What is prediciton by extrapolation?

Answer 1

Prediction by Extrapolation

Hello:

Prediction by extrapolation usually involves taking known dependent variables and independent variables and using those to predict what will happen when one has an unknown independent variable.

For example, imagine you want to investigate the effect of tequila on goldfish.

You are investigating the murder of fish at a pet store. You have found eight tanks of gold fish, each containing 100 gold fish. To the first, the bad guy put in one shot of tequila, to the second, 2 shots, to the third tank three shots and so forth. Then you observe the results. In the first tank, 9 fish went belly up; in the second tank 18, in the third tank 24, fourth tank 35, fifth tank was 42, sixth tank there were 54 dead fish, and 60 dead fish in the seventh tank. But in the eighth tank, there were 98 dead fish, but the bad guy wont tell you how many shots of tequila she put in the tank.

Here are the known data:

Shots ................Death Rate

1 ...................... 9

2 ......................18

3 ........................24

4 .........................35

5 .......................42

6 .......................54

7 ........................60

Unknown.............. 98

In this case, you notice that there seems to be a relationship wherein the number of dead fish directly and proportionally increases with the number of shots. And in fact, if you chart out the data, you notice that if you draw a line between the dots, it forms almost a straight line. (I have placed a graph of the data here: www.forensic-applications.com/misc/Goldfish.jpg )Ah ha! You have found a "linear" dose-response curve.

But you have to testify in court as to how many shots the bad guy put in the eighth tank needed to kill 98 fish. That is, you need to predict, without harming any more fish, how many shots she put in the tank.

To do this, you will mathematically perform a linear extrapolation. You can do it one of several ways - for example you can do the long complicated way using math, or, my favorite way, you literally draw an "extrapolation line" through your data points (the red line in my example). Next find "98" on the Y axis (the vertical axis), and draw another straight line horizontally outward until it intersects the "extrapolation line." (Go to www.forensic-applications.com/misc/Goldfish1.jpg for an example. ) The point where your two lines intersect is directly above the answer to your question, so now draw a third line straight down. (Go to www.forensic-applications.com/misc/Goldfish2.jpg for an example. ) You will see that the line crosses the X axis (at the bottom) at about 11. You have now performed the most simple "prediction by extrapolation." You know the bad guy put in about 11 shots in the eighth tank.

Not all relationships are linear, and not all linear extrapolations are valid. For example, there is not one single study on Earth, that demonstrates that radon gas, as found in homes, causes cancer. However, the only studies that suggest that radon is a risk are those by, or based upon, the US Environmental Protection Agency wherein they used a "linear no-threshold dose-response relationship" even though there is absolutely no science to support the argument that the relationship is linear (in fact, we know that the relationship is NOT linear, but rather looks like a "W," and the cancer rate at radon levels found in homes is actually LOWER than in houses with no radon!)

Frequently the inappropriate use of such relationships are termed "junk science" (as in the case of the EPA radon risk estimates), and sometimes called "pathological science" (as in the case seen in "global warming studies"), where there is an intentional desire to mislead.