New to econometrics.....HELP!

[replicator]

Hi everyone, first time poster so please be gentle.

Basically I'm a student and I've just started an introduction to econometrics module however I'm finding it quite difficult to grasp some of the concepts. We are using Eviews so I was hoping I'd be able to find some answers here. One of my main issues is to do with understanding residuals and how to interpret them. I know that the actual = fitted + residual and that the residual is basically the error term.

So in Eviews when I look at the residual chart of my model and see that the actual line is above the fitted line I have a positive residual. This is where the confusion sets in. Could someone please give me a definition of a positive residual. What does it mean for my model? Does it mean that my model is over-fitted or under-fitted?

We have been studying a very simple multiple regression model for the sales of a soft drink. The explanatory variables we are using include the price, a competitors price, the level of availabilty or distribution, hours of sunshine and levels of advertising. I understand that over periods that we see large positive or negative residuals we are failing to fit or explain our model accuratley and there must be something happening over that time period that we are not allowing for with our explanatory variables.

What I don't understand is how to interpret the difference between a positive and negative residual.

If I have a positive residual does it mean that I am not including a variable in my model that should be increasing sales over that period? Liewise if I have a negative residual does that mean that I should be including a variable that will have a negative impact on sales in that time period in order to lower the fitted inline with the actual?

Sorry for the long, rambling post, I'm not even sure if it makes much sense. I would be so appreciative if someone could offer me some insight.

Thanks in advance :D

[replicator]

Hi guys.

Can anyone help me out? I'm really struggling with this (I know it may seem basic to most), I'd be so appreciative for any help.

Even a link to a good website that could explain it to me would be great.

Cheers.

[JimForest]

Hi Replicator,

After running a regression a series is created to hold the residuals. The user manual describes this well. You may graph these residuals or do whatever test you want with them.

Positive residuals indicate that the actual value of the dependent variable was above the estimate of the dependent variable (based on the parameter values from the regression results).

In general, you want your residuals to be random white noise and normally distributed. You do not want there to be autocorrelation, seasonality, etc. as it would indicate that there are omitted variables in the specification.

Not sure what econometrics text you are using but it should cover these topics. Hang in there. You might want to also consult additional texts. A gentle introduction would be "Introductory Econometrics for Finance" by Chris Brooks. A more detailed text would be that of Greene or Judge, et. al..

You seem frustrated but very interested; so I suggest you keep at it. You might also want to consult Kennedy's guide to econometrics.

Here is a link to a more extensive listing of the current econometrics texts that is segmented into difficulty level:

http://econweb.umd.edu/~prucha/Handouts ... tbooks.pdf

Hope this helps.

[replicator]

Thanks for the reply Jim, you're a hero! What you're saying makes a lot of sense.

Just so I'm clear on my logic, is what I'm saying here a correct interpretation:

If I have a positive residual does it mean that I am not including a variable in my model that should be increasing sales over that period? Liewise if I have a negative residual does that mean that I should be including a variable that will have a negative impact on sales in that time period in order to lower the fitted inline with the actual?

Just one more thing.....If I have a positive residual does that mean my model or over or under fitted?

Thanks again for the reply, I really appreciate it! Will take a look at your reading list too.

[JimForest]

Hi Rep,

I think you are perhaps jumping ahead by trying to look at a single residual as an indication of whether the model is over-fitting or under-fitting.

Your summary statistics, such as the F-statistic and the adjusted R^2, will give you a feel for how well the data relate to the functional form. But you need to build up your knowledge of regression analysis and learn how to recognize potential violations of the OLS assumptions first.

I don't know what your dependent variable is, nor do I know your functional form, etc.. So I can't say anything about your model's fit unless I know what you are doing.

However, it does sound like you are enthusiastic about learning this material. I am happy to share feedback with you if I can help. But please try to digest a good introductory text and you will find that you can do many interesting things in EViews.

If you can get through the first five chapters or so of the Brooks text and take the online quizzes that come with the text, you will be in much better shape to go forward. :D

[JimForest]

I thought this link might also be helpful to you with respect to the concept of over-fitting:

http://en.wikipedia.org/wiki/Overfitting

To put it loosely, you might over-fit a model by adding too many parameters. You might achieve a higher R^2 by doing so, but when you use the model for out-of-sample prediction it may perform poorly. In fact, a simpler model may turn out to be a better source of prediction. If such is the case, I would say you have over-fitted the underlying relationship with your model.

[replicator]

Thanks Jim, your help's been great. I do really like econometrics but i think that somtimes I get caught up in some areas and just end up going around in circles.

I will try to get my hands on the Brooks text book to give me a better understanding.

Thanks again! Much appreciated.

Rep.