1. ## Modelling From Data

Howdy All,

In class we are modelling from data, including linear, exponential, power, logarithmic and quadratic models.

Normally, to find the correct model, I would use the R2 value, however, our teacher has now informed us that this is not a valid argument.

What others arguments could I put forward to state that the model of best fit is each of these forms (linear, exponential etc.)?

Howdy All,

In class we are modelling from data, including linear, exponential, power, logarithmic and quadratic models.

Normally, to find the correct model, I would use the R2 value, however, our teacher has now informed us that this is not a valid argument.

What others arguments could I put forward to state that the model of best fit is each of these forms (linear, exponential etc.)?
There is no one way of doing this, but a number of techniques can be of
some use.

1. Plot the residuals against the independent variable. They should be
randomly scattered above and below 0 for a good model. The should not

2. For a homoscadastic process the scatter of the points on the residual
plot should not increase of decrease with the independent variable.

3. The histogram of residuals should be approximately normal.

RonL

3. How do I plot said residuals against the independent variable?

How do I plot said residuals against the independent variable?
We have data: x1, x2, x3, ..., xN ; y1, y2, ... , yN, where xi is the
independent variable (time or something like that) and yi the corresponding
observed value of the dependent variable (population, concentration ...)

We have a model Y(x) which allows us to predict from the model what we
would expect the values of the y's to be at the corresponding x's.

The residuals are: Ri = (yi -Y(xi)), i=1, .., N
they are the differences between the observations and the model
predictions, in a sense the unmodelled part of the variation in the y's.

The residual plot is a plot of the x's against the corresponding R's.

For a good model the residulal plot should be a more or less random