plot x and y, with optional straight line fit and display of squared residuals

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Description

Plot x and y, with optional fitted line and display of squared residuals. By default the least squares line is calculated and used. Any other straight line can be specified by placing its coefficients in coef.model. Any other fitted model can be calculated by specifying the model argument. Any other function of one variable can be specified in the alt.function argument. At most one of the arguments model, coef.model, alt.function can be specified.

Usage

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regr1.plot(x, y,
           model=lm(y~x),
           coef.model,
           alt.function,
           main="put a useful title here",
           xlab=deparse(substitute(x)),
           ylab=deparse(substitute(y)),
           jitter.x=FALSE,
           resid.plot=FALSE,
           points.yhat=TRUE,
           pch=16,
           ..., length.x.set=51,
           x.name,
           pch.yhat=16,
           cex.yhat=par()$cex*.7,
           err=-1)

Arguments

x

x variable

y

y variable

model

Defaults to the simple linear model lm(y ~ x). Any model object with one x variable, such as the quadratic lm(y ~ x + I(x^2)) can be used.

coef.model

Defaults to the coefficients of the model argument. Other intercept and slope coefficients for a straight line (for example, c(3,5)) can be entered to illustrate the sense in which they are not "least squares".

alt.function

Any function of a single argument can be placed here.
For example, alt.function=function(x) {3 + 2*x + 3*x^2}.
All coefficients must be specified.

main, xlab, ylab

arguments to plot.

jitter.x

logical. If TRUE, the x is jittered before plotting. Jittering is often helpful when there are multiple y-values at the same level of x.

resid.plot

If FALSE, then do not plot the residuals. If "square", then call resid.squares to plot the squared residuals. If TRUE (or anything else), then call resid.squares to plot straight lines for the residuals.

points.yhat

logical. If TRUE, the predicted values are plotted.

...

other arguments.

length.x.set

number of points used to plot the predicted values.

x.name

If the model argument used a different name for the independent variable, you might need to specify it.

pch

Plotting character for the observed points.

pch.yhat

Plotting character for the fitted points.

cex.yhat

cex for the fitted points.

err

The default -1 suppresses warnings about out of bound points.

Note

This plot is designed as a pedagogical example for introductory courses. When resid.plot=="square", then we actually see the set of squares for which the sum of their areas is minimized by the method of "least squares".

Author(s)

Richard M. Heiberger <rmh@temple.edu>

References

Heiberger, Richard M. and Holland, Burt (2004b). Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS. Springer Texts in Statistics. Springer. ISBN 0-387-40270-5.

Smith, W. and Gonick, L. (1993). The Cartoon Guide to Statistics. HarperCollins.

See Also

resid.squares

Examples

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data(hardness)

## linear and quadratic regressions
hardness.lin.lm  <- lm(hardness ~ density,                data=hardness)
hardness.quad.lm <- lm(hardness ~ density + I(density^2), data=hardness)

anova(hardness.quad.lm)  ## quadratic term has very low p-value

par(mfrow=c(1,2))

regr1.plot(hardness$density, hardness$hardness,
           resid.plot="square",
           main="squared residuals for linear fit",
           xlab="density", ylab="hardness",
           points.yhat=FALSE,
           xlim=c(20,95), ylim=c(0,3400))

regr1.plot(hardness$density, hardness$hardness,
           model=hardness.quad.lm,
           resid.plot="square",
           main="squared residuals for quadratic fit",
           xlab="density", ylab="hardness",
           points.yhat=FALSE,
           xlim=c(20,95), ylim=c(0,3400))

par(mfrow=c(1,1))

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