mydata, or explicitly specified with the dframe option. The name mydata is by default provided by the rad function included in this package for reading and displaying information about the data in preparation for analysis. If all the variables in the model are not in the same dataframe, the analysis will not be complete.The default analysis provides the model's parameter estimates and corresponding hypothesis tests and confidence intervals, goodness of fit indices, the ANOVA table, correlation matrix of the model's variables, collinearity analysis of the predictor variables, adjusted R-squared for the corresponding models defined by each possible subset of the predictor variables, and, for each observation in the model, analysis of residuals and influence as well as the confidence and prediction intervals. By default the residual analysis lists the data and fitted value for each observation as well as the residual, Studentized residual and Cook's distance, with the first 25 observations listed and sorted by Cook's distance. The output for the confidence and prediction intervals also provides the data and fitted value for each observations, as well as the lower and upper bounds for each of the two intervals. The observations are sorted by the lower bound of each prediction interval. The default analysis for the prediction intervals is for the values of the predictor variables in the data, but additional values can also be specified for the calculation of the prediction intervals.
Three default graphs are also provided. A histogram is provided with superimposed normal and general density plots from the color.density function included in this package. A scatterplot of the residuals with the fitted values is also provided from the color.plot function included in this package. For models with a single predictor variable, a scatterplot of the data is produced, along with the regression line and corresponding confidence and prediction intervals. For multiple regression models, a scatterplot matrix of the variables with the lowess best-fit lines in the model is produced.
Overriding the default settings can turn off features and reduce the number of provided analyses.
reg(my.formula, dframe=mydata, sig.digits=4,
res.rows=NULL, res.sort=c("cooks","rstudent","off"),
pred=TRUE, pred.all=FALSE, pred.sort=c("predint", "off"),
cor=TRUE, subsets=TRUE, collinear=TRUE, relations=TRUE,
cook.cut=1, results=c("full", "brief"), scatter.cor=FALSE,
X1.new=NULL, X2.new=NULL, X3.new=NULL, X4.new=NULL,
X5.new=NULL, show.R=FALSE)formula for specifying a model. For
example, for a response variable named Y and two predictor variables, X1 and X2, specify the corresponding linear model as Y ~ X1 + X2.mydata, otherwise explicitly specify.options
function regarding the digits option. The distinction is that this value applies selectively to portions of the output, the different type of r"all"."cooks", for specifying Cook's distance as the sort
criterion for the display of the rows of data and associated residuals. Other values are "rstudent" for Studentized residuals, and "off" to not prTRUE, which, produces confidence and prediction intervals
for each row of data.FALSE, which, produces prediction intervals only for the first,
middle and last five rows of data."predint", which sorts the rows of data and associated
intervals by the lower bound of each prediction interval. Turn off this sort by specifying a value of "off".TRUE, which prints a correlation matrix of the model variables.TRUE, for producing an analysis from the leaps package
for the adjusted R-squared of all possible models from the set of predictor variables.TRUE, for producing a collinearity analysis from the car
package.TRUE, which indicates to perform all three analyses of relations among
the variables: correlations, collinearity and predictor variable subsets."full".FALSE.lm. The output of the analysis of lm is stored in the object lm.out, which is available for further analysis in the R environment when the reg function has completed. Usually, however, reg automatically provides the analyses from the standard R functions, summary, confint and anova. The residual analysis invokes fitted, resid, rstudent, and cooks.distance. The option for prediction intervals calls the standard R function predict, once with the argument interval="confidence" and once with interval="prediction". Thomas Lumley's leaps package contains the leaps function that provides the analysis of the fit of all possible model subsets.
The purpose of reg is to combine these function calls into one, as well as provide ancillary analyses such as as graphics and of sorting to assist in interpretation, and the analysis of the adjusted R-squared for the models defined by all possible subsets of the predictor variables.For graphics, if there is only one predictor variable in the model, a scatterplot of the data with regression line is produced, along with the plotted confidence and prediction intervals, otherwise the scatterplot matrix of all the variables in the model is generated. Also generated are the histogram of the residuals with superimposed general density curve and the plot of the residuals against the fitted values of the model. For the fitted values plot, the point corresponding to the largest value of Cook's distance is plotted in red with the corresponding value of Cook's distance specified in the subtitle of the plot.
The output for the residual analysis displays by default just the first 25 observations with the largest values of Cook's distance, sorted by this criterion. The output of the prediction intervals is re-organized so that each row's computed fitted value and prediction interval are listed adjacent to the corresponding values of the predictor variables and response variable. Each row of information, the data and corresponding intervals, is by default sorted by the lower bound of the prediction interval. If, by providing values for the options X1.new, X2.new and so forth, to provide new data values for the computation of the corresponding fitted values and prediction intervals, then all combinations of the values for each predictor variable are analyzed.
The analysis of the models defined by each subset of the predictor variables is computed by the leaps function, written by Thomas Lumley, from the leaps package.
The options function is called to turn off the stars for different significance levels (show.signif.stars=FALSE) and to turn off scientific notation for the output (scipen=30).
leaps function from the leaps package.formula, lm, summary.lm, anova, confint, fitted, resid, rstudent, cooks.distance# Generate random data, place in dataframe mydata
X1 <- rnorm(20)
X2 <- rnorm(20)
Y <- .7*X1 + .2*X2 + .6*rnorm(20)
mydata <- data.frame(X1, X2, Y)
# One-predictor regression
# Provide all default analyses including scatterplot etc.
reg(Y ~ X1)
# Multiple regression model
# Provide the full range of default analyses
reg(Y ~ X1 + X2)
# Provide only the brief analysis
reg(Y ~ X1 + X2, results="brief")
# Modify the default settings as specified
reg(Y ~ X1 + X2, res.row=8, res.sort="rstudent", sig.digits=8, pred=FALSE)
# Specify values of the predictor variables for calculating forecasted
# values and the corresponding prediction interval
# Note in this analysis it is just a coincidence that the variables are
# named X1 and X2, which always begin the names X1.new and X2.new
reg(Y ~ X1 + X2, X1.new=seq(.4,.8,.2), X2.new=c(.5,.7))
# Scatterplot matrix with correlation coefficients in upper triangle
# Specify an input dataframe other than mydata
# help(mtcars) to see description of the data, included with R
reg(mpg ~ cyl + disp + hp + drat + wt + gear, scatter.cor=TRUE, dframe=mtcars)Run the code above in your browser using DataLab