Least squares introduction This is a common application of min-max problems that most people don't think about as such. The reason you don't think about it this way is because your calculator or computer can do the work for you, but it is based on the theory of minimizing two variables. In experimental sciences, you must often perform least squares interpolation. The idea is that you perform an experiment and record some data. For example, in measuring frogs, you might look at the size of a frog's leg compared to the frog's eyes, or at how much of one reactant you used compared to how much of a product you generated by synthesizing it. To a mathematician, the two functions are unrelated, but to an experimental scientist, this linear relationship indicates a causal connection between them. The scientist will therefore plot the results on a graph and claim that the two variables are related. Given experimental data (xi, yi), the line that best fits the data is the one that minimizes the distance between each data point and its corresponding point on the line. The question would be to find a line that fits well with the given data, so that you can predict future sales. For example, if you look at your new homework problems, the first problem asks you to predict how many iPods will be on this planet in 10 years based on past sales and how they behave. One thing before you lose all your money though: You cannot use this technique to predict the stock market because it doesn't work.