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(2b) Read from the graph the gill weight you would predict for a body weight of
20 grams and write your answer in the space immediately below:
(f) save the ﬁle as: CRAB3
Answer the following questions using your Excel printout:
1. What is the correlation?
2. What is the y-intercept?
3. What is the slope of the line?
4. What is the regression equation for these data (use two decimal places for the
yintercept and the slope)?
5. Use that regression equation to predict the gill weight you would expect for a
body weight of 15 grams.
(Note that this correlation is not the multiple correlation as the Excel table
indicates, but is merely the correlation r instead).
Note that you found a positive correlation of +.87 between body weight and gill
weight in crabs above. You know that the correlation is a positive correlation for
two reasons: (1) the regression line slopes upward and to the right on the chart,
signaling a positive correlation, and (2) the slope is +14.58 which also tells you
that the correlation is a positive correlation.
But how does Excel treat negative correlations?
Since Excel does not recognize negative correlations in the
SUMMARY OUTPUT but treats all correlations as if they were
positive correlations, you need to be careful to note when there
is a negative correlation between the two variables under study.
You know that the correlation is negative when:
(1) The slope, b, is a negative number which can only occur when there is a
(2) The chart clearly shows a downward slope in the regression line, which can
only happen when the correlation is negative.
3. Suppose that you wanted to study mayﬂies in lakes in western Montana.
Mayﬂies are common aquatic insects found in rivers, streams, and lakes across
the United States. You are trying to study the relationship between the body
length and the forewing length of mayﬂies.
You want to study the body length (from the head to the start of the tail) in
millimeters (mm) and the forewing (front wing) length (in mm). You have decided
to use body length as the predictor and forewing length as the criterion. You have
collected a small sample of mayﬂies from various lakes in Montana to test your
Excel skills and to make sure that you can do this type of research. The
hypothetical data appear in Fig. 6.32 :
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