So I am still trying to puzzle through the logic of regression, particularly the importance of the error term.

My recollection is that there must be nothing in the error term that is systematically related to both the independent and the dependent variable. Is this correct?

If so, then the question is: is it accurate to then say that noise in the error term that is systematically related to the dependent variable but NOT to the independent variables will in fact change the value of the coefficients on the included independent variable terms, but not the general relationship?

Alternatively, it seems to me that an omitted variable that was unrelated to the independent variables could still explain all of the variance in the dependent variable. Then the coefficients would be entirely meaningless, except in a sense devoid of any causal inference.

(i am oversimplifying). let's say, just for the sake of argument, that the "true" determinant of level of foreign ownership was a completely exogenous factor unrelated to these independent variables-- like a WTO Rule that strictly regulated levels of foreign ownership based on another set of criteria like how close the president of the host country was to the president of the WTO. Say that one could in fact model the entire dependent variable perfectly against this independent variable if one knew about it, and could measure "friendliness." But this researcher did not know about it, nor how to measure it.

Would I be correct to infer that the coefficients from the model he did use (if this model were OLS and the assumption of linearity held) were useful in summarizing the relationship between these independent variables and the dependent variable (in the way of cross-tabs, as we discussed last time) but that they tell you nothing about the causal relationship?

Would i be further correct in saying that these coefficients are "correct" insofar as we take them to be measuring this direct relationship and not a causal relationship? Or are they "biased" or "incorrect" because of the exclusion of the key variable?

in this fake example, am i correct to assume that the inclusion of the key independent variable (assuming no measurement error) would reduce the other coefficients to zero? Or is this not mathematically quite right?

Hi Jas. How are you? So I am still trying to puzzle through the logic of regression, particularly the importance of the error term. My recollection is that there must be nothing in the error term that is systematically related to both the independent and the dependent variable. Is this correct? If so, then the question is: is it accurate to then say that noise in the error term that is systematically related to the dependent variable but NOT to the independent variables will in fact change the value of the coefficients on the included independent variable terms, but not the general relationship? Alternatively, it seems to me that an omitted variable that was unrelated to the independent variables could still explain all of the variance in the dependent variable. Then the coefficients would be entirely meaningless, except in a sense devoid of any causal inference. to take an example: in a paper from my IPE class, the model (which does not use OLS, actually, but something called Tobit because the distribution is truncated at the top-- forget about this for the moment), is the following: dependent variable: percent of US versus Host Country ownership of U.S. multi-national subsidiaries in LDC's the independent variables are: index of bargaining power of gov't, index of bargaining power of Multi-National Corporation, economic controls. (i am oversimplifying). let's say, just for the sake of argument, that the "true" determinant of level of foreign ownership was a completely exogenous factor unrelated to these independent variables-- like a WTO Rule that strictly regulated levels of foreign ownership based on another set of criteria like how close the president of the host country was to the president of the WTO. Say that one could in fact model the entire dependent variable perfectly against this independent variable if one knew about it, and could measure "friendliness." But this researcher did not know about it, nor how to measure it. Would I be correct to infer that the coefficients from the model he did use (if this model were OLS and the assumption of linearity held) were useful in summarizing the relationship between these independent variables and the dependent variable (in the way of cross-tabs, as we discussed last time) but that they tell you nothing about the causal relationship? Would i be further correct in saying that these coefficients are "correct" insofar as we take them to be measuring this direct relationship and not a causal relationship? Or are they "biased" or "incorrect" because of the exclusion of the key variable? in this fake example, am i correct to assume that the inclusion of the key independent variable (assuming no measurement error) would reduce the other coefficients to zero? Or is this not mathematically quite right? i hope this is not too confusing... thanks jason <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1276" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Hi Jas.&nbsp; How are you?&nbsp; </FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>So I am still trying to puzzle through the logic of regression, particularly the importance of the error term.&nbsp; My recollection is that there must be nothing in the error term that is systematically related to both the independent and the dependent variable.&nbsp; Is this correct?</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>If so, then the question is: is it accurate to then say that noise in the error term that is systematically related to the dependent variable but NOT to the independent variables will in fact change the value of the coefficients on the included independent variable terms, but not the general relationship?&nbsp; Alternatively, it seems to me that an omitted variable that was unrelated to the independent variables could still explain all of the variance in the dependent variable.&nbsp; Then the coefficients would be entirely meaningless, except in a sense devoid of any causal inference.&nbsp; </FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>to take an example:</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>in a paper from my IPE class, the model (which does not use OLS, actually, but something called Tobit because the distribution is truncated at the top-- forget about this for the moment), is the following:</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>dependent variable: percent&nbsp;of US versus Host Country&nbsp;ownership of&nbsp;U.S. multi-national&nbsp;subsidiaries in LDC's</FONT></DIV> <DIV><FONT face=Arial size=2>the independent variables are: index of bargaining power of gov't, index of bargaining power of Multi-National Corporation, economic controls.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>(i am oversimplifying).&nbsp; let's say, just for the sake of argument, that the&nbsp;"true" determinant of level of foreign ownership was a completely exogenous factor unrelated to these independent variables-- like a&nbsp;WTO&nbsp;Rule that strictly regulated&nbsp;levels of foreign ownership based on another set of criteria like how close the president of the host country was to the president of the WTO.&nbsp; Say that one could in fact model the entire dependent variable perfectly against this independent variable if one knew about it, and could measure "friendliness."&nbsp; But&nbsp;this researcher did not know about it, nor how to measure it.&nbsp;&nbsp;</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>Would I be correct to infer that the coefficients from the model&nbsp;he did&nbsp;use (if this model were OLS and the assumption of linearity held)&nbsp;were useful in summarizing&nbsp;the relationship between these independent&nbsp;variables and the dependent variable (in the way of cross-tabs, as we discussed last time) but that they tell you nothing about the causal relationship?&nbsp; Would i be further correct in saying that these coefficients are "correct" insofar as we take them to be measuring this direct relationship and not a causal relationship?&nbsp; Or&nbsp;are they "biased" or "incorrect" because of&nbsp;the&nbsp;exclusion of the key variable?&nbsp;&nbsp;in this fake example, am i correct to assume that&nbsp;the inclusion of the key independent variable (assuming no measurement error) would reduce the other coefficients to zero?&nbsp;Or is this not mathematically quite right?</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>i hope this is not too confusing...</FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV> <DIV><FONT face=Arial size=2>thanks</FONT></DIV> <DIV><FONT face=Arial size=2>jason&nbsp;&nbsp;&nbsp; </FONT></DIV> <DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV></BODY></HTML>