 <dbl> 0.1601, 0.3481, 0.3771, 0.1276, 0.2467, 0.1833, 0.1401, 0.0613, …
## $ V9 <dbl> 0.3109, 0.3337, 0.5598, 0.0598, 0.3564, 0.2105, 0.2083, 0.1465, …
## $ V10 <dbl> 0.2111, 0.2872, 0.6194, 0.1264, 0.4459, 0.3039, 0.3513, 0.2838, …
## $ V11 <dbl> 0.1609, 0.4918, 0.6333, 0.0881, 0.4152, 0.2988, 0.1786, 0.2802, …
## $ V12 <dbl> 0.1582, 0.6552, 0.7060, 0.1992, 0.3952, 0.4250, 0.0658, 0.3086, …
## $ V13 <dbl> 0.2238, 0.6919, 0.5544, 0.0184, 0.4256, 0.6343, 0.0513, 0.2657, …
## $ V14 <dbl> 0.0645, 0.7797, 0.5320, 0.2261, 0.4135, 0.8198, 0.3752, 0.3801, …
## $ V15 <dbl> 0.0660, 0.7464, 0.6479, 0.1729, 0.4528, 1.0000, 0.5419, 0.5626, …
## $ V16 <dbl> 0.2273, 0.9444, 0.6931, 0.2131, 0.5326, 0.9988, 0.5440, 0.4376, …
## $ V17 <dbl> 0.3100, 1.0000, 0.6759, 0.0693, 0.7306, 0.9508, 0.5150, 0.2617, …
## $ V18 <dbl> 0.2999, 0.8874, 0.7551, 0.2281, 0.6193, 0.9025, 0.4262, 0.1199, …
## $ V19 <dbl> 0.5078, 0.8024, 0.8929, 0.4060, 0.2032, 0.7234, 0.2024, 0.6676, …
## $ V20 <dbl> 0.4797, 0.7818, 0.8619, 0.3973, 0.4636, 0.5122, 0.4233, 0.9402, …
## $ V21 <dbl> 0.5783, 0.5212, 0.7974, 0.2741, 0.4148, 0.2074, 0.7723, 0.7832, …
## $ V22 <dbl> 0.5071, 0.4052, 0.6737, 0.3690, 0.4292, 0.3985, 0.9735, 0.5352, …
## $ V23 <dbl> 0.4328, 0.3957, 0.4293, 0.5556, 0.5730, 0.5890, 0.9390, 0.6809, …
## $ V24 <dbl> 0.5550, 0.3914, 0.3648, 0.4846, 0.5399, 0.2872, 0.5559, 0.9174, …
## $ V25 <dbl> 0.6711, 0.3250, 0.5331, 0.3140, 0.3161, 0.2043, 0.5268, 0.7613, …
## $ V26 <dbl> 0.6415, 0.3200, 0.2413, 0.5334, 0.2285, 0.5782, 0.6826, 0.8220, …
## $ V27 <dbl> 0.7104, 0.3271, 0.5070, 0.5256, 0.6995, 0.5389, 0.5713, 0.8872, …
## $ V28 <dbl> 0.8080, 0.2767, 0.8533, 0.2520, 1.0000, 0.3750, 0.5429, 0.6091, …
## $ V29 <dbl> 0.6791, 0.4423, 0.6036, 0.2090, 0.7262, 0.3411, 0.2177, 0.2967, …
## $ V30 <dbl> 0.3857, 0.2028, 0.8514, 0.3559, 0.4724, 0.5067, 0.2149, 0.1103, …
## $ V31 <dbl> 0.1307, 0.3788, 0.8512, 0.6260, 0.5103, 0.5580, 0.5811, 0.1318, …
## $ V32 <dbl> 0.2604, 0.2947, 0.5045, 0.7340, 0.5459, 0.4778, 0.6323, 0.0624, …
## $ V33 <dbl> 0.5121, 0.1984, 0.1862, 0.6120, 0.2881, 0.3299, 0.2965, 0.0990, …
## $ V34 <dbl> 0.7547, 0.2341, 0.2709, 0.3497, 0.0981, 0.2198, 0.1873, 0.4006, …
## $ V35 <dbl> 0.8537, 0.1306, 0.4232, 0.3953, 0.1951, 0.1407, 0.2969, 0.3666, …
## $ V36 <dbl> 0.8507, 0.4182, 0.3043, 0.3012, 0.4181, 0.2856, 0.5163, 0.1050, …
## $ V37 <dbl> 0.6692, 0.3835, 0.6116, 0.5408, 0.4604, 0.3807, 0.6153, 0.1915, …
## $ V38 <dbl> 0.6097, 0.1057, 0.6756, 0.8814, 0.3217, 0.4158, 0.4283, 0.3930, …
## $ V39 <dbl> 0.4943, 0.1840, 0.5375, 0.9857, 0.2828, 0.4054, 0.5479, 0.4288, …
## $ V40 <dbl> 0.2744, 0.1970, 0.4719, 0.9167, 0.2430, 0.3296, 0.6133, 0.2546, …
## $ V41 <dbl> 0.0510, 0.1674, 0.4647, 0.6121, 0.1979, 0.2707, 0.5017, 0.1151, …
## $ V42 <dbl> 0.2834, 0.0583, 0.2587, 0.5006, 0.2444, 0.2650, 0.2377, 0.2196, …
## $ V43 <dbl> 0.2825, 0.1401, 0.2129, 0.3210, 0.1847, 0.0723, 0.1957, 0.1879, …
## $ V44 <dbl> 0.4256, 0.1628, 0.2222, 0.3202, 0.0841, 0.1238, 0.1749, 0.1437, …
## $ V45 <dbl> 0.2641, 0.0621, 0.2111, 0.4295, 0.0692, 0.1192, 