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where a = the y-intercept (24.73 in our example in cell B66) and b = 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:
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 (g) (this is about 6.6 pounds)
Important note: Remember that the weight of the ﬁsh is in grams.
Since the weight is 3,000 (i.e., X = 3,000), substituting this number into our
regression equation gives:
Y ¼ 24 : 73 þ 0 : 0165 ð 3000 Þ
Y ¼ 24 : 73 þ 49 : 5
Y ¼ 74 : 23 00 ðÞ or 74 ; 230 eggs
ð
Þ
since the eggs are measured in thousands of eggs
Important note: If you look at your chart, if you go directly upwards for a
weight of 3,000 until you hit the regression line, you see that
you hit this line between 70 and 80 on the y-axis to the left
when you draw a line horizontal to the x-axis (actually, it is
74.23), the result above for predicting eggs produced from a
weight of 3,000 g.
Now, let’s do a second example and predict what the number of eggs produced
would be if we used a weight of 3,500 grams (g).
Y ¼ 24 : 73 þ 0 : 0165 X
Y ¼ 24 : 73 þ 0 : 0165 3 ; 500
ð
Þ
Y ¼ 24 : 73 þ 57 : 75
Y ¼ 82 : 48 or 82 ; 480 eggs
Important note: If you look at your chart, if you go directly upwards for a
weight of 3,500 until you hit the regression line, you see that
you hit this line between 80 and 90 on the y-axis to the left
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