plotly_regtol: Plotting Tolerance Intervals for Regressions

Description

Provides interactive tolerance intervals for regression data. More specifically, plotly_regtol presents tolerance bounds for linear regression, nonlinear regression, and nonparametric regression models. In addtion, this updated function is capable of showing tolerance plane for trivariate regression models.

Usage

plotly_regtol(tol.out,
              x,
              new.x = NULL,
              y,
              side = c("two","upper", "lower"),
              rect = FALSE,
              smooth = 4,
              x.lab = NULL,
              x.lab.size = NULL,
              y.lab = NULL,
              y.lab.size = NULL,
              z.lab = NULL,
              z.lab.size = NULL,
              x.tick.size = NULL,
              y.tick.size = NULL,
              z.tick.size = NULL,
              x.col = NULL,
              x.cex = NULL,
              fit.col = NULL,
              fit.lwd = NULL,
              fit.line.type = c("dash","dot","dashdot","solid"),
              fit.opacity = NULL,
              tol.col = NULL,
              tol.lwd = NULL,
              tol.line.type = c("dash","dot","dashdot","solid"),
              tol.opacity = NULL,
              title.position.x = NULL,
              title.position.y = NULL,
              title = NULL,
              title.size = NULL)

Value

plotly_regtol returns tolerance intervals for linear regression, nonlinear regression, nonparametric regression, as well as tolerance planes for multivariate (multiple) linear regression models.

Arguments

tol.out: Output from regtol.int, nlregtol.int, npregtol.int or mvregtol.region for regressional data.
x: Data frame for explanatory variables. If there are more than one explanatory variables, columns of x represents regressors.
new.x: An optional data frame in which to look for variables with which to predict. new.x can be used to plot linear regression, nonlinear regression, and multivariate linear regression. new.x has to be a subset of new data in the original output.
y: Data frame for response variable. y is in the formate of a vector.
side: side = "two" produces plots for either the two-sided tolerance intervals or both one-sided tolerance intervals. This will be determined by the output in tol.out. side = "upper" produces plots showing the upper tolerance bounds. side = "lower" produces plots showing the lower tolerance bounds. Note that if the output of in tol.out shows 2-sided tolerance intervals, side = "upper" and side = "lower" still shows both upper AND lower tolerance intervals.
rect: This argument is used for plotting tolerance plane(s) of multivariate regression region. When rect=TRUE the x1-x2 plane is a rectangle.
smooth: The smooth parameter for the x1-x2 plane when rect=TRUE.
x.lab: Label of the x-axis.
x.lab.size: Size of label of the x-axis.
y.lab: Label of the y-axis.
y.lab.size: Size of label of the y-axis.
z.lab: Label of the z-axis.
z.lab.size: Size of label of the z-axis.
x.tick.size: Size of tick marks on the x-axis.
y.tick.size: Size of tick marks on the y-axis.
z.tick.size: Size of tick marks on the z-axis.
x.col: Color of original data points.
x.cex: Size of original data points.
fit.col: Color of fitted line or fitted plane.
fit.lwd: Width of fitted line or fitted plane.
fit.line.type: Type of fitted line or fitted plane.
fit.opacity: Opacity of fitted line or fitted plane.
tol.col: Color of tolerance intervals or tolerance plane.
tol.lwd: Width of tolerance intervals.
tol.line.type: Line type of tolerance intervals
tol.opacity: Opacity of tolerance region.
title.position.x: Horizontal position of the title.
title.position.y: Vertical position of the title.
title: The main title on top of the plot.
title.size: Size of the title.

References

Montgomery, D. C. (2005), Introduction to Statistical Quality Control, Fifth Edition, John Wiley & Sons, Inc.

Examples

Run this code

## 95%/95% 1-sided linear regression tolerance bounds
## for a sample of size 100.

library(plotly)

set.seed(100)
x <- runif(100, 0, 10)
y <- 20 + 5*x + rnorm(100, 0, 3)
out1 <- regtol.int(reg = lm(y ~ x), new.x = c(3,6,20), new=TRUE ,
                    side = 1, alpha = 0.05, P = 0.95)
plotly_regtol(tol.out = out1 , x=x , y=y , new.x = c(6,20), side = "two" ,
                   fit.line.type = "dash" , tol.line.type = "solid")
########################
set.seed(100)
x1 <- runif(100, 0, 10)
x2 <- rpois(100 , 5)
y <- 20 + 5*x1 + 3*x2 + rnorm(100, 0, 3)
x1.new <- runif(10 , 0 , 10)
x2.new <- rpois(10 , 5)
out2 <- regtol.int(reg = lm(y ~ x1 + x2), new.x = cbind(x1.new , x2.new), new=TRUE,
                    side = 1, alpha = 0.05, P = 0.95)
plotly_regtol(tol.out = out2 , y=y , x=cbind(x1,x2) , new.x = cbind(x1.new , x2.new) , 
                   rect = TRUE , side = "two")
###########################
## 95%/95% 2-sided nonlinear regression tolerance bounds
## for a sample of size 50.
set.seed(100)
x <- runif(50, 5, 45)
f1 <- function(x, b1, b2) b1 + (0.49 - b1)*exp(-b2*(x - 8)) +
  rnorm(50, sd = 0.01)
y <- f1(x, 0.39, 0.11)
formula <- as.formula(y ~ b1 + (0.49 - b1)*exp(-b2*(x - 8)))
out1 <- nlregtol.int(formula = formula,
                      xy.data = data.frame(cbind(y, x)),
                      x.new=c(10,20,50), side = 2,
                      alpha = 0.05, P = 0.95 , new = TRUE)
plotly_regtol(tol.out = out1 , x=x , y=y , new.x = c(20,50) , side = "two",
                   fit.line.type = "dot")
###############

## 95%/95% 1-sided nonparametric regression tolerance bounds
## for a sample of size 50.
set.seed(100)
x <- runif(50, 5, 45)
f1 <- function(x, b1, b2) b1 + (0.49 - b1)*exp(-b2*(x - 8)) + rnorm(50, sd = 0.01)
y <- f1(x, 0.39, 0.11)
y.hat <- loess(y~x)$fit
out1 <- npregtol.int(x = x, y = y, y.hat = y.hat, side = 1,
                      alpha = 0.05, P = 0.95, method = "WILKS" , new = TRUE)
plotly_regtol(tol.out = out1 , x=x , y=y , side = "two" , fit.line.type = "dash")
############
set.seed(100)
x1 <- runif(50, 5, 45)
x2 <- rnorm(50 , 0 , 1)
f1 <- function(x1 , x2 , b1, b2) {b1 + (0.49 - b1)*exp(-b2*(x1 + x2 - 8)) + rnorm(50, sd = 0.01)}
y <- f1(x1 , x2 , 0.39, 0.11)
y.hat <- loess(y~ x1 + x2)$fit
out2 <- npregtol.int(x = cbind(x1 , x2), y = y, y.hat = y.hat, side = 1,
                      alpha = 0.05, P = 0.95, method = "WILKS" , new = TRUE)
plotly_regtol(tol.out = out2 , y=y , x=cbind(x1,x2) , 
                   rect = TRUE , smooth = 100 ,  side = "two")