How Do Linear Regression and R-Squared Differ?

[xeon123]

I am trying to understand how linear regression and R-squared differ.

1 - Can anyone give me an example of use of linear regression and R-squared?

2 - They have some relation between them? E.g., they are useful for each other?

3 - What are the dangers when analysing the linear regression results?

 

[Stephen Tashi]

You should use the term "coefficient of determination" instead of "R-squared". Perhaps someone interested in that statistic will jump on your question.

 

[HallsofIvy]

The "least squares line" is the line that (in the "least squares" sense) best fits the given points. "R^2" is a numerical measure of just how good that fit is.

 

[chiro]

Hey xeon123.

1 - The measure looks at the level of linear correlation between two variables (assuming pair-wise relationships exist).

2 - There is a connection between this and the linear coefficient for a simple linear regression involving two variables (with an intercept and slope term), and you can find this by reading a decent book on the subject (i.e. linear regression).

3 - Just make sure you put the model, statistics, and data into context. Understand the models limitations, the limitations of the data, and the shortcomings of both when trying to answer the question you initially set out to.

Typically you are always trying to answer a question and you want to find an answer that is good enough to use for your application and simples enough to use and understand.

Applications vary quite a lot from say designing a computer to modelling fish harvest and birth processes. One application requires extremely specific models and the other just requires something that is "good enough".