Graphing

2015-10-23T21:40:54Z

JL: /* Introduction */

Graphing

2015-10-23T21:29:24Z

JL: /* Line Plots */

= Introduction =

= Line Plots =

For this example we use one of Matlab's sample dataset to plot a simple line plot showing the time series movement of the stock market data.
First Load the data.
<source>
load stockreturns
</source>

The data contains a (100x10) matrix of stock market observations and we are going to plot all of these data point on a single line plot using the <source enclose="none">plot</source> function.

<source>
figure
plot(stocks(:))
</source>

[[File:lineplot1.png]]

To modify an existing plot use the <source enclose="none">hold on</source> command. Subsequent plots will then be added to the current figure. For example to add to a horizontal lines for the mean and another two indicating +/- 1 standard deviation from the mean for the stocks data:

<source>
avg=mean(stocks(:));
sd=std(stocks(:));
hold on
plot(xlim, [avg avg],'-k')
plot(xlim, [avg+sd avg+sd],'--r')
plot(xlim, [avg-sd avg-sd],'--r')
</source>

[[File:lineplot2.png]]

Here, in each case the <source enclose="none">plot</source> function is plotting a straight line between two points. The first argument, <source enclose="none">xlim</source> queries the figure to get the coordinates of the start and end of the x-axis (a two element vector), provides the x coordinates. The second argument is a vector containing the corresponding y coordinates of the two points.

The '-k' argument specifies the plotted line to be a solid black line, whereas the '--r' arguments specifies the plotted line as a red dashed line. Matlab supports a number of line (and marker) types of varying colours; for full details refer to Matlab's documentation on [http://uk.mathworks.com/help/matlab/ref/linespec.html LineSpec].

= Scatter Diagrams =

In this example we use the wage data from the Wooldridge dataset 'wages1'

<source>
figure
scatter(educ,wage)
</source>
[[File:scatterplot1.png]]

Scatter by group, in this case on gender.

<source>
gscatter(educ,wage,female,'rk','do')
xlabel('years of education')
ylabel('average hourly earnings')
legend('female','male','Location','northwest')
</source>
[[File:scatterplot2.png]]

= Histograms =

<source>
hist(stocks(:))
</source>
[[File:histplot1.png]]

<source>
figure
hist(stocks(:),40)
set(get(gca,'child'),'FaceColor','cyan','EdgeColor','blue');
title('Histogram of stock prices')
</source>
[[File:histplot2.png]]

= Distribution Plots =

== Theoretical Distributions ==

<source>
x=linspace(-5,5,1000);
xnorm = normpdf(x);
figure
plot(x,xnorm,'-k','LineWidth',2)
title('Probability density plot of standard Normal distribution')
</source>
[[File:TheoreticalPlot1.png]]

<source>
hold all
df = [1,5,10];
for ii=1:length(df)
xt = tpdf(x,df(ii));
plot(x,xt)
end
title('Comparing t-distributions with standard Normal')
legend('Normal','T-dist df=1','T-dist df=5','T-dist df=10')
</source>
[[File:TheoreticalPlot2.png]]

== Observed Distributions/Kernel Density Plots ==

<source>
figure
[f,xi] = ksdensity(stocks(:));
plot(xi,f,'-k','LineWidth',1.5)
title('Kernel density plot of stock market returns')
</source>
[[File:KernelPlot1.png]]

File:Lineplot2.png

2015-10-23T21:27:27Z

JL: JL uploaded a new version of File:Lineplot2.png

File:Lineplot2.png

2015-10-23T21:26:44Z

JL: JL uploaded a new version of File:Lineplot2.png

2015-07-20T09:10:44Z

JL: /* Data Sets */

R is an open source software that has been been adopted by the statistical community as its standard software package. It is a command driven software, meaning that you will have to give the software written commands to indicate what you do. On first sight this is not as convenient as a menu driven software, but it has the huge advantage that you can collect a large set of commands in a file (script file) and then have R execute all these commands in one go. This then serves as a great documentation of the work you have done and most importantly it makes it easy to change a small aspect of your work and rerun the entire project on the press of a button rather than having to laboriously retrace all your steps through menus.

The fixed cost of learning this software is higher than learning a menu driven statistical software package. But if you engage with this process the rewards will be great.

Last not least, R has a killer advantage. It is free!!!

== Installing the Software ==

[https://youtu.be/EHjakj38Nnw?hd=1 Installation Demonstration]

To work with R you will have to install the basic software package R, but we also advise you to install RStudio, which is an add-on to R (formally called an Integrated Development Environment - IDE) which makes working with R easier.

As this is open-source software that you get for free it is perhaps understandable that the webpages from which you get the R software aren't as slick as you expect. And the language tends to be somewhat more techy, but don't worry, you'll be fine.

So here are the steps you should take.

# Download and install the R software, which is available from the [http://cran.rstudio.com/ CRAN] website. Follow the "Download and Install R" link (and do not be tempted to download the source code!) for your operating system. If you have a window OS only choose the "base" package on the following screen. Then follow the usual installation instructions. You could now already work with R, but we recommend that you first undertake the next step.
# Once we have installed R, we can download and install RStudio. You can download it from the [http://www.rstudio.com/products/rstudio/download/ RStudio] download page.

The basic R software has some basic functionality, but the power of R comes from the ability to use code written to perform statistical and econometric techniques that has been written by other people. These additional pieces of software are called packages and the next step will be to learn how ot use these.

