Microsoft Office Tutorials and References
In Depth Information
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
.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
þ
.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).
þ
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
(6.3)
where a
¼
the y-intercept (24.73 in our example in cell B66) and b
¼
the slope of
the line (
0.0165 in our example in cell B67)
Therefore, the equation for the best-ﬁtting regression line for our example is:
þ
Y
¼
a
þ
bX
Y
¼
24.73
þ
0.0165 X
Remember that Y is the eggs produced that we are trying to predict, using the
weight of the ﬁsh as the predictor, X.
Let’s try an example using this formula to predict the number of eggs produced
for a female ﬁsh.
6.5.4 Using the Regression Line to Predict the y-value for a Given
x-value
Objective : To ﬁnd the eggs produced predicted from a ﬁsh that
weighted 3,000 grams (this is about 6.6 pounds)
Important note: Remember that the weight of the ﬁsh is in grams.
Since the weight is 3000 (i.e., X
¼
3000), substituting this number into our
regression equation gives:
Y
¼
24.73
þ
0.0165 (3000)
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