Fitting Rules to Data

In the last exercise you were asked to find the rule that applied to all the sets of data points.

Sometimes, in life, you have sets of data that don't follow the same rule exactly like in the Function Machine. For these you need to find a rule that fits most of the points.

How do you do that?

Look at the following example:
A statistics class collected cylindrical objects like coffee cans, juice cans, and a candle. They measured the circumference (distance around) and the diameter (the distance across) and prepared a table like the one below.

The data do look like the are making a trend don't they?

How would you find a rule, say in the form of a line y= mX+b, where m is the slope and b is the y-intercept?

Try drawing a graph.

This is a graph of the data points. Make your own graph now so you can draw and write on it.

Now draw a line which you feel that passes through most of the data points and find its equation.

Note: the graph will pass through the mean point.
This is the point which is the average of the diameter and the average of the circumference.
This makes sense because the object with average diameter should always have the average circumference, so this point must be on the line.

Then go on to see how the other statistics class did it.