Linear and Quadratic Regression
Hi, I am currently writing a Uni paper that looks into how worsening housing conditions affect the vote share change of the incumbent party in US presidential elections.
So far, I've established with regressions that worsening housing conditions negatively affect the incumbent (statistically significant, robust effect).
But when I did a fitted residuals plot, the plot shows a clear curve. This leads me to believe that the nonlinear assumption of my basic models is not correct and the effect is nonlinear.
I then ran the same model but added a quadratic factor, and it is also statistically significant and has a way higher (like over 10x and positive) regression coefficient than my linear models.
However, I am not quite sure as to how to proceed now. I have never done quantitative analysis on such a level, and I am unsure whether the nonlinear model only adds complications. But the fitted residual and statistical significance leads me to believe that the nonlinear model is the better model, that tells the whole story.
I would greatly appreciate it if someone who was more experience with things like this, would provide me with typical steps to determine if my choice was right.
Also I am aware that the model is quite basic, but my prof advised me to make my model less detailled and just be transparent in the limitations. I am in my bachelor's.
If this helps, the regression results are:
Linear:
OLS estimation, Dep. Var.: inc_diff
Observations: 8,907
Fixed-effects: factor(NAME): 1,733, factor(Year): 3
Standard-errors: Clustered (STATE)
Estimate Std. Error t value Pr(>|t|)
OACB_diff -0.092745 0.029711 -3.12155 0.0030744 **
MHI_diff 0.003187 0.001762 1.80878 0.0768852 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 0.031982 Adj. R2: 0.282804
Within R2: 0.008405
Nonlinear:
OLS estimation, Dep. Var.: inc_diff
Observations: 8,907
Fixed-effects: factor(NAME): 1,733, factor(Year): 3
Standard-errors: IID
Estimate Std. Error t value Pr(>|t|)
OACB_diff -0.053746 0.014853 -3.61843 2.9843e-04 ***
0.014853 -3.61843 2.9843e-04 ***I(I(OACB_diff^2)) 1.398048 0.207885 6.72509 1.8899e-11 ***
I(I(OACB_diff^2)) 1.398048 0.207885 6.72509 1.8899e-11 ***MHI_diff 0.003150 0.000943 3.34006 8.4187e-04 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 0.031881 Adj. R2: 0.287201
Within R2: 0.014621
