Can some one explain
If there is erronious omitting of independent variable not correlated to other independent variable then will you be the intercept be imprecise
And standard errors and other regresssion coefficients will be okk??
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if an independent variable is erroneously omitted from a regression model and that variable is not correlated with any of the other independent variables, then the intercept term may be imprecise. The standard errors and other regression coefficients, however, should still be unbiased and consistent, meaning they will still provide valid estimates of the true population parameters.
When an independent variable is omitted from a regression model, the other independent variables may not fully capture the effect of the omitted variable on the dependent variable. This can result in a bias in the intercept term, which represents the value of the dependent variable when all the independent variables are zero. If the omitted variable has a non-zero effect on the dependent variable, the intercept will be shifted by an amount that depends on the magnitude of the omitted variable’s effect.
However, the standard errors and other regression coefficients are not affected by the omission of an independent variable that is uncorrelated with the other independent variables. This is because the regression coefficients are estimated using only the available data, and the standard errors account for the variability of the dependent variable around the regression line. As long as the assumptions of the regression model are met, the estimates of the regression coefficients will still be unbiased and consistent, even if an independent variable is omitted from the model.