What are the reasons of having insignificant coefficient (p value) from regression output?


An insignificant coefficient in a regression output typically indicates that the corresponding predictor variable does not have a statistically significant relationship with the dependent variable. There are several reasons why this might occur:

  1. Multicollinearity: When predictor variables are highly correlated with each other, it can cause inflated standard errors for the coefficients, leading to insignificant p-values.

  2. Sample Size: A small sample size can result in insufficient statistical power to detect significant effects, leading to higher p-values.

  3. Measurement Error: If the predictor variable is measured with error, it can reduce the observed association between the predictor and the dependent variable, resulting in an insignificant coefficient.

  4. Model Misspecification: If the model is incorrectly specified (e.g., omitting important variables, using an incorrect functional form), it can lead to biased and inefficient estimates, making the coefficients insignificant.

  5. High Variability: High variability in the data can make it difficult to detect significant relationships, leading to insignificant p-values.

  6. Outliers or Influential Points: Outliers or influential points can distort the results of the regression analysis, potentially leading to insignificant coefficients.

  7. Non-linearity: If the relationship between the predictor and the dependent variable is non-linear and this non-linearity is not accounted for in the model, it can result in insignificant coefficients.

  8. Insufficient Variation: If the predictor variable has little variation, it may not provide enough information to estimate its effect accurately, leading to an insignificant coefficient.


To address insignificant coefficients, you can consider:

  • Checking for multicollinearity using variance inflation factors (VIF) and addressing it if present.
  • Increasing the sample size if feasible.
  • Ensuring accurate measurement of variables.
  • Revisiting the model specification to include relevant variables and appropriate functional forms.
  • Addressing outliers or influential points.
  • Exploring and modeling non-linear relationships if suspected.
  • Ensuring sufficient variation in the predictor variables.

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