wc.at <- read.csv("D:\\New Volume\\DataScience Yogesh\\R _Codes\\Simple Linear Regression\\wc-at.csv") # choose the wc-at.csv data set
dim(wc.at) # dimesnsion of Dataset
## [1] 109 2
#View(wc.at)
attach(wc.at)
summary(wc.at) # Summary Statistics
## Waist AT
## Min. : 63.5 Min. : 11.44
## 1st Qu.: 80.0 1st Qu.: 50.88
## Median : 90.8 Median : 96.54
## Mean : 91.9 Mean :101.89
## 3rd Qu.:104.0 3rd Qu.:137.00
## Max. :121.0 Max. :253.00
windows()
plot(AT,Waist)
#plot(x,y) # Syntax
# Correlation coefficient value for Waist and FAT Data
#cor(x,y) # Syntax
cor(AT,Waist)
## [1] 0.8185578
cor(Waist,AT)
## [1] 0.8185578
#dim(wc.at)
class(wc.at)
## [1] "data.frame"
colnames(wc.at)
## [1] "Waist" "AT"
str(wc.at)
## 'data.frame': 109 obs. of 2 variables:
## $ Waist: num 74.8 72.6 81.8 84 74.7 ...
## $ AT : num 25.7 25.9 42.6 42.8 29.8 ...
sum
## function (..., na.rm = FALSE) .Primitive("sum")
sd(Waist)
## [1] 13.55912
# Implementation of Linear
m1 <- lm(AT ~ Waist,data = wc.at)
summary(m1)
##
## Call:
## lm(formula = AT ~ Waist, data = wc.at)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.288 -19.143 -2.939 16.376 90.342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -215.9815 21.7963 -9.909 <2e-16 ***
## Waist 3.4589 0.2347 14.740 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 33.06 on 107 degrees of freedom
## Multiple R-squared: 0.67, Adjusted R-squared: 0.667
## F-statistic: 217.3 on 1 and 107 DF, p-value: < 2.2e-16
PV <- predict(m1,newdata = wc.at)
PV
## 1 2 3 4 5 6 7
## 42.568252 35.131704 66.953210 74.389758 42.222366 32.537559 63.840237
## 8 9 10 11 12 13 14
## 72.487385 3.656083 37.207020 32.710502 43.432966 36.861134 57.268404
## 15 16 17 18 19 20 21
## 50.350685 22.160981 46.718883 40.492936 39.282335 46.545940 49.831856
## 22 23 24 25 26 27 28
## 63.840237 60.381377 92.548770 67.644982 102.233576 83.555735 62.456693
## 29 30 31 32 33 34 35
## 81.480420 69.374412 72.833271 88.744024 98.082945 93.240542 136.822170
## 36 37 38 39 40 41 42
## 110.880725 98.774717 140.281029 60.727263 57.268404 72.833271 46.891826
## 43 44 45 46 47 48 49
## 62.456693 83.209849 71.103842 154.462353 110.188953 110.880725 59.689606
## 50 51 52 53 54 55 56
## 58.306062 94.624085 73.870929 78.713332 45.162396 55.193088 55.884860
## 57 58 59 60 61 62 63
## 87.706367 82.518078 79.750990 73.525043 52.426001 77.675674 60.035492
## 64 65 66 67 68 69 70
## 158.612984 197.698095 198.735753 117.798443 148.928178 147.198748 154.116467
## 71 72 73 74 75 76 77
## 154.116467 133.363311 119.527873 129.904451 157.575326 129.904451 140.281029
## 78 79 80 81 82 83 84
## 143.739889 150.657608 161.034186 142.010459 164.493045 164.493045 171.410764
## 85 86 87 88 89 90 91
## 159.304756 143.739889 167.951905 159.304756 202.540498 161.034186 121.257303
## 92 93 94 95 96 97 98
## 148.928178 122.986732 110.880725 119.527873 147.198748 150.657608 126.445592
## 99 100 101 102 103 104 105
## 98.774717 138.551600 150.657608 161.380072 181.787342 133.363311 130.250337
## 106 107 108 109
## 106.730093 136.130398 157.229440 159.304756
class(PV)
## [1] "numeric"
PV <- as.data.frame(PV)
final1 <-cbind(wc.at,PV)
x <- read.csv("D:\\New Volume\\DataScience Yogesh\\R _Codes\\Simple Linear Regression\\x.csv") # choose the wc-at.csv data set
pred1 <- predict(m1,newdata = x)
pred1
## 1 2 3 4
## 40.31999 -19.86416 36.86113 9.88203
m2 <- lm(log(AT) ~ Waist,data = wc.at)
summary(m2)
##
## Call:
## lm(formula = log(AT) ~ Waist, data = wc.at)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.05086 -0.21688 0.03623 0.23044 0.82862
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.741021 0.232628 3.185 0.00189 **
## Waist 0.040252 0.002504 16.073 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3529 on 107 degrees of freedom
## Multiple R-squared: 0.7071, Adjusted R-squared: 0.7044
## F-statistic: 258.3 on 1 and 107 DF, p-value: < 2.2e-16