Testing nonlinearity given linear fit

by Fortranner   Last Updated September 11, 2019 13:19 PM

After fitting a multiple linear regression model, how do you test that the relationship between the response and the predictions is actually linear? For example, if the true relationship is

y = tanh(x1 + x2) + e

with x1 and x2 uniformly distributed on (0,1) and e normally distributed, but you don't know the generating process, then a linear regression

y = c0 + c1*x1 + c2*x2 + e

can be fit. How do you test whether y has a linear dependence on c1*x1 + c2*x2?

Tags : regression


Related Questions


Multiple regression, full and restricted model

Updated March 12, 2017 19:19 PM

Models under Regression Analysis list

Updated October 15, 2018 00:19 AM

Fitting polynomial equation and combined effect

Updated November 14, 2018 13:19 PM

Restricted Weighted Linear Regression in R

Updated June 06, 2019 19:19 PM