IT and Business Applications Lab - Day9 Assignments

Assignment 1: Create 3 vectors, x, y, z and choose any random values for them, ensuring they are of equal length,
T<- cbind(x,y,z)
Create 3 dimensional plot of the same (of all the 3 types as taught)

Commands :

3D plots:

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

 

>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 the function "geom"

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

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

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

IT and Business Applications Lab - Day8 Assignments

Data Visualization

Visualization can be defined as the graphical representation of information, aimed at providing the viewer with a qualitative understanding of the contents of the information. This may be data, processes, relations, or concepts. Graphical presentation may entail manipulation of graphical entities (points, lines, shapes, images, text) and attributes (color, size, position, shape). Understanding may involve detection, measurement, and comparison, and is enhanced via interactive techniques and provision of the information from multiple views and with multiple techniques.

Why go for data visualization?

• Effective: the viewer gets it (ease of interpretation)
• Accurate: sufficient for correct quantitative evaluation. Lie factor = size of visual effect/size of data effect
• Efficient: minimize data-ink ratio and chart-junk, show data, maximize data-ink ratio, brase non-data-ink, brase redundant data-ink
• Aesthetics: must not offend viewer's senses (e.g. moire patterns)
• Adaptable: can adjust to serve multiple needs

Wolfram Alpha

 The Wolfram Alpha is in the trend these days as the latest search engine. Well, it is not just a search engine, a "computational knowledge engine". While the conceptualization of the this search engine, the creators of Wolfram Alpha were keen to make something better than Google. These include mathematical graphs, unit conversions, historical events, and scientific formulas in the general searches. 

Now, what is it that make Wolfram Alpha better than other visualization tools. Well, the Wolfram Alpha is better than Google as it doesn't just search for web pages but, it gives the exact answers to the vast and ever expanding collection of knowledge and allows the user to discover so much more.

As managers, we are interested in Business Research ie; using data to aid business decision making. Wolfram Alpha is an excellent data analysis tool.

Wolfram Alpha’s Facebook Analytics Tool 

Who’s your oldest friend on Facebook? What’s the most popular photo you've ever posted? When are you most likely to be found updating your status?

I actually know the answers to those questions—and a lot of other arcane facts about my life in social-space, thanks to a new feature on Wolfram Alpha. That’s the ultra-geeky search engine that specializes in providing factual responses to questions rather than directing you to relevant web pages.


My Data Visualization Project - Wolfram Alpha using Facebook data :

This is a video that takes you through the various analysis results that have been made using my facebook data as the input.

Other Features: 

• Interactively manipulate parameters: Move controls and sliders to fully interact with and understand your results.
• Animate dynamic processes: Input physical system parameters and see the associated animation evolve in time.
• Rotate 3D graphics: Click and drag 3D images to rotate and view from any angle.
• Control enhanced visualizations: Click to reveal special controls for many types of visualizations.
• nstantly build interactive interfaces: Use Wolfram|Alpha linguistics to create custom interactive interfaces.
• Resize images: Click maps, plots, or any image and drag the corner to expand the image size.
• Read plot values: Interact with plots with dynamic coordinate labels and crosshairs on the axes.

In other words, there’s little chance that the gatekeepers of our digital lives will stop compiling minutiae about us. But we can hope for—or insist upon—more chances to look at that data ourselves and hopefully gain some insights. In that sense, Wolfram Alpha’s new Facebook reports are an instructive example. And hey, who wouldn’t want to learn more about how to get their friends’ attention?

IT and Business Applications Lab - Day7 Assignments

Panel Data Analysis  -  "Produc" data

Here we analyze three types of model :

• Pooled effect model
• Fixed effect model
• Random effect model 

Then we will determine the best model by using functions:

• pFtest : for determining between fixed and pooled
• plmtest : for determining between pooled and random
• phtest: for determining between random and fixed

Code :

> data(Produc , package ="plm")
> head(Produc)

Data

Pooled Effect Model

> pool <- br="" data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" pooling="" state="" unemp="" util="" water="" year=""> > summary(pool)

Fixed Effect Model:


> fixed <- data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" span="" state="" unemp="" util="" water="" within="" year="">
> summary(fixed)

Random Effect Model:
> random <- data="Produc," emp="" gsp="" hwy="" index="c(" log="" model="(" pc="" pcap="" plm="" random="" span="" state="" unemp="" util="" water="" year="">
> summary(random)

The comparison between the models would be a Hypothesis testing based on the following concept:


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


H0: Pooled Effect Model
H1 : Fixed Effect Model


Code:
> 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 Effect Model.

Random vs Fixed


Null Hypothesis: No Correlation . Random Effect Model
Alternate Hypothesis: Fixed Effect 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 Effect Model.

Inference:

We infer that Fixed effect 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 difference.