In Science, we are doing graphs, and my teacher said that line of best fit can be wavy or straight depending on the graph. But I was taught last year in math that you draw a straight line to average the points out so each side is roughly equal. Now, she says it's not like connect the dots, but you want to touch through as many as you can. And some can be wavy...I'm lost. any help?
2007-09-05 14:22:11 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Other - Science
If you want to be a stickler for terminology, a line is always straight (in Euclidean geometry). The process of 'curve-fitting' aims to find a mathematical relationship that is a good approximation to observed data.
The eye is much better at fitting to a line, so if you suspect an exponential relationship, try to plot a line on semi-log graph paper. Or, instead of plotting X and Y, plot X and the square root of Y.
2007-09-06 20:10:01 · answer #1 · answered by Frank N 7 · 0⤊ 0⤋
I'm sure it's also possible to have curved lines of best fit, but there have to be some rules, man!
The traditional line is a straight one, and it is chosen to minimize the sum of the squares of the distances of the points from the line.
Some data does actually fall on a curved line. It you measure the position of a ball rolling down an inclined plane at equal intervals, it will increase in a quadratic fashion. However, the line of best fit will be a smooth curve that has a well-defined formula. It isn't 'wavy'.
The equation of the line, either curved or straight, must be rigorously defined. Oherwise you haven't achieved anything except to have drawed a pretty line on a page.
2007-09-05 21:33:41 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Data points are taken experimentally from real things (experiments) designed to focus on certain natural occurrences. Like measuring gravity, pressure, weight, or resistance.
These data points are representative of the math used to describe these occurrences. As such the data can take many forms. Straight lines or curves. You can absolutely have a 'best fit' 'curve' to straight lines or *curves*.
What it means is, you are finding a curve that fits closest to each and every data point as possible. In this way you are more assured that the curve generated will give rise to a mathematical function which can be used to manipulate and discover other aspects of the process of the experiment conducted. In other words, the best fit curve means the curve represents the data as closely as possible with minimal error.
Does this help at all??
2007-09-05 21:37:37 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Yes, the line of best fit can definitely be curved.
But, unless it's clear or there's a physical explanation why it should be curved, the usual first choice is to try and fit a straight line.
There are a number of measures of average distance from the points to the line that can be used to decide whether the best fit is a straight line or a curve.
2007-09-05 21:47:32 · answer #4 · answered by Bob 7 · 0⤊ 0⤋