Linear Regression and Correlation

Linear regression is the process of modeling the relationship between two variables by drawing a best-fit line that represents the trend revealed by a scatter plot of the data.  When it comes to linear regression, it is worth noting that this linear equation is not an absolute representation of the reality of this situation. It is only a model that can be used to illustrate the potential relationship between variables in order to make an informed decision.  

Spreadsheets and statistical calculators are very efficient at computing the best fit lines for scatter plots. This is done by applying a least-squares regression line to obtain the best fit line.  This approach attempts to limit the error (or residual) difference between points in the scatter plot and points on the best-fit line.  

The correlation coefficient r (also known as Pearson’s r) tells us the strength of the relationship between the independent variable x and dependent variable y. The coefficient of determination r² is simply the square of the correlation coefficient r.  The coefficient of determination is typically reported as a percentage that represents the amount of variability in the dependent variable y that can be explained by variation in the independent variable x using the least squares regression line.  

The following presentation provides a more detailed treatment of the application of linear regression and correlation to statistical analysis:

The following Excel spreadsheet was used in the video above to conduct the analysis:

This video provides a demonstration of the linear regression Excel sheet:

There are many free linear regression calculators available.  The following video demonstrates just one of them:

Here are some demos on how to perform linear regression and correlation using Rstudio.