Econometrics/Statistics Linear Regression?

Question

You are interested in estimating the relationship between y and x_1. You also have data on x_2 and x_3. Let Beta_1_tilde be the simple regressions estimate from regressing y on x_1 only. Let Beta_1_hat be the multiple regression estimate from regressing y on x_1, x_2, and x_3.

If x_1 is uncorrelated with x_2 and x_3, but x_2 and x_3 are highly correlated, will Beta_1_tilde and Beta_1_hat be similar or different?

If someone could explain the intuition in this question, that would be the most helpful.

Answer 1

I would expect the two of them to be different if there was a high correlation between x2 and x3 (multi-collinearity problem).



Lack of multi-collinearity among the independent variables is an assumption when performing multiple linear regression.

Answer 2

it is extremely complicated regrettably: The formula of the line of regression is y=a+bx the place a= (the advise of y)-b(the advise of x) and b= Sxy/Sxx Sxy= (the sum of each x situations each y fee)- [(the sum of x)(the sum of y)/(the type of values) ] Sxx=(the sum of each x fee squared)-[(the sum of all values of x then squared)/(the type of values)]

Answer 3

it is extremely complicated regrettably: The formula of the line of regression is y=a+bx the place a= (the advise of y)-b(the advise of x) and b= Sxy/Sxx Sxy= (the sum of each x situations each y fee)- [(the sum of x)(the sum of y)/(the type of values) ] Sxx=(the sum of each x fee squared)-[(the sum of all values of x then squared)/(the type of values)]