Linear regression vs r-squared

[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".

 

[blue_raver22]

1 - Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps to identify the linear trend or pattern in the data and make predictions based on this trend. An example of using linear regression could be predicting the sales of a product based on its price, advertising budget, and other factors.

R-squared, also known as the coefficient of determination, is a measure of how well the regression model fits the data. It ranges from 0 to 1, with higher values indicating a better fit. An example of using R-squared could be comparing the performance of different regression models to determine which one best explains the variation in the data.

2 - Linear regression and R-squared have a close relationship as R-squared is derived from the linear regression model. R-squared can be interpreted as the percentage of variation in the dependent variable that can be explained by the independent variables in the regression model. Therefore, a higher R-squared value indicates a stronger relationship between the variables and a better fit of the model.

3 - There are a few dangers to consider when analyzing the results of a linear regression model. First, it is important to ensure that the model assumptions are met, such as linearity, normality, and homoscedasticity. Violation of these assumptions can lead to biased and unreliable results. Additionally, it is crucial to consider the context and potential confounding variables that may influence the relationship between the variables. Lastly, it is important to remember that correlation does not imply causation, so further research and analysis may be needed to establish a causal relationship.