[R] testing goodness of fit of linear model

[Dewez Thomas]

Dear R-users,

I've been reading a bunch of things on linear models but cannot quite find a
clear answer. How can one determine whether a linear model is significant or
not?

For background info, I am modelling the response of topographic slope to the
distance of a catchment's outlet. Some guys have shown that if there is a
significant fit to a linear model, one can deduce the dynamic state of the
basin, that is, whether erosion is as strong as rock uplift, erosion is
smaller than rock uplift, or erosion is greater than rock uplift. I am thus
to test 4 situations:

Situation 1: a linear model is inappropriate for describing the data, the
scatter is too large, and thus a linear model is unfit to explain the data.

Situation 2: the linear model of the kind "y = b0 + b1 * x" is fit to
describe the data, ie data points lie close to a straight line.

Situation 2a: the relationship between slope and distance is significantly
positive
Situation 2b: the relationship between slope and distance is significantly
null (ie data is clustered around a line with b1 non-significantly different
from 0)
Situation 2c: the relationship between slope and distance is significantly
negative

I am confused as to what test I should use for discriminating these
situations.

The glm offers an indication about the significance of regression
parameters. So in the case where b1 is significantly different from 0 (p
value <=0.05 for a test where H0: b1=0; H1: b1 != 0), it is straightforward.
But I don't know how to discriminate between situation 1 and situation 2 (ie
whether a linear model is significant).

Any suggestion are welcome

Cheers,

Thomas
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