Web-based Statistics: Lecture 10

Web-based Statistics:
Lecture 10
Tuesday, May 23, 2000

An Introduction to Rweb

Rweb is a Web-based interface into the statistical analysis package R. R itself is a non-commercial package that has been developed by Robert Gentleman and Ross Ihaka. Its source code is almost compatible with S or Splus. If you know any of these languages it should be easy for you to use R and Rweb.

Main References on R and Rweb

Banfield, J. (1999): "Rweb: Web-based Statistical Analysis", Journal of Statistical Software, Vol. 4, Issue 1.
Gentleman, R., Ihaka, R. (1997): "The R Language", Computing Science and Statistics, Vol. 28, 326-330.
Ihaka, R. (1998): "R: Past and Future History", Computing Science and Statistics, Vol. 30, 392-396.
Ihaka, R., Gentleman, R. (1996): "R: A Language for Data Analysis and Graphics", Journal of Computational and Graphical Statistics, Vol. 5, No. 3, 299-314.

Some References on S and S-Plus

Becker, R. A., Chambers, J. M., and Wilks, A. R. (1988): "The New S Language", Wadsworth & Brooks/Cole, Pacific Grove, CA.
Chambers, J. M. (1998): "Programming With Data", Springer, New York.
Chambers, J. M. and Hastie, T. J. (1993): "Statistical Models in S", Chapman & Hall, New York, London.
Krause, A., Olson, M. (1997): "The Basics of S and S-Plus", Springer, New York.
Spector, P. (1994): "An Introduction to S and S-Plus", Duxbury Press, Belmont, CA.
Venables, W. N. and Ripley, B. D. (1994): "Modern Applied Statistics with S-Plus", Springer, New York, Berlin, Heidelberg.

R and Rweb on the Web

Rweb Home Page: http://www.math.montana.edu/Rweb/
R Home Page: http://www.stat.auckland.ac.nz/r/r.html
R Archive: http://lib.stat.cmu.edu/R/CRAN/
R Notes: http://www.math.montana.edu/Rweb/Rnotes/R.html

Versions of Rweb

Rweb modules: point and click forms useful for introductory statistics classes.
Rweb: simple Web interface into R (not discussed in class).
JavaScript Version of Rweb: similar to, but more enhanced than the simple Rweb interface.

Use of the Rweb modules

Start at http://www.math.montana.edu/Rweb/. Then click on "Rweb modules".

Scroll down on this page until you see Choose Analysis and Data Set. Then make the following selections:

Analysis Menu: Summary
Data Set Menu: External Menu: Use an option below.
Remote Dataset URL: http://www.math.usu.edu/~vukasino/teaching/spring2000/complab/student_data1.prn

Then click on Submit. You should now see the following menu:

Now activate the variables Age, Siblings, Height, and Weight. Also activate Numerical Summaries. Then click on Submit.

You should now see a page that reads Summary Results and has the following output at the bottom:

Rweb:> print(rbind ( Rweb.sum, paste( 'Std Dev:', Rweb.stdv) ), quote=F) 
      Age           Siblings          Height          Weight      
 Min.   :19.00   Min.   : 1.000   Min.   :59.00   Min.   :108.0   
 1st Qu.:21.00   1st Qu.: 3.000   1st Qu.:67.00   1st Qu.:142.5   
 Median :23.00   Median : 4.000   Median :69.00   Median :155.0   
 Mean   :23.07   Mean   : 4.233   Mean   :69.12   Mean   :159.9   
 3rd Qu.:25.00   3rd Qu.: 5.000   3rd Qu.:72.50   3rd Qu.:173.0   
 Max.   :28.00   Max.   :11.000   Max.   :74.00   Max.   :250.0   
 Std Dev: 2.35   Std Dev: 2.1     Std Dev: 3.98   Std Dev: 28.9   
Rweb:>

Now click on Back in your browser. Deactivate Numerical Summaries. See what happens when you select Scatterplots, Histograms, Boxplots, etc.

Experiment with some of the other options for a few minutes and see what happens.

Click Back twice in your browser. You should now be back at the page that contains the Choose Analysis and Data Set menu.

Excercise 1: Now try yourself to calculate a simple linear regression where Weight is the response and Age is the predictor variable. Also display some useful residual plots, e.g., residuals vs. predictor and residuals vs. some of the lurking variables. So, do you think that Age is a good predictor variable for Weight?

