Fitting a function in R

Question

I have a few datapoints (x and y) that seem to have a logarithmic relationship.

> mydata
    x   y
1   0 123
2   2 116
3   4 113
4  15 100
5  48  87
6  75  84         


        

Answer 1

Try taking the log of your response variable and then using lm to fit a linear model:

fit <- lm(log(y) ~ x, data=mydata)

The adjusted R-squared is 0.8486, which at face value isn't bad. You can look at the fit using plot, for example:

plot(fit, which=2)

But perhaps, it's not such a good fit after all:

last_plot() + geom_line(aes(x=x, y=exp(fit$fitted.values)))

Answer 2

Check this document out: http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf

In brief, first you need to decide on the model to fit onto your data (e.g., exponential) and then estimate its parameters.

Here are some widely used distributions: http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm

Answer 3

Maybe using a cubic specification for your model and estimating via lm would give you a good fit.

# Importing your data
dataset <- read.table(text='
    x   y
1   0 123
2   2 116
3   4 113
4  15 100
5  48  87
6  75  84
7 122  77', header=T)

# I think one possible specification would be a cubic linear model
y.hat <- predict(lm(y~x+I(x^2)+I(x^3), data=dataset)) # estimating the model and obtaining the fitted values from the model

qplot(x, y, data=dataset, geom="line") # your plot black lines
last_plot() + geom_line(aes(x=x, y=y.hat), col=2) # the fitted values red lines

# It fits good.