Page 306 - Statistics for Dummies

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Part V: Statistical Studies and the Hunt for a Meaningful Relationship
Always calculate the slope before the y-intercept. The formula for the y-intercept

contains the slope!
Interpreting the regression line
Even more important than being able to calculate the slope and y-intercept
to form the best-fitting regression line is the ability to interpret their values;
I explain how to do so in the following sections.
Interpreting the slope
The slope is interpreted in algebra as rise over run. If, for example, the slope
is 2, you can write this as ⁄1 and say that as you move from point to point on
the line, as the value of the X variable increases by 1, the value of the Y vari-
able increases by 2. In a regression context, the slope is the heart and soul of
the equation because it tells you how much you can expect Y to change as X
increases. 2
In general, the units for slope are the units of the Y variable per units of the X
variable. It’s a ratio of change in Y per change in X. Suppose in studying the
effect of dosage level in milligrams (mg) on systolic blood pressure (mmHg),
a researcher finds that the slope of the regression line is –2.5. You can write
this as ⁄1 and say that systolic blood pressure is expected to decrease by
–2.5
2.5 mmHg on average per 1 mg increase in drug dosage.
Always make sure to use proper units when interpreting slope. If you don’t
consider units, you won’t really see the connection between the two variables
at hand. For example if Y is exam score and X = study time, and you find the
slope of the equation is 5, what does this mean? Not much without any units
to draw from. Including the units, you see you get an increase of 5 points
(change in Y) for every 1 hour increase in studying (change in X). Also be sure
to watch for variables that have more than one common unit, such as tem-
perature being in either Fahrenheit or Celsius; know which unit is being used.
If using a 1 in the denominator of slope is not super-meaningful to you, you
can multiply the top and bottom by any number (as long as it’s the same
number) and interpret it that way instead. In the systolic blood pressure
example, instead of writing slope as ⁄1 and interpreting it as a drop of
–2.5
2.5 mmHg per 1 mg increase of the drug, you can multiply the top and bottom
–25
by 10 to get ⁄10 and say an increase in dosage of 10 mg results in a decrease
in systolic blood pressure of 25 mmHg.
Interpreting the y-intercept
The y-intercept is the place where the regression line y = mx + b crosses the
y-axis where x = 0, and is denoted by b (see the earlier section “Finding the
y-intercept”). Sometimes the y-intercept can be interpreted in a meaningful

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