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Basic Analysis in S-PlusHere's our sample data file again, in comma-delimited format. Copy it to a text file, save it and read it into an S-Plus object called data to follow along with the tutorial. country,ud,sd Sweden,82.4,111.84 Israel,80,73.17 Iceland,74.3,17.25 Finland,73.3,59.33 Belgium,71.9,43.25 Denamrk,69.8,90.24 Ireland,68.1,0 Austria,65.6,48.67 NZ,59.4,60 Norway,58.9,83.08 Australia,51.4,33.74 Italy,50.6,0 UK,48,43.67 Germany,39.6,35.33 Netherlands,37.7,31.50 Switzerland,35.4,11.87 Canada,31.2,0 Japan,31,1.92 France,28.2,8.67 USA,24.5,0
Referring to VariablesApart from the identifier country, there are two variables in this data set: union density (ud) and social democratic government ( sd). S-Plus gives you several ways to refer to variables in a data.frame. S-Plus recognizes a $ as indicating a sub-object for a particular object. For example, if you type data$ud you will get a listing of the union density variable. A simple way to make the variables available is to attach the data frame, which makes the variables available act as if they were objects themselves: attach(data)Now the variables can be referred to simply by their names. Summary StatisticsYou might want to know some things about these variables, like their mean, range, standard deviation, and so forth. Several commands provide convenient ways to extract basic summary statistics. They are: mean(), median(), cor(), var(), and summary(). The command summary(object) is the most useful because it outputs several statistics of interest. Now let's move on to regression. Regression - Linear Models using lm()The lm() function of S-Plus fits a simple linear regression model based on several parameters. Here is a description of a basic command, and a listing of those parameters:
data = dataframe, na.action = na.fail) Note that all S-Plus commands which fit a model include a ~ in the equation. The ~ separates the dependent variable from the independent variables. Now
Lets do an example with the data from before so that we can understand the different parts of regression output.
Reading OutputLearning to read the output and get the full extent of output from Splus is very important. To see the model you just created, you can type out1 and it will give you some output which is not particularly interesting. It does not give us significance tests and other useful information. We can get this information with the summary() command. To see the object we just created type summary(out1). You should see the following output. Call: lm(formula = ud ~ sd, data = data1) Residuals: Min 1Q Median 3Q Max -15.38 -10.27 -3.558 10.81 28.22 Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 39.8841 4.8127 8.2873 0.0000 sd 0.3764 0.0962 3.9131 0.0010 Residual standard error: 14.16 on 18 degrees of freedom Multiple R-Squared: 0.4597 F-statistic: 15.31 on 1 and 18 degrees of freedom, the p-value is 0.001019 Correlation of Coefficients: (Intercept) sd -0.753 Notice all the pieces of information. First it gives you the call or formula and specifications that S-Plus uses to create the linear model object. Next it gives you summary statistics of the residuals which we will not deal with for now. Then note that it gives you coefficients, standard errors, and t-values and their associated probabilities for each of the variables in your equation. These you should know how to read. Remember that in general you're looking for significance levels less than .05. Then you get some statistics for the model: residual standard error, multiple R-squared, and the F-statistics with its associated probability. Finally you're given the correlation of the coefficients in your model. There are some good things to know about the way Splus works. Do you remember that you can extract sub-objects with a $. We used this to look at individual variables in a data frame. We can also use it to look at sub-objects of regression output. Before we do that, we need to know what all the sub-objects are. To find this out, type names(out1) You should see a list of subobjects like this: [1] "coefficients" "residuals" "fitted.values" "effects" [5] "R" "rank" "assign" "df.residual" [9] "contrasts" "terms" "call" Each of these subobjects can now be extracted. For example, if we are interested in the residual values, we can type out1$residuals to see the residuals. This will be very convenient when you need to do diagnostics. |