I have a time series data that is stationary. There is no multicollinearity (VIF value is less than 5).
My dependent variable is industrial turnover, and one of my independent variables is export data. There is a positive correlation between exports and industrial production. In simple linear regression, the model is significant, and the regression coefficient is significant and positive. The scatter plot also shows a positive relationship.
Also, the correlation between the export variable and other variables is very low; the highest correlation is 0.6 with imports. Others are less than 0.5.
However, in multiple regression, the regression coefficient is significant but negative. In the Lasso regression model, the coefficient is also negative. What could be the reason for this?"
If your library has it, take a look at the "Woes of Regression Coefficients" chapter in Mosteller & Tukey (1977):
Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression. A second course in statistics. Addison-Wesley series in behavioral science: quantitative methods.
I cannot find that chapter online, but it is mentioned in these comments on the interpretation of regression coefficients:
- https://imstat.org/2012/07/18/terences-stuff-multiple-linear-regression-1/
HTH.
I would recommend taking a look at the literature on suppressor/suppression effects. This is usually what explains this issue. For example,
Article Suppressor Variables in Multiple Regression/Correlation
It is not unusual for the coefficient to reverse as other variables are added or subtracted in multiple regression. When a variable is added, it often picks up the pattern of the current residuals, and when another variable has already been used, those residuals might be negatively correlated with the one you are adding. If I understand your question correctly, this might be the cause.
This happens due to presense of bad leverage points. For detection of bad leverage points and methods to regression see:
Rousseeuw, P. J., & van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Jr. of the American Statistical Association, 85(411), 633–639. https://doi.org/10.1080/01621459.1990.10474920
Wilcox, R. R. (2023). Robust Correlation Coefficients That Deal With Bad Leverage Points. Methodology, Vol. 19(4), 348–364. https://doi.org/10.5964/meth.11045
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