reg, reg.brief, reg.explainAutomatically provides a comprehensive regression analysis with graphics from a single, simple function call with many default settings, each of which can be re-specified. By default the data exists as a data frame with the default name of mydata, such as data read by the lessR rad function. Specify the model in the function call according to an R formula, that is, the response variable followed by a tilde, followed by the list of predictor variables, each pair separated by a plus sign.
Default output includes the inferential analysis of the estimated coefficients and model, correlation matrix, sorted residuals and Cook's Distance, and sorted prediction intervals for existing data or new data. For multiple regression models, also included is an analysis of the fit of all possible model subsets and an analysis of collinearity. The default output also includes three graphs beginning with a histogram of the residuals with superimposed normal and general density curves. The second graph is a scatterplot of the fitted values with the residuals and the corresponding lowess curve. The point corresponding to the largest value of Cook's Distance is labeled accordingly. Also provided, for a model with one predictor variable, is a scatterplot of the data with regression line and confidence and prediction intervals. For multiple regression models the graph is the scatterplot matrix of the model variables with the lowess curve displayed for each constituent scatterplot. If the model has exactly two predictor variables, a 3D scatterplot about the regression plane is optionally produced.
Can also be called from the more general model function.
Regression(my.formula, dframe=mydata,
digits.d=4, text.width=120, graphics.save=FALSE,
brief=FALSE, explain=FALSE, show.R=FALSE,
colors=c("blue", "gray", "rose", "green", "gold", "red"), res.rows=NULL, res.sort=c("cooks","rstudent","dffits","off"),
pred=TRUE, pred.all=FALSE, pred.sort=c("predint", "off"),
subsets=TRUE, cooks.cut=1,
scatter.coef=FALSE, scatter.3d=FALSE,
X1.new=NULL, X2.new=NULL, X3.new=NULL, X4.new=NULL,
X5.new=NULL, ...)
reg(my.formula, ...)
reg.brief(my.formula, brief=TRUE, ...)
reg.explain(my.formula, explain=TRUE, ...)
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.TRUE, save graphics output as a pdf file, otherwise, by
default, write graphics to the standard graphics output window.TRUE then brief labels of different
sections of output are replaced by more complete explanations of the output."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" tTRUE, 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".leaps package. Set to FALSE to
turn off.FALSE.lm which provides the core computations.Regression is to combine the following function calls into one, as well as provide ancillary analyses such as as graphics, organizing output into tables and sorting to assist interpretation of the output. The basic analysis successively invokes several standard R functions beginning with the standard R function for estimation of a linear model, lm. The output of the analysis of lm is stored in the object lm.out, available for further analysis in the R environment upon completion of the reg function by any R function that uses the output of lm as input. By default reg automatically provides the analyses from the standard R functions, summary, confint and anova, with some of the standard output modified and enhanced. The correlation matrix of the model variables is obtained with cor function. The residual analysis invokes fitted, resid, rstudent, and cooks.distance functions. The option for prediction intervals calls the standard R function predict, once with the argument interval="confidence" and once with interval="prediction". The lessR den function provides the histogram and density plots for the residuals and the plt function provides the scatter plots of the residuals with the fitted values and of the data for the one-predictor model. The pairs function provides the scatterplot matrix of all the variables in the model. Thomas Lumley's leaps package contains the leaps function that provides the analysis of the fit of all possible model subsets. The car package provides Henric Nilsson and John Fox's vif function for the computation of the variance inflation factors for the collinearity analysis. The scatter3d function from Fox and Weisberg's car package provides the interactive 3d scatterplot for models with exactly two predictor variables.`
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, analysis of residuals and influence as well as the confidence and prediction intervals for each observation in the model. Also provided, for multiple regression models, collinearity analysis of the predictor variables and adjusted R-squared for the corresponding models defined by each possible subset of the predictor variables. Because the results of the initial call to the linear model function, lm, are available after reg has completed in the R object lm.out.
DATA FRAME
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 data frame, the analysis will not be complete. The data frame does not need to be attached, just specified by name with the dframe option if the name is not the default mydata.
GRAPHICS
At least three default graphs are provided, and a fourth graph is provided for models with two predictor variables. By default the graphs are written to separate graphics windows (which may overlap each other completely, in which case move the top graphics windows). Or, the graphics.save option may be invoked to save the graphs to a single pdf file called regOut.pdf. The directory to which the file is written is displayed on the console text output.
1. A histogram of the residuals includes the superimposed normal and general density plots from the den function included in this lessR package. The overlapping density plots, which both overlap the histogram, are filled with semi-transparent colors to enhance readability.
2. A scatterplot of the residuals with the fitted values is also provided from the plt function included in this package. The point corresponding to the largest value of Cook's distance, regardless of its size, is plotted in red and labeled and the corresponding value of Cook's distance specified in the subtitle of the plot. Also by default all points with a Cook's distance value larger than 1.0 are plotted in red, a value that can be specified to any arbitrary value with the cooks.cut option. This scatterplot also includes the lowess curve.
