Linear Regression Analysis

Many relationships resemble linear relationships of some kind. For instance, it may be expected that the price of an item and how much of it is purchased resembles a linear relationship. Mathematically, it is possible to fit a line to such data where fluctuations in one piece of data, in this case the price of an item, correlates with fluctuatons in some other piece of data, quantity in our example. One can fit a line to this pattern so as to make reasonable predictions about the behavior of the relationship at hand. You may enter two data sets, much like price and quantity as illustrated here, call them x (independent variable) and y (dependent variable). The y variable is the variable you are trying to predict. In the table, Y' is the predicted value, that value that the line is determining for the given X. Then you have the difference between the observed and the predicted (Y - Y') and that value squared. The graph that emerges shows the observed Ys (blue dots) and the prediction line calculated (blue line). Try it and see.

Enter the number of (x,y) data pairs:

X Y Y' Y - Y' (Y - Y')2