Linear regression is the process of determining whether or not a line is the best model for a given set of data, and, if it is, the equation of the line of best fit must then be determined. The following flowchart summarizes the procedure for the process of linear regression.



The equations for r, a, and b are as follows:



(r is the correlation coefficient)





('a' is the slope of the line of best fit)




('b' is the y-intercept)



Note that 'a', and the averages of y and x must be found before 'b'.

Example: The following data was obtained in a Physics experiment and plotted. Determine if a straight line is a good model for this data and if so, determine the line of best fit.

time (s)	distance (cm)
1	2
3	5
5	8
7	11
9	15

When this data is plotted as a raw graph, it appears that a straight line is the best model:



A calculation of r should be done. Using the above equations, r=0.9981, which indicates a strong correlation.

According to the flowchart above, the next step is to calculate 'a' and 'b', which are calculated to be
a= 1.6 s and b=0.2 cm.

Therefore, the equation of the line of best fit is d=1.6t+0.2.

The graph below demonstrates a strong correlation:



This entry would have received a full 8/8, with a possible additional 2 marks from the writer's comments on another writer's entry.
The graphs were done in Excel, and then they were copied and pasted in MS Paint. In Paint, the graphs were saved as jpg images, then uploaded to the wiki.
the equations were done in MS Word using Equation Editor, and then copied and pasted into MS Paint. In Paint, they were saved as jpg images, then uploaded to the wiki.