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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: Plot of one of the independent variables against the dependent one 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.

C4X
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    I’m voting to close this question because Stack Overflow is for _programming_ questions. General questions about probability and statistics may be suitable on our sibling site [stats.se] (but check their help pages before asking there). – tripleee Dec 27 '21 at 12:18
  • Thank you for your feedback. I am suspecting a programming error, or rather that I didn't use the package in the correct way. I'll update my question to make this clearer. – C4X Dec 27 '21 at 12:37
  • I believe it means your p-value is less than 0.0005 (suggesting you can reject the null hypothesis of a zero coefficient at alpha=0.05, for example). As a side note, it does not look like you've plotted the dependent against independent variable (x=share_yes, y=party_percentage). You've plotted them both (x1=share_yes, x2=party_percentage) against some exogenous factor, unique_district. If unique_district is a covariate you may want to decorrelate both variables with this one prior to MLR. – jeremy Dec 27 '21 at 15:52

1 Answers1

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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.

Always Right Never Left
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