Page 97 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
48.5 pounds to 142 pounds). That best-fitting line must include a y-intercept,
and for this problem, that y-intercept happens to be 3.69.
The slope of the regression line
The value 0.113 from Figure 4-2 indicates the coefficient (or number in front of)
of the student-weight variable. This number is also known as the slope. It repre-
sents the change in y (textbook weight) due to a one-unit increase in x (student
weight). As student weight increases by one pound, textbook weight increases
by about 0.113 pounds, on average. To make this relationship more meaningful,
you can multiply both quantities by ten 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, just take that number and put it over
1. Doing this can help you get started on a proper interpretation of slope. For
⁄1. Using the idea that slope equals rise
example, a slope of 0.113 is rewritten as
0.113
over run, or change in y over change in x, you can interpret the value of 0.113 in
the following way: As x increases by one pound, y increases by 0.113 pounds.
Making estimates by using
the regression line
Now that you have a line that estimates y given x, you can use it to estimate
the (average) value of y for a given value of x. The basic idea is to take a rea-
sonable value of x, plug it in to the equation of the regression line, and see
what the value of y gives you.
In the textbook-weight example, the best-fitting line (or model) is the line y =
3.69 + 0.113x. For an average student that weighs 60 pounds, for example, the
estimated average textbook weight is 3.69 + 0.113 60 = 10.47 pounds (those
*
poor little kids!). If the average student weighs 100 pounds, the estimated aver-
age textbook weight is 3.69 + 0.113 100 = 14.99, or nearly 15 pounds.
*
Checking the Model’s Fit (The Data,
Not the Clothes!)
After you’ve established a relationship between x and y and have come up
with an equation of a line that represents that relationship, you may think
your job is done. (Many researchers erringly stop here, so I’m depending on
you to break the cycle on this!) But the most-important job remains to be
completed: checking to be sure that the conditions of the model are truly met