0.1304, 0.2146, …
## $ V46 <dbl> 0.1386, 0.0203, 0.0176, 0.3654, 0.0528, 0.1089, 0.0597, 0.2360, …
## $ V47 <dbl> 0.1051, 0.0530, 0.1348, 0.2655, 0.0357, 0.0623, 0.1124, 0.1125, …
## $ V48 <dbl> 0.1343, 0.0742, 0.0744, 0.1576, 0.0085, 0.0494, 0.1047, 0.0254, …
## $ V49 <dbl> 0.0383, 0.0409, 0.0130, 0.0681, 0.0230, 0.0264, 0.0507, 0.0285, …
## $ V50 <dbl> 0.0324, 0.0061, 0.0106, 0.0294, 0.0046, 0.0081, 0.0159, 0.0178, …
## $ V51 <dbl> 0.0232, 0.0125, 0.0033, 0.0241, 0.0156, 0.0104, 0.0195, 0.0052, …
## $ V52 <dbl> 0.0027, 0.0084, 0.0232, 0.0121, 0.0031, 0.0045, 0.0201, 0.0081, …
## $ V53 <dbl> 0.0065, 0.0089, 0.0166, 0.0036, 0.0054, 0.0014, 0.0248, 0.0120, …
## $ V54 <dbl> 0.0159, 0.0048, 0.0095, 0.0150, 0.0105, 0.0038, 0.0131, 0.0045, …
## $ V55 <dbl> 0.0072, 0.0094, 0.0180, 0.0085, 0.0110, 0.0013, 0.0070, 0.0121, …
## $ V56 <dbl> 0.0167, 0.0191, 0.0244, 0.0073, 0.0015, 0.0089, 0.0138, 0.0097, …
## $ V57 <dbl> 0.0180, 0.0140, 0.0316, 0.0050, 0.0072, 0.0057, 0.0092, 0.0085, …
## $ V58 <dbl> 0.0084, 0.0049, 0.0164, 0.0044, 0.0048, 0.0027, 0.0143, 0.0047, …
## $ V59 <dbl> 0.0090, 0.0052, 0.0095, 0.0040, 0.0107, 0.0051, 0.0036, 0.0048, …
## $ V60 <dbl> 0.0032, 0.0044, 0.0078, 0.0117, 0.0094, 0.0062, 0.0103, 0.0053, …
## $ Class <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R…
ucla<-read.csv('https://stats.idre.ucla.edu/stat/data/binary.csv')
library(dplyr)
glimpse(ucla)
## Rows: 400
## Columns: 4
## $ admit <int> 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1…
## $ gre <int> 380, 660, 800, 640, 520, 760, 560, 400, 540, 700, 800, 440, 760,…
## $ gpa <dbl> 3.61, 3.67, 4.00, 3.19, 2.93, 3.00, 2.98, 3.08, 3.39, 3.92, 4.00…
## $ rank <int> 3, 3, 1, 4, 4, 2, 1, 2, 3, 2, 4, 1, 1, 2, 1, 3, 4, 3, 2, 1, 3, 2…
ucla$admit<-as.factor(ucla$admit)
glimpse(ucla)
## Rows: 400
## Columns: 4
## $ admit <fct> 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1…
## $ gre <int> 380, 660, 800, 640, 520, 760, 560, 400, 540, 700, 800, 440, 760,…
## $ gpa <dbl> 3.61, 3.67, 4.00, 3.19, 2.93, 3.00, 2.98, 3.08, 3.39, 3.92, 4.00…
## $ rank <int> 3, 3, 1, 4, 4, 2, 1, 2, 3, 2, 4, 1, 1, 2, 1, 3, 4, 3, 2, 1, 3, 2…
m<-glm(admit~.,data=ucla,family = "binomial")
summary(m)
##
## Call:
## glm(formula = admit ~ ., family = "binomial", data = ucla)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.449548 1.132846 -3.045 0.00233 **
## gre 0.002294 0.001092 2.101 0.03564 *
## gpa 0.777014 0.327484 2.373 0.01766 *
## rank -0.560031 0.127137 -4.405 1.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 499.98 on 399 degrees of freedom
## Residual deviance: 459.44 on 396 degrees of freedom
## AIC: 467.44
##
## Number of Fisher Scoring iterations: 4
exp(0.777014)
## [1] 2.174968
exp(-0.560031)
## [1] 0.5711914
s<-data.frame(gre=c(376),gpa=c(3.6),rank=c(3))
predict(m,newdata = s, type = 'response')
## 1
## 0.1869631
s<-data.frame(gre=c(376),gpa=c(4.0),rank=c(3))
predict(m,newdata = s, type = 'response')
## 1
## 0.2388382
s<-data.frame(gre=c(420),gpa=c(4.5),rank=c(3))
predict(m,newdata = s, type = 'response')
## 1
## 0.3385823