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Dropping of variables which are not significant and are having high VIF value

For more accuracy while fitting a linear model, we drop the input variables/features which are not significant(i.e pvalue>0.05) and whose variation inflation factor is  greater  than 5,I have landed up in a case where both input variables are highly correlated with each other and significant too,so which one should I drop?

Intercept in linear regression model

Why do we need an intercept in a linear regression model? If we use statsmodel.OLS do we need to add the intercept explicitly and how do we do it?

P-Value in Linear Regression

In Linear Regression, if the p-value of the f-stat is < 0.05 we reject the H0 and accept the Ha. Which means we know that at least one variable has a coefficient greater than zero. For individual variables, we consider the variable to be statistically significant if the p-value<0.05. Why this is so?

Model Export

Is it possible export or save a model so that whenever i want i can run the model if so how should i do it?