R help - Apr 2011 - Plotting a quadratic line on top of an xy scatterplot

Dear Listserv,

Here is my latest in a series of simple-seeming questions that dog me.

Consider the following data:

x <- read.table(textConnection("temperature probability
0.11 9.4
0 2.3
0.38 8.7
0.43 9.2
0.6 15.6
0.47 8.7
0.09 12.8
0.11 9.4
0.01 7.7
0.83 8
0.65 9.3
0.05 7.4
0.34 10.1
0.02 4.8
0.07 9.1
0.6 15.6
0.01 8.4
0.9 9.6
0.83 8
0.12 8.4
0.01 8
0 5
0.11 9.7
0.41 7.4
0.05 9.4
0.09 8.3
0 6.1
0.12 8.4
0.73 7.8
0 4.2"), header = TRUE, as.is = TRUE)
closeAllConnections()

I modeled the relationship: Probability = f(Temperature), i.e., probability as a
function of temperature.

I found that there is a significant quadratic term in the model:

summary(lm(x[,2] ~ x[,1] + I(x[,1]^2)))

Now the question is: how do I plot it?

I can do this:
plot(x[,2] ~ x[,1])

...but I would also like to add a line corresponding to the quadratic function. 
In other words, I want to visually show the relationship among the variables 
that is being modeled. How do I do it? I think the curve() command will be used,
but I don't know how to employ it.

Thanks very much in advance.

Sincerely,
-----------------------------------
Josh Banta, Ph.D
Center for Genomics and Systems Biology
New York University
100 Washington Square East
New York, NY 10003
Tel: (212) 998-8465
http://plantevolutionaryecology.org
	[[alternative HTML version deleted]]

Hi Josh,

This is by no means the fanciest solution ever, but as there are
predict methods for many types of models in R, I thought I would show
it this way.

## fit the model
model <- lm(probability ~ poly(temperature, 2), data = x)

## create line values
dat <- data.frame(temperature = seq(min(x$temperature, na.rm = TRUE),
max(x$temperature, na.rm = TRUE), by = .01))
## add predicted y values
dat$yhat <- predict(model, dat)

## plot data
plot(probability ~ temperature, data = x)
## add predicted line
lines(x = dat$temperature, y = dat$yhat, type = "l")

Hope this helps,

Josh

On Mon, Apr 11, 2011 at 12:29 PM, Josh B <joshb41 at yahoo.com>
wrote:
> Dear Listserv,
>
> Here is my latest in a series of simple-seeming questions that dog me.
>
> Consider the following data:
>
> x <- read.table(textConnection("temperature probability
> 0.11 9.4
> 0 2.3
> 0.38 8.7
> 0.43 9.2
> 0.6 15.6
> 0.47 8.7
> 0.09 12.8
> 0.11 9.4
> 0.01 7.7
> 0.83 8
> 0.65 9.3
> 0.05 7.4
> 0.34 10.1
> 0.02 4.8
> 0.07 9.1
> 0.6 15.6
> 0.01 8.4
> 0.9 9.6
> 0.83 8
> 0.12 8.4
> 0.01 8
> 0 5
> 0.11 9.7
> 0.41 7.4
> 0.05 9.4
> 0.09 8.3
> 0 6.1
> 0.12 8.4
> 0.73 7.8
> 0 4.2"), header = TRUE, as.is = TRUE)
> closeAllConnections()
>
> I modeled the relationship: Probability = f(Temperature), i.e., probability
as a
> function of temperature.
>
> I found that there is a significant quadratic term in the model:
>
> summary(lm(x[,2] ~ x[,1] + I(x[,1]^2)))
>
> Now the question is: how do I plot it?
>
> I can do this:
> plot(x[,2] ~ x[,1])
>
> ...but I would also like to add a line corresponding to the quadratic
function.
> In other words, I want to visually show the relationship among the
variables
> that is being modeled. How do I do it? I think the curve() command will be
used,
> but I don't know how to employ it.
>
> Thanks very much in advance.
>
> Sincerely,
> -----------------------------------
> Josh Banta, Ph.D
> Center for Genomics and Systems Biology
> New York University
> 100 Washington Square East
> New York, NY 10003
> Tel: (212) 998-8465
> http://plantevolutionaryecology.org
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/

Hi,

Is it just me or it appears the "temperature" and
"probability" should be
reversed? 
--------
Anyhow it should help you to assign your model to a variable (as Joshua did
with his own suggestion)

yourmodel <-lm(x[,2] ~ x[,1] + I(x[,1]^2)) # again, taking literally the way
you formulated it...

And you could then access the coefficients individually:

c <- coef(yourmodel)[1] # for the intercept 
b <- coef(yourmodel)[2] 
a <- coef(yourmodel)[3] 

To build yourself a vector of predicted y-values based on a vector of
x-values ("dat" as per Joshua's post)
and pass them to the "lines" function to be plotted over your existing
plot.

This is less convenient than using the "predict" but sometimes it
helps to
do the arithmetic at a lower level.
HTH


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