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Chapter 4: Getting in Line with Simple Linear Regression 59

change from pounds to ounces, the correlation coefficient doesn’t change.
(What a messed-up world it would be if this wasn’t the case!)

If the relationship between x and y is uphill, or positive (as x increases, so
does y), the correlation is a positive number. If the relationship is downhill,
or negative (as x increases, y gets smaller), then the correlation is negative.
The following list translates different correlation values:

✓ A correlation value of zero means that you can find no linear
relationship between x and y. (It may be that a different relationship
exists, such as a curve; see Chapter 7 for more on this.)
✓ A correlation value of +1 or –1 indicates that the points fall in a
perfect, straight line. (Negative values indicate a downhill relationship;
positive values indicate an uphill relationship.)
✓ A correlation value close to +1 or –1 signifies a strong relationship. A
general rule of thumb is that correlations close to or beyond 0.7 or –0.7
are considered to be strong.

✓ A correlation closer to +0.5 or –0.5 shows a moderate relationship.
You can calculate the correlation coefficient by using a formula involving the
standard deviation of x, the standard deviation of y, and the covariance of x
and y, which measures how x and y move together in relation to their means.
However, the formula isn’t the focus here (you can find it in your Stats I text-
book or in my other book, Statistics For Dummies, published by Wiley); it’s
the concept that’s important. Any computer package can calculate the corre-
lation coefficient for you with a simple click of the mouse.
To have Minitab calculate a correlation for you, go to Stat>Basic Statistics>
Correlation. Highlight the variables you want correlations for, and click Select.
Then click OK.

The correlation for the textbook-weight example is (can you guess before
looking at it?) 0.926, which is very close to 1.0. This correlation means that a
very strong linear relationship is present between average textbook weight
and average student weight for grades 1–12, and that relationship is positive
and linear (it follows a straight line). This correlation is confirmed by the
scatterplot shown in Figure 4-1.
Data analysts should never make any conclusions about a relationship
between x and y based solely on either the correlation or the scatterplot
alone; the two elements need to be examined together. It’s possible (but of
course not a good idea) to manipulate graphs to look better or worse than
they really are just by changing the scales on the axes. Because of this, statisti-
cians never go with the scatterplot alone to determine whether or not a linear

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