wc.at <- read.csv("E:\\New Volume\\DataScience Yogesh\\R _Codes\\Simple Linear Regression\\wc-at.csv") # choose the wc-at.csv #data set

x <- read.csv("E:\\New Volume\\DataScience Yogesh\\R _Codes\\Simple Linear Regression\\x.csv")
dim(wc.at)

## [1] 109   2

View(wc.at)
#var(Waist)
attach(wc.at)
summary(wc.at)

##      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 ...

summary(wc.at)

##      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

sd(Waist)

## [1] 13.55912

# Implementation of Linear

m1 <- lm(AT ~ Waist,data = wc.at)
coef(m1)

## (Intercept)       Waist 
## -215.981488    3.458859

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

pv1 <- predict(m1,newdata = x)
pv1

##         1         2         3         4 
##  40.31999 -19.86416  36.86113   9.88203

class(pv1)

## [1] "numeric"

pv <- as.data.frame(pv1)

final1 <- data.frame(x,pv1)