Microsoft Office Tutorials and References

In Depth Information

But ﬁrst, let’s review some basic terms.

6.5.2.1 Finding the y-Intercept, a, of the Regression Line

The point on the y-axis that the regression line would intersect the y-axis if it were

extended to reach the y-axis is called the ‘‘y-intercept’’ and we will use the letter

‘‘a’’ to stand for the y-intercept of the regression line. The y-intercept on the

SUMMARY OUTPUT on the previous page is 24.73 and appears in cell B66.This

means that if you were to draw an imaginary line continuing down the regression

line toward the y-axis that this imaginary line would cross the y-axis at 24.73. This

is why it is called the ‘‘y-intercept.’’

6.5.2.2 Finding the Slope, b, of the Regression Line

The ‘‘tilt’’ of the regression line is called the ‘‘slope’’ of the regression line. It

summarizes to what degree the regression line is either above or below a

horizontal line through the data points. If the correlation between X and Y were zero,

the regression line would be exactly horizontal to the X-axis and would have a

zero slope.

If the correlation between X and Y is positive, the regression line would ‘‘slope

upward to the right’’ above the X-axis. Since the regression line in Fig.
6.27
slopes

upward to the right, the slope of the regression line is +0.0165 as given in cell B67.

We will use the notation ‘‘b’’ to stand for the slope of the regression line. (Note

that Excel calls the slope of the line: ‘‘X Variable 1’’ in the Excel printout.)

Since the correlation between weight and eggs produced was +0.87, you can see

that the regression line for these data ‘‘slopes upward to the right’’ through the

data. Note that the SUMMARY OUTPUT of the regression line in Fig.
6.27
gives

a correlation, r, of +0.87 in cell B53.

If the correlation between X and Y were negative, the regression line would

‘‘slope down to the right’’ above the X-axis. This would happen whenever the

correlation between X and Y is a negative correlation that is between zero and

minus one (0 and -1).

6.5.3 Finding the Equation for the Regression Line

To ﬁnd the regression equation for the straight line that can be used to predict the

number of eggs produced from the ﬁsh’s weight, we only need two numbers in the

SUMMARY OUTPUT in Fig.
6.27
: B66 and B67.

The format for the regression line is:

Y
¼
a
þ
bX

ð
6
:
3
Þ

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