Question

Question 3. For each of the following data sets use R to i) sketch a scatterplot and the line of best fit. ii) calculate the covariance, correlation and r2 values. Interpret each number. Data set 1. x: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 y: -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1 Data set 2. x: 1, 2, 3, 4, 5, 6, 7 y: 5.1, 8.0, 15.5, 10.3, 18.7, 25.3, 22.5 Data set 3. Same as Data set 2 but with a value at x=8. What is this value called? x: 1, 2, 3, 4, 5, 6, 7, 8 y: 5.1, 8.0, 15.5, 10.3, 18.7, 25.3, 22.5, 0

Answer 1

For Data Set 1=

d1 <- read.csv("C:/Users/pcc/Desktop/d1.csv")

>   View(d1)

> x=d1$x

> y=d1$y

> y

[1] -1 0 1 0 -1 0 1 0 -1 0 1 0 -1

## To plot scatter plot ##

> plot(x,y)

## To Add line nest fit ##

> l1=lm(y~x,data=d1)

> l1

 > abline(l1)

> -1.0 -0.5 0.0 0.5 1.0 - Á - No * O No Oo

The Scatter plot shows there is no relation between x and y

## Correlation = ##

> cor(x,y)

 [1] 0

The correlation between X and Y is 0.Hene there is no relation between x and y

## Covariance ##

> cov(y,x)

[1] 0

Here both variables constant,Because the coefficient is zero.

r square = 2.863e-32

### For data 2 = ###
> x= c(1,2,3,4,5,6,7)

y=c(5.1,8.0,15.5,10.3,18.7,25.3,22.5)
> l2=lm(y~x)
> l2

## to plot and add regression line ##
> plot(x,y)  
> abline(l2)

The Scatter plot shows there is strong positive correlation between the two variable.

5 10 15 20 و 25 N - کیا -

> cor(x,y)
[1] 0.9152279

From the correlation we observe that, there is strong positive correlation between the two variable.

> cov(x,y)
[1] 15

Here both variables tend to increase or decrease together,Because the coefficient is positive.

## r square ##

R square = 0.8376

r square imply that,Means the 83.76 % of variation explain by our explainatory variable to our dependent variable.

For data Set 3 =

> x=1:8
> x
[1] 1 2 3 4 5 6 7 8
> y=c(5.1,8.0,15.5,10.3,18.7,25.3,22.5,0)
> l3=lm(y~x)
> plot(x,y)
> abline(l3)

0 5 10 15 20 و 25 4 بی ۔ 5 ه ة ا

Here the Scatter plot shows there is low positive correlation between the two variable.

> cor(x,y)
[1] 0.2468258

Here the Scatter plot shows there is low positive correlation between the two variable.
> cov(x,y)
[1] 5.328571

Here both variables tend to increase or decrease together,Because the coefficient is positive.

> summary(l2)

r squre = 0.0692

r square imply that ,the 6.92 % of variation explain by our explainatory variable to our dependent variable.