Linear & Non-Linear Regression

In Statistics, there is a methodology to do forecasting based on either Linear or Non-Linear regression. In Linear Regression, we assume that the behavior is linear while in Non-Linear Regression we have to assume some equation for the behavior.


Linear Regression

When there are two sets of data inter-related, and if we can assume the behavior as a linear one, we can do a Forecasting based on the available data. In Microsoft Excel, there are 3 methods to do this exercise.

Method 1

When there are two sets of data naming X & Y, when you plot the points, you will get a Scatter diagram without any pattern. We can draw a line of best fit (called the Regression Line) using a mathematical formula. To draw a line, you should have the Slope and Intercept values, i.e. values of m and c of the equation y=mx + c. In MS Excel there are two functions called Slope() and Intercept() which will give you the expected values.


Method 2

Instead of using two functions, you can use Linest() function which is of the form of an Array Formula. Using this function you will get the same values of Slope & Intercept.


Method 3

Instead of calculating Slope & Intercept and using them to calculate the Forecast() values, you can use the Forecast function directly to calculate the forecast values.


Non-Linear Regression

Even though we assume that most behaviors are linear, they are not. If we can assume any equation we can calculate the forecast values. If you create a XY Chart in MS Excel, you can find-out the curve in Non-Linear Regression using one of the few standard equations given, of course with the equation with it. Just Right-Click on the XY curve and select “Add Trendline” Option. The rest is up to you.


The question is why we should learn these things. What is the use of it ? Why can’t you give a weightage to incidents you have faced in your life and draw a curve with respect to the Time. Then you will definitely see a curve. A pattern of your life. And in 99.999 cases, the curve is sinusoidal!!!. i.e. there are repetitions at regular intervals. Find out the interval and you will know what will happen to you in due future. Even this can be applied to any other living being such as a country, business or a union.

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