What is the method of least squares?

Question

And how do i use it to estimate the relationship between discharging voltage and time?

What is the equation for the method of least squares if the main equation of the data is Y = Be^mx OR
ln(Y) = mx + ln(b) (preferred)

Answer 1

Before you tackle the equations, it might help to understand the objectives. Sometimes points fall on a straight line (linear curve) and you can draw a line through them using any two points (preferably far apart for accuracy). At other times the points fall above and below any straight line perhaps because of inaccuracies in measuring say both time and distance, represented by the line. Anyone could draw a straight line through the points by eyeball observation to approximate the line. Sometimes this is easy because all the points are nearly on the line. Sometimes it is difficult because several points are well off the line and it is not clear that there have been an errors or the points are real. Any bad points (flyers) are eliminated based on good judgement. However, using a least squares fit of the remaining points will give you a representative line that scientists around the world would all obtain, good or bad. The process finds a line throught the field of points such that if you drew a perpendicular to the line from every point and measured the distances (deviations), squared the deviations and summed them up, the sum of the squares would be a minimum (least squares fit). Holding both ends of the line you could move it around to find the correct line, however the equations for least square fit do that for you. Squaring deviations changes positive and negative values to positive. The method of least squares fit reduces the influence of flyers that can not be eliminated. The rest is math. Good luck.

Answer 2

Least squares is a type of math technique used for statistics. Basic short version. It takes data and puts it in an equation. that answer is then put into the equation until you basically get the same answer over and over. when this happens it is the best equation or function that best fits the data in the first place. So if you have data (example: discharging votage and time) you put through least squares technique and get the best equation for that dat. Now you can use that equation to give any discharging voltage for any given time.

Answer 3

the method of least squares is a technique used to find an equation for data. to start, you might use Fourier series to come up with a series of possible equations. the method of least squares minimizes the rms (Root of Mean of the Squares) of the error (difference between actual data and data predicted by the equation).

Answer 4

It it way above my head.
Never heard about them. Sorry man.