The online homework file Homework_Assignment_6.pdf has been corrected. See http://www.courses.fas.harvard.edu/~gov1000/assignments/ Cheers, Jas. Jasjeet Singh Sekhon writes: > > Wherever it says "employment" in an equation it should say > "unemployment". I see that the typo is also in one equation in > question #3. I'll correct the online file. > > Jas. > > Jason Lakin writes: > > Greetings all. In problem 2, is the independent variable in the

correctly named, or should it say "unemployment"? charset=iso-8859-1"> independent "unemployment"? 

Jason, As I noted in lecture, there are a few ways of thinking about this. 1) The most direct and intuitively useful answer is Jacob's (see attached). Regression let's us ask what will happen to Y if X changes by some number of units. Correlation does not directly provide this information because it has removed both the units of X and Y. And covariance does not directly provide this information because it contains information about both the units of X and Y. What we want is how changes in X map to Y. 2) Although the formula for Beta which is presented is just for simple regression, multiple OLS regression can also be thought of as analysis of variance (and covariance)---the equation just looks a lot more complicated. Recall that covariance is a measure of linear relationships so in some sense it is not surprising that *linear* regression is also a way of analyzing variances and covariances. But OLS can be generalized to the setting of multiple independent variables while this cannot really be done with covariance or correlation. 3) Under a set of assumptions, OLS obtains some nice proprieties like unbiasedness and efficiency. Recall that under the 5 assumptions, OLS is BLUE: the Best Linear Unbiased Estimator. If these assumptions hold, these proprieties provide good reasons to favor the OLS beta equation. 4) Even if the assumptions do not hold, OLS has the orthogonality propriety mentioned in class and asked about in the homework. See the last homework question. This property implies that the linear information about Y contained in X has been extracted and that the remaining residual (Y minus our predicted Y) is uncorrelated with X. This is true even if none of the assumptions hold, and it is a nice property for any measure of relationship to have. This propriety comes from the fact that the OLS beta is the value of beta at which the least squares loss function is minimized. When minimizing the loss function we never explicitly said we want anything to do with covariance, but it just turns out that the beta which minimizes the loss is very closely related to covariance. Jas. >From: "Jacob Kline" <jkline(a)fas.harvard.edu> >Sender: gov1000-list-admin(a)fas.harvard.edu >To: "'Jason Morris Lakin'" <jlakin(a)fas.harvard.edu>du>, > "'Jasjeet Singh Sekhon'" <jasjeet_sekhon(a)harvard.edu> >Cc: <gov1000-list(a)fas.harvard.edu> >Subject: RE: [gov1000-list] RE: HW clarification >Date: Sun, 23 Nov 2003 11:19:05 -0500 > >Jason, > >Try to think about this way: When we calculate the correlation, we want >a number that is standardized to be between -1 and 1. We specifically >don't care about the range of either variable. On the other hand, when >we run a regression y~x, what we care about is how a change in x will >correspond to a change in y, so we wouldn't want to divide out something >like var(y) -- which you could think of as what tells us what a standard >change in the size of y looks like. > >Does this help? > >Hope you are well, > >Jacob > > > >Jason Morris Lakin writes: > > Hi Jas, others. > > > > Can i get some help with the intuition on the formula for the Betas?

> > it make sense that we would standardize the coefficient by only the

> > the independent variable? What is the difference between the

> > from the correlation (standardized by a version of the variance of

> > variables) and what we get from the B (standardized only by our

> > independent variable)? I understand the equations but not their

> > > > thanks. > > jason > > > > > > Quoting Jasjeet Singh Sekhon <jasjeet_sekhon(a)harvard.edu>du>: > > > > > > > > The online homework file Homework_Assignment_6.pdf has been

> > > See http://www.courses.fas.harvard.edu/~gov1000/assignments/ > > > > > > Cheers, > > > Jas. > > > > > > Jasjeet Singh Sekhon writes: > > > > > > > > Wherever it says "employment" in an equation it should say > > > > "unemployment". I see that the typo is also in one equation in > > > > question #3. I'll correct the online file. > > > > > > > > Jas. > > > > > > > > Jason Lakin writes: > > > > > Greetings all. In problem 2, is the independent variable in

> > > correctly named, or should it say "unemployment"? > > > > > > > > > > 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>Greetings all. In problem 2, is

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To find the total effect of inflation onto unemployment, I conceptualize:

Hi everyone, Am lost on one problem of the homework--and hoping that there is a soul with advice. Number 3, where we must find the total effect of inflation upon unemployment and vice-versa. Problem construct offers intercept and coefficient values for three regressions, two simple and one multiple. The first simple gives us the total effect of unemployment onto approval; the second gives us total effect of inflation onto approval; and the multiple gives partial effects of unemployment and inflation onto approval. From these alone, a shrewd person surmises the partial effects between unemployment and inflation, in both directions, using simple algebra. Visualizing a triangular model as in the notes, the third 'leg' of the triangle is quickly ascertained. Here is my mental roadblock. To find the total effect of inflation onto unemployment, I conceptualize: total effect = direct effect + indirect effect. Again I visualize a triangular model. Direct effect = effect of inflation onto unemployment. Indirect effect = effect of inflation onto approval (x) effect of approval onto unemployment. I have already the direct effect of inflation onto unemployment, calculated above. I also have the partial effect of inflation onto approval--that is given by the multiple regression construct (-1.51). But then I do not have the effect of approval onto unemployment (rather I am given unemployment onto approval, which is -1.21). I cannot figure out, unfortunately, how to compute this coefficient. Thus I am missing two variables in a single equation: one indirect effect, and also the total effect. Is there a simpler way of going about this problem--have I overlooked or misconceptualized any part? Sincerely, Sean<html> <font size=3>Hi everyone,<br><br> Am lost on one problem of the homework--and hoping that there is a soul with advice.&nbsp; Number 3, where we must find the total effect of inflation upon unemployment and vice-versa.<br><br> Problem construct offers intercept and coefficient values for three regressions, two simple and one multiple.&nbsp; The first simple gives us the total effect of unemployment onto approval; the second gives us total effect of inflation onto approval; and the multiple gives partial effects of unemployment and inflation onto approval.<br><br> From these alone, a shrewd person surmises the partial effects between unemployment and inflation, in both directions, using simple algebra.&nbsp; Visualizing a triangular model as in the notes, the third 'leg' of the triangle is quickly ascertained.<br><br> Here is my mental roadblock.<br><br> To find the total effect of inflation onto unemployment, I conceptualize: total effect = direct effect + indirect effect.&nbsp; Again I visualize a triangular model.<br> Direct effect = effect of inflation onto unemployment.<br> Indirect effect = effect of inflation onto approval (x) effect of approval onto unemployment.<br><br> I have already the direct effect of inflation onto unemployment, calculated above.&nbsp; I also have the partial effect of inflation onto approval--that is given by the multiple regression construct (-1.51).&nbsp; But then I do not have the effect of approval onto unemployment (rather I am given unemployment onto approval, which is -1.21).&nbsp; I cannot figure out, unfortunately, how to compute this coefficient.<br><br> Thus I am missing two variables in a single equation: one indirect effect, and also the total effect.&nbsp; Is there a simpler way of going about this problem--have I overlooked or misconceptualized any part?<br><br> <br><br> Sincerely,<br><br> Sean</font></html>