loading libraries

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 3.3.3

library(corrgram)

## Warning: package 'corrgram' was built under R version 3.3.3

library(gridExtra)

## Warning: package 'gridExtra' was built under R version 3.3.3

Dataset

# height in cms
hght <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131, 153, 177, 148, 189, 138, 146, 199, 167, 153, 130)
# weight in kgs
wght <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48, 65, 84, 59, 93, 49, 55, 79, 75, 66, 49)

Dataset

dfrModel <- data.frame(hght, wght)
names(dfrModel) <- c("hght","wght")
head(dfrModel)

##   hght wght
## 1  151   63
## 2  174   81
## 3  138   56
## 4  186   91
## 5  128   47
## 6  136   57

# check outliers in wght
WGHTPlot <- ggplot(dfrModel, aes(x="", y=wght)) +
            geom_boxplot(aes(fill=wght), color="green") +
            labs(title="WGHT Outliers")
                              
# check out hght
HGHTPlot <- ggplot(dfrModel, aes(x="", y=hght)) +
            geom_boxplot(aes(fill=hght), color="blue") +
            labs(title="HGHT Outliers")
# show plot
grid.arrange(HGHTPlot, WGHTPlot, nrow=1, ncol=2)

Correlation

# correlation coefficient
cor(dfrModel$hght, dfrModel$wght)

## [1] 0.944644

#cor(x, y, method = c("pearson", "kendall", "spearman"))
# correlation test
cor.test(dfrModel$hght, dfrModel$wght)

## 
##  Pearson's product-moment correlation
## 
## data:  dfrModel$hght and dfrModel$wght
## t = 12.215, df = 18, p-value = 3.788e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8627911 0.9782375
## sample estimates:
##      cor 
## 0.944644

#cor.test(x, y, method=c("pearson", "kendall", "spearman"))

Observation The cor function gives us 0.944644 correlations which indicates a strong positive correlation between the height of the person and his/her weight.

Correlation Visualization

# visualize correlation
pairs(dfrModel)

#plot(dfrModel)

# visualize correlation
corrgram(dfrModel)

Plot Graph

# base chart
plot(dfrModel$wght,dfrModel$hght, col="blue", main="Regression",
abline(lm(dfrModel$hght~dfrModel$wght)), cex=1, pch=16, xlab="Height in cms", ylab="Weight in kgs")

# ggplot
ggplot(dfrModel, aes(x=hght, y=wght)) +
    geom_point(shape=19, colour="blue", fill="blue") +
    geom_smooth(method='lm', formula=y~x) +
    labs(title="hght & Wght Regression") +
    labs(x="Height in cms") +
    labs(y="Weight in kgs")

Linear Model

x <- dfrModel$hght
y <- dfrModel$wght
slmModel <- lm(y~x)

Observation A linear model is created successfully

# print summary
summary(slmModel)

## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.1573  -1.7267   0.7701   2.6045   6.2102 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -33.55669    8.25032  -4.067 0.000723 ***
## x             0.63675    0.05213  12.215 3.79e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.846 on 18 degrees of freedom
## Multiple R-squared:  0.8924, Adjusted R-squared:  0.8864 
## F-statistic: 149.2 on 1 and 18 DF,  p-value: 3.788e-10

Observation For predicting the Values ,P value should be less then 0.05 hence indicating that the above model can be used for predicting the weights of the indiviuals

R square should be close to 1 as possibile as R sqaure is 0.88 it indicates that the model is good for predicting the weights of the individuals

Test Data

# find wght of a person with height  160,170,180
dfrTest <- data.frame(x=c(160,170,180))
#names(dfrTest) <- c("x")
dfrTest

##     x
## 1 160
## 2 170
## 3 180

Observation The above Data Frame is created for predicting the Weights of the Indivudals

Predict

result <-  predict(slmModel, dfrTest)
print(result)

##        1        2        3 
## 68.32394 74.69148 81.05902

Observation The above weights are of Indivudals with Heights of 160cm,170cm and 180cm as created in the data frame

Assignment 1

Yashvi Trivedi

18th July, 2017

Simple Linear Regression

Problem Defination

loading libraries

Dataset