Regression analysis is a modeling technique for analyzing the relationship between a continuous (real-valued) dependent variable Y and one or more independent variables X1, X2,...,Xk. (Regression analysis is a 'method' of determining and understanding any relationship between a dependent value and one or more independent values.) The goal in regression analysis is to identify a function that describes, as closely as possible, the relationship between these variables so that we can predict what value the dependent variable will assume given specific values for the independent variables. (The ultimate goal of regression analysis is to be able to predict the dependent variable, when given the independent variable values. In order to do this, a function must be established that reflects the relationship between the dependent variable and the independent variables.)

In any regression model, there is an element of systematic relationship between the dependent variable and the independent variables. This systematic relationship is represented by a mathematical function. However, there is also an element of unsystematic variance, also known as disturbance, in which the dependent variable fluctuates away from the function of the independent variables. In summary, the dependent variable is dependent upon the function of the independent variables AND a given tendency to fluctuate away from the function.

Because of the variance that occurs due to unsystematic disturbance, the best that regression can do is provide a 'probable' value for the dependent variable, given the independent variable values. Statistics are used to identify the probability distributions of the dependent variable, for different values of the independent variables. Measurements exist to inform how reliable, statisically speaking, a regression function predicts the independent variable value.

Comments

Post a Comment

Popular posts from this blog

The agony of victory....a.k.a. picking my jaw up off the floor

Allright. I've now had nearly 24 hours (although its taken me a couple of days to complete this post) to calm down, reflect upon and digest the improbable gut wrenching game yesterday in which the heavily favored Colts lost to the Steelers 21-18. I wrote last year of not being as emotionally attached to the Steelers as I have been in the past. I wrote last week of how I thought that I might be spending too much valuable time following the Steelers, especially since I have absolutely no control over the outcome of their games. Let me just say this: yesterday's game was probably in the top five emotionally draining, and ultimately gratifying, experiences of my life. Ouside of my wedding and the birth of my two sons, I can't remember being as nervous, deflated, joyful, stunned and exhilirated as I was yesterday----all withing about a ten minute stretch of seemingly neverending time! What could have been a devestating loss to live with in the offseason (and, forever, for Jerome...
Read more

"The Axis of Evil and the Doctrine of Preemption Three Years On"

Jerod and I attended a lecture by Brookings Institution fellow Michael O'Hanlon last night at Park University in Parkville, MO. The lecture was part of the Jerzy Hauptmann Distinguished Guest Lecture series. As a Park University M.B.A. alum, I received an invitation to the 13th annual lecture in the series. I like going to events like this, especially since I was interested in the content of this particular lecture, of which the title was the title of this post. Dr. O'Hanlon described himself as a Sam Nunn Democrat at the beginning of the lecture. It's always difficult to prevent political feeling from entering into objective analysis, and I don't know how you measure the "objectiveness" of analysis, but I feel that most Brookings scholars are at least "fair", and Dr. O'Hanlon was no exception. His analysis of the doctrine of preemption was focused on the effectiveness of the doctrine, as opposed to any moral righteousness or implications of the...
Read more

Removing a password that was created in a previous version from an Access 2007 database

Earlier this week I was banging my head against the wall trying to figure out how to remove a password from an Access 2007 database (file extension .accdb). The database was created in a previous version of access and subsequently "upgraded" to the Access 2007 format. I believe some type of a wizard was used to perform the "upgrade." The security model is evidently different in Access 2007 than in previous versions. It doesn't appear that you can set/unset database passwords. Instead, in Access 2007, there is an option to Encrypt with Password. I'm not sure if this is supposed to be logically similar to the earlier version password architecture, but there was no way that I could find to easily remove the password that had been created in the earlier version when using the Access 2007 interface. Access security has always been confusing to me, and I need to take the time someday to understand how the security model is supposed to work in Access 2007. An...
Read more