Adding Dimensions in R

Assignment 1: 

Create 3 vectors, x, y, z and choose any random values for them, ensuring they are of equal length, bind them together.Create 3 dimensional plots of the same.

Data Set Creation Commands and DataSet :

> data<-rnorm(50,mean=20,sd =10)
> x<-sample(data,10)
> y<-sample(data,10)
> z<-sample(data,10)
> t<-cbind(x,y,z)       

                                                                                                                                                                           

Normal Plot:   plot3d(T[, 1:3])   

Colour Plot: plot3d(T[, 1:3], col = rainbow(1000))

Color Plot of spheres:  plot3d(T[, 1:3], col = rainbow(1000), type = 's')

Assignment 2:

Choose 2 random variables
Create 3 plots:
1. X-Y
2. X-Y|Z (introducing a variable z and cbind it to z and y with 5 diff categories)
3. Color code and draw the graph
4. Smooth and best fit line for the curve

Data set creation for two random variables and then introducing third variable z

> x<-rnorm(5000,mean=20,sd=10)
> y<-rnorm(5000,mean=20,sd=10)
> z1<-sample(letters,5)
> z2<-sample(z1,5000,replace=TRUE)
> z<-as.factor(z2)

Plots:

>qplot(x,y)

>qplot(x,z)

                             

Semi-transparent plot

> qplot(x,z, alpha=I(2/10))

                           

Colour plot

> qplot(x,y, color=z)

                             

Logarithmic colour plot

> qplot(log(x),log(y), color=z)

                               

Best Fit and Smooth curve using "geom"

> qplot(x,y,geom=c("path","smooth"))

                                     

> qplot(x,y,geom=c("point","smooth"))

                                   

> qplot(x,y,geom=c("boxplot","smooth"))

                                         

> qplot(x,y,geom=c("boxplot","jitter"))

                 

WOLFRAM/ALPHA Personal Analytics for Facebook

To get your personal analytics report of Facebook all you have to do is type “Facebook report” into the standard Wolfram|Alpha website.

1) If you’re doing this for the first time, you’ll be prompted to authenticate the Wolfram Connection app in Facebook, and then sign in to Wolfram|Alpha . And as soon as you’ve done that, Wolfram|Alpha will immediately get to work generating a personal analytics report from the data it can get about you through Facebook.

Here’s the beginning of the report I get today when I do this:

2)After this , I get my report .Reports start with my basic personal information & which places I belong to :

     

3)We can get demographic profile of our friends which tells you % of males & females as well age profile of all friends.

4)We come to know what are the words that we talk the most while we use the facebook .

6) We can also get to know the time when when we use the facebook the most .

                      

 7) We can find the pictures as well as the status update which we were like the most .

8) We can find the places where are friends are located. 

9) We can also find Relationship status of the friends on this with the help of a pie diagram.

           Note : Wolfram Alpha has a wide number application apart from this . It is helpful in various area such as statistic,corporate finance ,Investment banking etc.http://www.wolframalpha.com/

Assignment 8 : Panel Data Analysis

There are three types of models:

•       Pooled affect model
•       Fixed affect model
•       Random affect model 

We will be determining which model is the best by using functions:
       pFtest : for determining between fixed and pooled
       plmtest : for determining between pooled and random
       phtest: for determining between random and fixed

The data can be loaded using the following commands:-
data(Produc , package =”plm”)

head(Produc)

Pooled Affect Model 
pool <-plm( log(pcap) ~log(hwy)+ log(water)+ log(util) + log(pc) + log(gsp) + log(emp) + log(unemp), data=Produc,model=(“pooling”),index =c(“state”,”year”))
summary(pool)

Fixed Affect Model:

fixed<-plm( log(pcap) ~log(hwy)+ log(water)+ log(util) + log(pc) + log(gsp) + log(emp) + log(unemp), data=Produc,model=(“within”),index =c(“state”,”year”))

summary(fixed)

                 

                    

Random Affect Model:

random <-plm( log(pcap) ~log(hwy)+ log(water)+ log(util) + log(pc) + log(gsp) + log(emp) + log(unemp), data=Produc,model=(“random”),index =c(“state”,”year”))

> summary(random)

Comparison

This can be done through Hypothesis testing between the models as follows:

H0: Null Hypothesis: the individual index and time based params are all zero

H1: Alternate Hypothesis: atleast one of the index and time based params is non zero

Pooled vs Fixed

Null Hypothesis: Pooled Affect Model

Alternate Hypothesis : Fixed Affect Model

Command:

 > pFtest(fixed,pool)

Result:

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)
F = 56.6361, df1 = 47, df2 = 761, p-value < 2.2e-16
alternative hypothesis: significant effects 

Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Fixed Affect Model.

Pooled vs Random

Null Hypothesis: Pooled Affect Model

Alternate Hypothesis: Random Affect Model

Command :

> plmtest(pool)

Result:

 Lagrange Multiplier Test – (Honda)

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

normal = 57.1686, p-value < 2.2e-16
alternative hypothesis: significant effects 

 Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Random Affect Model.

Random vs Fixed

Null Hypothesis: No Correlation . Random Affect Model

Alternate Hypothesis: Fixed Affect Model

Command:

 > phtest(fixed,random)

Result: 

 Hausman Test

data:  log(pcap) ~ log(hwy) + log(water) + log(util) + log(pc) + log(gsp) + log(emp) + log(unemp)

chisq = 93.546, df = 7, p-value < 2.2e-16
alternative hypothesis: one model is inconsistent . 

Since the p value is negligible so we reject the Null Hypothesis and hence Alternate hypothesis is accepted which is to accept Fixed Affect Model.

Conclusion: 

So after making all the tests we come to the conclusion that Fixed Affect Model is best suited to do the panel data analysis for “Produc” data set.

Hence , we conclude that within the same id i.e. within same “state” there is no variation