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I have a relative straight forward question.

Lets say we have a typical multiple regression model. With lets say 3 different independent variables. If one independent variable with its beta parameter has a very low value compared to the other parameters, lets say 0.00025.

Would it be better to not include this variable in the model?

/Peter

$$ \log y = 5.32 + 0.3\log(x_1) +0.15(x_2) + 0.00025(x_3) + u $$ where y is measured in pounds and the independent variables are measured in percentages.

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    $\begingroup$ That must depend on what the purpose of your model is, what the scale of that variable is, what the relationship between the predictor variables is. $\endgroup$
    – mdewey
    Commented Nov 16, 2016 at 15:26
  • $\begingroup$ okej @mdewey I've added a more specific model, does this help? $\endgroup$
    – user358065
    Commented Nov 16, 2016 at 15:32
  • $\begingroup$ my theory is that we can omit x_3 since, it has such a small effect on logy. $\endgroup$
    – user358065
    Commented Nov 16, 2016 at 15:39

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There is no relation between estimated parameter value and it's significance. Basically, parameter should be selected based on the significance of the partial r-squared value not the estimated value of the parameter. You can try the step wise regression method and build the model.

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