Page 78 - Statistics II for Dummies

62 Part II: Using Different Types of Regression to Make Predictions

the y-intercept is just a constant — it never changes). The y-intercept is the
point where the line crosses the y-axis; in other words, it’s the value of y
when x equals zero.

The y-intercept of a regression line may or may not have a practical meaning
depending on the situation. To determine whether the y-intercept of a
regression line has practical meaning, look at the following:

✓ Does the y-intercept fall within the actual values in the data set? If yes, it
has practical meaning.
✓ Does the y-intercept fall into negative territory where negative y-values
aren’t possible? For example, if the y-values are weights, they can’t be
negative. Then the y-intercept has no practical meaning. The y-intercept
is still needed in the equation though, because it just happens to be the
place where the line, if extended to the y-axis, crosses the y-axis.
✓ Does the value x = 0 have practical meaning? For example, if x is tem-
perature at a football game in Green Bay, then x = 0 is a value that’s
relevant to examine. If x = 0 has practical meaning, then the y-intercept
does too, because it represents the value of y when x = 0. If the value
of x = 0 doesn’t have practical meaning in its own right (such as when
x represents height of a toddler), then the y-intercept doesn’t either.

In the textbook example, the y-intercept doesn’t really have a practical
meaning because students don’t weigh zero pounds, so you don’t really care
what the estimated textbook weight is for that situation. But you do need to
find a line that fits the data you do have (where average student weights go
from 48.5 to 142 pounds). That best-fitting line must include a y-intercept, and
for this problem, that y-intercept happens to be 3.69 pounds.

The slope of the regression line

The value 0.113 from Figure 4-2 indicates the coefficient (or number in front)
of the student-weight variable. This number is also known as the slope. It
represents the change in y (textbook weight) is associated with a one-unit
increase in x (student weight). As student weight increases by 1 pound, text-
book weight increases by about 0.113 pounds, on average. To make this rela-
tionship more meaningful, you can multiply both quantities by 10 to say that
as student weight increases by 10 pounds, the textbook weight goes up by
about 1.13 pounds on average.

Whenever you get a number for the slope, take that number and put it over 1
to help you get started on a proper interpretation of slope. For example, a slope
of 0.113 is rewritten as . Using the idea that slope equals rise over run,
or change in y over change in x, you can interpret the value of 0.113 in the follow-
ing way: As x increases on average by 1 pound, y increases by 0.113 pounds.

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