Page 72 - Statistics II for Dummies

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

Exploring Relationships with Scatterplots

and Correlations

Before looking ahead to predicting a value of y from x using a line, you
need to
✓ Establish that you have a legitimate reason to do so by using a straight
line.
✓ Feel confident that using a line to make that prediction will actually work
well.

In order to accomplish both of these important steps, you need to first plot
the data in a pairwise fashion so you can visually look for a relationship; then
you need to somehow quantify that relationship in terms of how well those
points follow a line. In this section, you do just that, using scatterplots and
correlations.
Here’s a perfect example of a situation where simple linear regression is
useful: In 2004, the California State Board of Education wrote a report entitled
“Textbook Weight in California: Analysis and Recommendations.” This report
discussed the great concern over the weight of the textbooks in students’
backpacks and the problems it presents for students. The board conducted a
study where it weighed a variety of textbooks from each of four core
areas studied in grades 1–12 (reading, math, science, and history — where’s
statistics?) over a range of textbook brands and found the average total
weight for all four books for each grade.

The board consulted pediatricians and chiropractors, who recommended
that the weight of a student’s backpack should not exceed 15 percent of
his or her body weight. From there, the board hypothesized that the total
weight of the textbooks in these four areas increases for each grade level
and wanted to see whether it could find a relationship between the average
child’s weight in each grade and the average weight of his or her books. So
along with the average weight of the four core-area textbooks for each grade,
researchers also recorded the average weight for the students in that grade.
The results are shown in Table 4-1.

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