Exercise 2: Now try an ANOVA. Make Weight your response and select Gender, Eyecolor, and Major as your factors. Which factors (or interactions) are significant at the 5% level?

Use of the JavaScript Version of Rweb

Start at http://www.math.montana.edu/Rweb/. Then click on "JavaScript Version of Rweb".

Scroll down on this page until you see the Open Code Window button. Click this button. A new window appears. You may have to enlarge this window to see all of its features and controls. The last line in this window should read "Last Modified: ..."

In the field Enter a dataset URL, enter

http://www.math.usu.edu/~vukasino/teaching/spring2000/complab/student_data1.prn

Then copy the following lines into the big input area:

mean(X[,3])
mean(X[,4])
hist(X[,4], main="Siblings")
plot(X[,3], X[,4], main="Age vs Siblings")

Now click on Submit. It takes a few seconds to calculate the results. Then you should see three new windows.

One Window (without a name) contains the input and output produced when executing R. Here you see which commands have been executed internally, possible warnings, and error messages. Check this window carefully if you do not get the expected results in the other two windows.
The window entitled "Rweb Analysis Output" should contain
```
[1] 23.06977
[1] 4.232558
```
which are the arithmetic means for Age and Siblings, respectively.
The window entitled "Rweb images" should contain a histogram of Siblings and a scatterplot of Age vs. Siblings.

Now let us look at these commands line by line:

X is the default name used for the data matrix that is created from the data stored at the given URL. In our case, X is a matrix that consists of 43 rows and 8 columns. For example, column 3 is Age and column 4 is Siblings. Note that R and Rweb are case sensitive, i.e., X is different from x. You will get an error message when you type x instead of X in any of your commands.
With X[,3] and X[,4], we select the entire third column and fourth column of the matrix X. Thus, mean(X[,3]) and mean(X[,4]) provide us with the means of the third column and fourth column of the matrix X, with the means of Age and Siblings.
With hist(X[,4], main="Siblings"), we create a histogram of the fourth column of the matrix X. Note what happens when we omit the part main="Siblings" and just type hist(X[,4]).
Finally, with plot(X[,3], X[,4], main="Age vs Siblings"), we create a scatterplot of the third column (horizontal) and the fourth column (vertical) of the matrix X. Note what happens when we omit the part main="Age vs Siblings" and just type plot(X[,3], X[,4]).

If you made a mistake while typing in your commands, just make a correction in the input area and click on Submit again.

Excercise 3: Now try yourself to calculate a few more summary statistics such as the median and the variance of Height and Weight. First make sure to identify the appropriate columns of the matrix X that represent these two variables. Can you also calculate the correlation between these two variables and draw a scatterplot of Height (horizontal) vs. Weight (vertical)?

Excercise 4: Now try yourself to calculate a simple linear regression where Weight is the response and Age is the predictor variable. The required syntax is result <- lm(response ~ predictor). Here, result <- means that we assign the outcome of the calculation right of <- to a new variable called result. lm represents a function that calculates a linear model. response ~ predictor represents the expression that should be calculated. You have to replace response and predictor with the appropriate columns of the matrix X. Finally, you have to produce some visible output using the command summary(result).

Similarity between R/Rweb and S/Splus

As we said earlier, R/Rweb is very similar to S/Splus. Let us verify this.

Open a new browser window that contains the notes I used in 1997 for a workshop on S and Splus:
http://www.math.usu.edu/~symanzik/teaching/1997_scourse/sintro

Scroll down on this page until you reach the part that reads "A first Example". We do not have to start a graphics window in Rweb (this is done automatically) so we can directly issue some of the commands.

Copy the following commands into the input area of the Rweb code window:

0:10
0:10 * .314
x0 <- 0:10
x0
x1 <- 0:10 * .314
x1
y _ sin (x1)
y
plot (x1, y)
plot (x1, y, main = "Sine of x")
plot (x1, y, main = "Sine of x", xlab = "X Coordinates", ylab = "Y Coordinates")
plot (x1, y, main = "Sine of x", xlab = "X Coordinates", 
  ylab = "Y Coordinates", type = "l")

What happens? Carefully look at the results of the "Rweb Images" and the "Rweb Analysis Output" window. Is this what you expected?

If you have some time during the next few days, you may want to continue working through the S/Splus workshop material and see which commands are working in R/Rweb and which are not working. A homwork question on R/Rweb will be posted later this week.