Question

Suppose you are interested in estimating the ceteris paribus relationship between y and x. For this purpose, you can collect data on two control variables, x2 and x3. Let B1 be the simple linear regression estimate from y on xi, and let ß, be the multiple regression estimate from y on x,, X2, and x,3. a. Assume that xi is not correlated with x2 but that x2 and x3 have a large partial 6.3 effect on y. Would you expect Bi and ßi to be similar or very different? Explain, and draw a Venn diagram to illustrate your answer.

Answer 1

Given that data, implies (a) That x_1 is not correlated with x_2 but that x_2 and x_3 have a large partial Effect on y would you Except beta_1^similarto to beta_1^similarto to be similar or very different. The difference between a Simple Linear regression Which just requires a Linear relationship between two variables and in latter there has to be a more Explanatory variables In case one moves from multiple to a Simple regression by removing a relevant variable which may be correlated with other explanatory variables then it is called variable bias. The Simple and multiple regression coefficient on X_1 can differ be large amount and the amount of correlation between x_2 & x_3 does not directly effect the multiple regression Estimate on x_1 if x_1 is essentially un correlated with x_2 So, we would except beta_1^similarto to be Similar \r\n if x_1 highly correlated with x_2 Suppose there is a Linear regression equation of with two Explanatory variables a