What can I do to address the violated assumption of linearity in my simple linear regression model?

Question

Overview

I built a linear regression model using the lm() function in R, and the linearity assumption has been violated. All other assumptions have been met. I tried a multitude of transformations on the predictor, but that didn't improve the linearity. The independent variables is U.S. GDP/Capita in a specific year, and the dependent variable is number of suicides in a specific year in the U.S. The regression model has a significant F-statistic and a R-squared value of .69.

The Data (only the first 2 rows)

| year | | gdp/capita | | suicides |
| ---- | | ---------- | | -------- |
| 1987 | | 259574.2   | | 30784    |
| 1988 | | 277240.9   | | 30388    |

Scatter Plot of the Data

Residuals vs Fitted Plot indicating non-linearity

Answer 1

So I'm assuming that your model looked like this:

m1 <- lm(suicides ~ gdp/capita, data = df)

There are a few ways of fitting non-linear models, but the most straightforward at this point would be to fit a quadratic term to your model. You could do that like this:

df$gdp2 <- df$gdp/capita^2
m2 <- lm(suicides ~ gdp/capita + gdp2, data = df)

Another way would be to look into generalized additive models. One package to use would be mgcv, in which case the code could look like this:

library(mgcv)
m3 <- gam(suicides ~ s(gdp/capita), data = df)

Hope this helps. I've pasted a few helpful links about these methods below.

Non-linear terms in linear models: https://www.theanalysisfactor.com/r-tutorial-4/

Generalized additive models: http://environmentalcomputing.net/intro-to-gams/