I am doing a multiple regression test with statsmodels.
I am very confident that there is a relationship in the data, both from what I already know about this data through other sources and from plotting, but when I do a multiple regression test with statsmodels, the p-value is shown as 0.000. My interpretation of low p-values is that there is no relation. However, a value of 0.000 seems more like something has failed computationally, because I would assume that statistical noise alone would give me a low p-value of at least 0.1.
What could be the reason for a multiple regression test that computes without errors but gives a p-value of 0.000 when there is clearly a relationship in the data?
EDIT:
I am not sure if this is a statistical or a code problem. It would therefore be really helpful if people with experience woth statsmodels could tell me whether I used it correctly. If there is consensus about this being a data-related problem I would close this question here and reopen it on Cross Validated as suggested in a comment
In the below image I have plotted the independent variable against the dependent one. I think this shows that there is some kind of relationship there:
But when I do a multiple regression test:
import statsmodels.api as sm
df = df.dropna()
Y = df['share_yes']
X = df[[
'party_percent',
]]
X = sm.add_constant(X)
ks = sm.OLS(Y, X)
ks_res = ks.fit()
ks_res.summary()
print(ks_res.summary())
... the p-value is shown as 0.000:
OLS Regression Results
==============================================================================
Dep. Variable: share_yes R-squared: 0.504
Model: OLS Adj. R-squared: 0.504
Method: Least Squares F-statistic: 2288.
Date: Mon, 27 Dec 2021 Prob (F-statistic): 0.00
Time: 13:41:57 Log-Likelihood: 2152.1
No. Observations: 2256 AIC: -4300.
Df Residuals: 2254 BIC: -4289.
Df Model: 1
Covariance Type: nonrobust
=================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------
const 0.4296 0.004 103.536 0.000 0.421 0.438
party_percent 1.2539 0.026 47.831 0.000 1.202 1.305
==============================================================================
Omnibus: 10.487 Durbin-Watson: 0.931
Prob(Omnibus): 0.005 Jarque-Bera (JB): 10.492
Skew: -0.166 Prob(JB): 0.00527
Kurtosis: 3.044 Cond. No. 13.6
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
This is what my pandas dataframe looks like:
unique_district party_percent share_yes
0 1100 0.089320 0.588583
1 1101 0.099448 0.505556
2 1102 0.146040 0.545226
3 1103 0.094512 0.496875
4 1104 0.136538 0.513672
... ... ... ...
2252 12622 0.040000 0.274827
2253 12623 0.038660 0.322917
2254 12624 0.016453 0.439539
2255 12625 0.060952 0.386774
2256 12626 0.032882 0.306452
Please note that I am actally using more than one variable, therefore multiple regression, but for the sake of brevity I only used one here.
While this is not a programming question (aside from the possibility of a bug, which is impossible to tell without providing full dataset), I'll answer here since it's not closed yet and I don't see you asking it on Cross Validated.
P-values are mostly a function of sample size (which is easy enough to see, e.g. refer to chapter 7.6 of The Truth about Linear Regression) and (for nonzero parameters) approach zero in the limit (w.r.t. sample size). You have a univariate regression of decent sample size, so the p-value obtained should come as no surprise.