R Statistical tool Assignment-3

Purpose-
The class focused on using regression analysis on a Data Set. The user needs to identify whether a linear model can at all be fitted, thus performing a check on non-linearity. Importance of QQ plot is also showed from the point of view of finding the range of the independent variable in which the regression analysis can be done. 

Assignment 1: Using mileage groove data,   fit 'lm' and comment on the applicability of 'lm'.

>Data<-read.csv(file.choose,header=T)

>Data

>z1<-Data[,1]

>z2<-Data[,2]

>reg1<-lm(z1~z2)

>reg1

For normal distribution pattern...

>res<-resid(reg1)

>res

Plotting the residues vs the independent variable

>plot(z2,res)

Now the QQ plot 

> qqnorm(res)

> qqline(res)

Verdict: As the plot of the residuals versus the independent variable shows a parabolic plot so we cannot draw a regression on the data set. The function over here is non-linear.

Assignment 2: The alpha-pluto Data

>Data<-read.csv(file.choose( ), header=T)

>Data
>reg1<-lm(Data[,2]~Data[,1])
>res<-resid(reg1)
>res
>plot(Data[,1],res)

Now plotting the Standard deviation of the residuals vs the independent variable

>stdres<-rstandard(reg1)
>stdres
>plot(data[,1],stdres)
>qqnorm(stdres)
>qqline(stdres)

Assignment 3: Hypothesis testing using Anova

>Data<-read.csv(file.choose( ), header=T)
>Data
>Data.anova<-aov(Data[,2]~Data[,1])
>summary(Data.anova)


The P value comes out to be as 0.687 which is greater than 0.05 so we do not have sufficient proof to negate the null hypothesis.