Teachers hate this kind of math abuse (and to this former physics teacher, this abuse of math is near unforgivable.
First, a bit of math terminology. A "linear function" (so named because it makes a line on a graph) means that each time one variable (called the independent variable) changes one unit, another variable (the dependent variable) changes a set amount. For example if I make $8/hr... it represents a linear function. When the time I work (the independent variable) increases 1 hour, the money I get increases exactly $8. To be a true linear function this relationship must be predictable and consistant.
Mathmaticians invented a "linear regression" as a way to find the linear function
behind a set of data. If there is data that is made by a process that makes a linear function
, then this technique can account for "noise" (other factors that might change the data) to find the specifics.
A basic precept of this math is (and listen closely)-- A linear regression is meaningless unless there is an underlying linear function
Let's look at todays case in point, from pollster.com.
This guy not only calculates a linear regression (which he drew on the graph), he goes so far as to claim that predictions of the future based on this graph are someone not completely meaningless. And, he even calculates the future result- (McCain wins by 2.3%). Keep this future result in mind as we discuss.
Why is this unforgivably stupid to anyone with a basic understanding of math?
1) What is the linear function?
Well he is relating days before the election with popular support for the candidates. The function he is implying is
Every day for the past 150 days, the same number of people have changed their mind from Obama to McCain, and the same number of people will change their minds each day for the next 50 days.
This idea alone should be silly enough to completely reject this graph.
2) The result is basically random (based on start day).
Let's look at a strange property his type of flawed analysis.
This guy gets a result (McCain will win by 2.3%) based on the past 150 days of data. If the number of McCain supporters gained per day were constant over the past 150
, then you would get the same result if you did the same analysis over the past 100 days.
As it turns out, the poll numbers have clearly were not linear over the past 150 days. So if you take the past 100 days, you would get a different results. If you take the past 5 days (as the polls have "corrected" a bit after the Palin thing), you would have a line and an answer that would have Obama winning by a very big margin.
So the number this guy calculated is basically a random number... it changes based on what day he plugged into his little formula. How can that be meaningful?
3) What's with the range.
Think about what happened in this election over the past 150 days? You think the same function applies over the past 150 days?
4) The really silly cases
. Linear functions imply a zero. If his function were mathematically true... and couple be applied backwards indefinitely (and remember he applies it backward himself 150 days (and forward another 50), there was some point when McCain had 0 supporters.
What does this mean?
Of course if the election is held in a couple of years... everybody will be a McCain supporter. (Don't ask about negative McCain supporters... since I think they are all negative).
What's the big deal?
The language of Math is designed to make statements about truth. When you put a linear regression line on a graph, you are stating that the data are represented by a linear function.
When the data are clearly not linear... the line is a lie.
This line, is mathematically meaningless. It is nothing more than a random number. But this abuse of math makes it seem like there is some principle to back up the dubious point he is trying to make-- simply because he plugged numbers into a calculator.
Any professor would have no choice but to give an 'F'