== Data Sets ==

We use a number of datasets on this page. For convenience they are listed here:

{| class="wikitable"
|-
! scope="col"|
! scope="col"| Women's wages
! scope="col"| Crime Statistics
! scope="col"| Baseball Wages
|-
| '''Description'''
| Observations for 753 females on wages, familiar and work circumstances hours worked and wages
| Crime Statistics for 90 counties in North Carolina (US) for Years 1981 to 1987 (Panel Data); includes a number of variables to characterise the counties
| Salary and other information (such as race, position and performance information) for 353 Baseball Players in 1993
|-
| '''Files'''
| [[media:mroz.xls|mroz.xls]] [[media:mroz.csv|mroz.csv]] [[media:mroz.RData|mroz.RData]]
| [[media:crim4.xls|crime4.xls]] [[media:crim4.csv|crime4.csv]]
| [[media:mlb1.xls|mlb1.xls]] [[media:mlb1.csv|mlb1.csv]]
|-
| '''Source'''
| [http://www.cengagebrain.com/cgi-wadsworth/course_products_wp.pl?fid=M20b&product_isbn_issn=9781111531041&token=8D04240DC39B22D05B49B265F2C8E62C6876DDE99FE979BC4A500075EC976963ED1045639B2C75C4B5B2337F07088998 Wooldridge Book Companion Page]
| [http://www.cengagebrain.com/cgi-wadsworth/course_products_wp.pl?fid=M20b&product_isbn_issn=9781111531041&token=8D04240DC39B22D05B49B265F2C8E62C6876DDE99FE979BC4A500075EC976963ED1045639B2C75C4B5B2337F07088998 Wooldridge Book Companion Page]
| [http://www.cengagebrain.com/cgi-wadsworth/course_products_wp.pl?fid=M20b&product_isbn_issn=9781111531041&token=8D04240DC39B22D05B49B265F2C8E62C6876DDE99FE979BC4A500075EC976963ED1045639B2C75C4B5B2337F07088998 Wooldridge Book Companion Page]
|}

Following the links in the above table you will also be able to download R data files for these datasets.

== Basic Tasks ==

To illustrate how to perform basic tasks in R we will use data that you can download from here: [[media:mroz.xls|mroz.xls]]. This is an Excel file that contains a dataset which we will use for our first steps in R. It is a well used cross-sectional dataset with 753 observations of female members of the labour force in the US (in 1975). It contains variables such as the number of children, the wage, the hours worked etc. A bit more detail on the data and the variables can be found in this [[media:mroz_description.pdf|file]]. See also [https://ideas.repec.org/p/boc/bocins/mroz.html].

{| class="wikitable"
|-
! scope="col"| First Steps
! scope="col"| Loading Data and Date Formats
! scope="col"| Basic Data Analysis
! scope="col"| A Regression
|-
| [[R_FirstSteps|Discussion]]
| [[R_Data|Discussion]]
| [[R_Analysis|Discussion]]
| [[R_Regression|Discussion]]
|}

{| class="wikitable"
|-
! scope="col"| Using Packages
! scope="col"| Saving Data and Screen Output
|-
| [[R_Packages|Discussion]]
| [[R_SavingData|Discussion]]
|}

== Bread and Butter Techniques ==

These are standard econometric problems tasks that any applied econometrician, and indeed aspiring economics students, should be familiar with.

{| class="wikitable"
|-
! scope="col"| Dummy variables
! scope="col"| Standard inference
! scope="col"| Regression diagnostics
! scope="col"| Robust standard errors
|-
| [[Dummy Variables in R|Discussion]]
| [[Regression Inference in R|Discussion]]
| [[R_reg_diag|Discussion]]
| [[R_robust_se|Discussion]]
|}

== Intermediate Techniques ==

{| class="wikitable"
|-
! scope="col"| Panel Data
! scope="col"| Instrumental Variables Estimation
! scope="col"| Univariate Time Series Modelling
|-
| [[Panel in R|Discussion]]
| [[IV in R|Discussion]]
| [[R_TimeSeries|Discussion]]
|}

== Econometric Demonstrations ==

In this section you can find code that can be useful to demonstrate a few econometric issues.

{| class="wikitable"
|-
! scope="col"| Demonstrating OLS estimator unbiasedness
! scope="col"| Demonstrating OLS estimator asymptotic behaviour
|-
| [[R_Unbiasedness|Discussion]]
| [[R_Asymptotics|Discussion]]
|}

== Authors, Maintenance and Contributions ==

This wiki was created by [mailto:ralf.becker@manchester.ac.uk Ralf Becker] and [mailto:james.lincoln@manchester.ac.uk James Lincoln] with the financial support of a University of Manchester CHERIL grant. If you have any suggestions please contact us by email. Contributions to this wiki are encouraged. Please contact us for details.

== More references ==

There is a plethora of resources if you want to learn R (which is one reason why this resource does not go into too much detail). Here are a few places to start.

* [http://www.computerworld.com/article/2497143/business-intelligence-beginner-s-guide-to-r-introduction.html?null A Beginner's Guide to R]
* Some R resources provided by [http://www.ats.ucla.edu/stat/r/ UCLA]
* [http://www.statmethods.net Quick-R] web-site and [http://www.manning.com/kabacoff2/RiA2E_meap_ch1.pdf first chapter of R in Action]
* Just TryR it! [http://tryr.codeschool.com/levels/1/challenges/1]