What does best fit line show regarding the variables plotted and the work of experimenter?
Answers
Answer:
Explanation:In this lab you will need to determine whether or not a graph expresses a linear relationship. To do this you must draw what is known as a "best fit" straight line, also called a "regression line".
The purpose of the graph is to visually display relationships which may not be apparent from data tables. Experimental errors which are always present may obscure the relationships. The best fit line averages out the errors.
There are ways of calculating a regression line. You can find the formula in any statistics text. Most of the time an "eyeball" line will suffice. Many computer graphing software programs such as Excel will draw a regression line for you. The software will quickly draw the line and calculate its slope, intercept, and regression coefficient.
The regression coefficient is used to determine how nearly the points fall on a straight line, or how nearly linear they are. A perfect correlation will have a regression coefficient of R = 1.000 . . . Normally in the physical sciences we would like to have a "confidence level' of 0.01 or better. That means that a coefficient of R = .990 or higher gives us the confidence to say that a relationship is linear within a margin of tolerable error.
Without computer software you will need to draw the lines "by hand" and then make a judgement about whether the points are "linear". This judgement depends upon the nature of the experiment and how far you are willing to go in saying the relationship is linear. In other words, "how close is close enough"? The answer depends on your confidence and your judgement.
Here are two examples of graphs. The regression line has been drawn for each by the computer, but the regression coefficients have been left out for now. Clicking on the graph will give a full set of statistics for each graph so you can see how the numbers relate to your own judgement.