Page 34 - Intermediate Statistics for Dummies

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Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis
And, you can’t study a negative number of hours, so a negative number for x
itself isn’t even possible.
On the other side of the coin, x probably isn’t a number in the two-digit range
(10 or more). Why is this? Say someone did study ten hours for this exam.
Plugging in 10 for x in Bill’s equation, you get y = 10 10 + 30, which equals
130. Remember, y is the predicted exam score. Because most exams are out
of 100 possible points, a score of 130 isn’t possible. (I’m all for extra credit on
exams, but 30 points of extra credit is too much, even for me.)
The point is that there are limits on the values of x that make sense in this
equation. However, the equation itself, y = 10x + 30, doesn’t know that, and if
you graph this line, it’ll go on forever in both the positive and negative direc-
tions (see Figure 1-1).
200 y * 13
150 y=10x+30
100
50
x
−20 −15 −10 −5 5 10 15 20
−50
Figure 1-1: −100
The line y =
10x + 30, for −150
all possible
values of x. −200

Data snooping isn’t cool

Statisticians have come up with a saying that you may have heard of: “Figures
don’t lie. Liars figure.” Make sure that you find out about all the analyses that
were performed on a data set, not just the ones reported as being statistically
significant.

Suppose Bill Prediction tries to apply his simple model (from the preceding
section) to predict exam scores for his whole class, based on their reported
amounts of study time, and he finds out that his results fall flat. He figures out