test names that can assess linearity ​​​​​​

[Hesham Ali]

Hello friends
I want to test of linearity exists between my dependent variable and my independent variables.
Can any one tell me "tests" names that can test linearity for me?
I do not want graphs like q q plot or a histogram, i am looking for a test (like Shapiro-Wilk test for normality).
I am sorry my knowledge of statistics are not good enough...
Thank you

[Marcos Almeida]

I don't know the purpose you need it. That said, linearity is assumption...to be checked. Indeed, scatter plots and fit lines are a nice start. Under linear regression, you may check the addition of squared terms, for example. That said, as a starting point, you may have Pearson correlation.

[Joao Santos Silva]

Adding to Marcos's advice, look up "RESET test". (Note that the way Stata implements it does not use robust standard errors.)

Best wishes,

Joao

[Nick Cox]

I don't disagree one bit with Joao, but I think the RESET test is much more specific than what is being asked for.

We could quibble about whether y = Xb is an assumption or a specification of functional form. What no-one has pointed out yet is that if there's an overall test it's arguable that it's the F test you have already. But, but, but:

1. The F test itself is mute on whether there is much nonlinearity (in variables or parameters) not captured by your functional form. By answering several questions at once it fails to answer that one unequivocally.

2. Despite your preference for tests over graphs, you'll not make much progress checking this without looking at one or more of

* scatter plot matrix for variables in the model

* residual vs fitted and observed vs fitted for model

* added variable plots.

I find myself writing ideal condition, not assumption, wherever I can. The word assumption, although dominant in much of the literature, carries too much flavour of a condition that may be right or wrong, whereas ideal condition can be made to convey that ideals can be Utopian or asymptotic or (most to the point) approximated at least roughly.

[Hesham Ali]

Thank you all very much. I am very sorry for my late response.