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

standardize it by dividing by the standard error (see Chapter 3 for more on
this process).

Using the formula for standard error for b, the test statistic for the

hypothesis test of whether or not the slope equals zero is , where

. On the Minitab output from

Figure 4-2, the test statistic is located right next to the SE Coef column; it’s
cleverly marked T. In this case T = 7.78. Compare this value to t* = 2.228 from
the t-table. Because T > t*, you have strong evidence to reject Ho and con-
clude that the slope of the regression line for the textbook-weight data is not
zero. (In fact, it has to be greater than that, according to your data.)
You can also just find the exact p-value on the output, right next to the T
column, in the column is marked P. The p-value for the test for slope in this
case is 0.000, which means it’s less than 0.001. You conclude that the slope
of this line is not zero, so textbook weight is significantly related to student
weight. (See Chapter 3 to brush up on p-values.)

To test to see whether the slope is some value other than zero, just plug that
value in for b in the formula for the test statistic. Also, you may conduct
0
one-sided hypothesis tests to see whether the slope is strictly greater than
zero or strictly less than zero. In those cases, you find the same test statistic
but compare it to the value t* where the area to the right (or left, respectively)
is α.

Inspecting the y-intercept

The y-intercept is the place where the regression line y = a + bx crosses the
y-axis and is denoted by a (see the earlier section “The y-intercept of the
regression line”). Sometimes the y-intercept can be interpreted in a meaningful
way, and sometimes not. This differs from slope, which is always interpretable.
In fact, between the two elements of slope and intercept, the slope is the star
of the show, with the y-intercept serving as the somewhat less famous but
still noticeable sidekick.
There are times when the y-intercept makes no sense. For example, suppose
you use rain to predict bushels per acre of corn; if you have zero rain, you
have zero corn, but if the regression line crosses the y-axis somewhere else
besides zero (and it most likely will), the y-intercept will make no sense.

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