suppose a regression model has two explanatory variables (x and z). If we add a new...

suppose a regression model has two explanatory variables (x and z). If we add a new variable to to the model (m), and this new variable is correlated to x and z, how would we use the new variable m to test the impact of variable x on our dependent variable y when z and m remain the same?

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Expert Solution

So here we have x & z are two explanatory variable

y is dependent variable.

we add a new variable to to the model (m), and this new variable is correlated to x and z

first thing if m is correlated with x & z that means there will be multicollinearity between thses varaiables. now the multicollinearity means dependency between explanatory variables.

In regression analysis explanatory variables should not correlated with each this our assumption. So you to check whether there is multicollinearity exist or not. If it exist then we should remove it.

Now we use the new variable m to test the impact of variable x on our dependent variable y by checking adjusted R-Square value you check whether it makeing impact or not.

S here first you build regression model using y as dependent variable and x & z are two explanatory variable, note down the value of R-adjusted.

Now build regression model using y as dependent variable and x , z ,m are explanatory variable, note down the value of R-adjusted.

If value of R-adjusted changes then you can say that the new variable m to test the impact of variable x on our dependent variable y

orchestra answered 1 year ago

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