3. For models with a single predictor variable, a scatterplot of the data is produced, which also includes the regression line and corresponding confidence and prediction intervals. As with the density histogram plot of the residuals and the scatterplot of the fitted values and residuals, the scatterplot includes a colored background with grid lines. For multiple regression models, a scatterplot matrix of the variables in the model with the lowess best-fit line of each constituent scatterplot is produced. If the scatter.coef option is invoked, each scatterplot in the upper-diagonal of the correlation matrix is replaced with its correlation coefficient.
4. A fourth graph is provided for a model with exactly two predictor variables, which is an interactive three dimensional scatterplot projected into two dimensions about the regression plane. This graph is generated by the scatter3d function in the car package. In turn, the code in the car package depends on code in the rgl package. To turn off this option for two predictor variable models, set the scatter.3d option to FALSE.
RESIDUAL ANALYSIS
By default the residual analysis lists the data and fitted value for each observation as well as the residual, Studentized residual, Cook's distance and dffits, with the first 20 observations listed and sorted by Cook's distance. The res.sort option provides for sorting by the Studentized residuals or not sorting at all. The res.rows option provides for listing these rows of data and computed statistics statistics for any specified number of observations (rows). To turn off the analysis of residuals, specify res.rows=0.
PREDICTION INTERVALS
The output for the confidence and prediction intervals includes a table with the data and fitted value for each observation, as well as the lower and upper bounds for the confidence interval and the prediction interval. The observations are sorted by the lower bound of each prediction interval. If there are more than 50 observations then the information for only the first five, the middle five and the last five observations is displayed. To turn off the analysis of prediction intervals, specify pred=FALSE, which also removes the corresponding intervals from the scatterplot produced with a model with exactly one predictor variable, yielding just the scatterplot and the regression line.
The data for the default analysis of the prediction intervals is for the values of the predictor variables for each observation, that is, for each row of the data. New values of the predictor variables can be specified for the calculation of the prediction intervals by providing values for the options X1.new for the values of the first listed predictor variable in the model, X2.new for the second listed predictor variable, and so forth for up to five predictor variables. To provide these values, use functions such as seq for specifying a sequence of values and c for specifying a vector of values. For multiple regression models, all combinations of the specified new values for all of the predictor variables are analyzed.
RELATIONS AMONG THE VARIABLES
By default the correlation matrix of all the variables in the model is displayed, and, for multiple regression models, collinearity analysis is provided with the vif function from the Fox and Weisberg (2011) car package as well as the adjusted R squared of each possible model from an analysis of all possible subsets of the predictor variables. This all subsets analysis requires the leaps function from the leaps package. These contributed packages are automatically loaded if available. If not available, an appropriate warning is provided to the user with instructions to install the corresponding package with the install.packages function, and the analysis continues without the output that would have been provided by invoking that package. To turn off the all possible sets option, set subsets=FALSE.
OUTPUT
The text output is organized to provide the most relevant information while at the same time minimizing the total amount of output, particularly for analyses with large numbers of observations (rows of data), the display of which is by default restricted to only the most interesting or representative observations in the analyses of the residuals and predicted values. Additional economy can be obtained by invoking the brief=TRUE option, or run reg.brief, which limits the analysis to just the basic analysis of the estimated coefficients and fit. An explanation of each section of the output can be obtained by setting the explain option to TRUE, or run reg.explain. Much of the underlying relevant R code run by reg is obtained by setting the show.R option to TRUE.
INVOKED R OPTIONS
The options function is called to turn off the stars for different significance levels (show.signif.stars=FALSE), to turn off scientific notation for the output (scipen=30), and to set the width of the text output at the console to 120 characters. The later option can be re-specified with the text.width option. After reg is finished with a normal termination, the options are re-set to their values before the reg function began executing.
VARIABLE LABELS
A labels data frame named mylabels, obtained from the rad function, can list the label for some or all of the variables in the data frame that contains the data for the analysis. If this labels data frame exists, then the corresponding variable labels are listed next to the variable name at the beginning of the output.
leaps function from the leaps package.
Nilsson, H. and Fox, J., vif function from the car package.formula, lm, summary.lm, anova, confint, fitted, resid, rstudent, cooks.distance# Generate random data, place in data frame mydata
X1 <- rnorm(20)
X2 <- rnorm(20)
Y <- .7*X1 + .2*X2 + .6*rnorm(20)
# instead, if read data with the rad function
# then the result is the data frame called mydata
mydata <- data.frame(X1, X2, Y)
rm(Y); rm(X1); rm(X2)
# One-predictor regression
# Provide all default analyses including scatterplot etc.
Regression(Y ~ X1)
# short name
reg(Y ~ X1)
# Provide only the brief analysis
reg.brief(Y ~ X1)
# Provide an explanation for each section of output
reg.explain(Y ~ X1)
# Provide a brief analysis with explanation
reg.brief(Y ~ X1, explain=TRUE)
# Modify the default settings as specified
Regression(Y ~ X1, res.row=8, res.sort="rstudent", digits.d=8, pred=FALSE)
# Multiple regression model
# Provide all default analyses
Regression(Y ~ X1 + X2)
# Specify new values of the predictor variables to calculate
# forecasted values and the corresponding prediction intervals
# Specify an input data frame other than mydata, see help(mtcars)
Regression(mpg ~ hp + wt + disp, dframe=mtcars,
X1.new=seq(50,350,50), X2.new=c(2,3), X3.new=c(100,300))Run the code above in your browser using DataLab