Notes for HW 6:
•
When there’s a strong correlation between
x
and
y
(i.e., the coefficient of correlation,
r
, is
greater than .7), we use the equation of the regression line to predict
y
for a given
x
value.
Otherwise, we use the average of
y
for any given
x
values.
o
For example, given a set of
x
and
y
values, say the average of the
y
values is 10 and the
equation of the regression line is
ˆ
2
4
y
x
=
+
. If
r
is .8, then to predict
y
when
x
is 5 will
be
y
= 2(5) + 4 = 13. On the other hand, when
r
is .6, then to predict
y
when
x
is 5 (or any
value of
x
) will be 10 since 10 is the average of the
y
values.
•
Even there’s a strong correlation between
x
and
y
, we use the equation of the regression line
to predict
y
for
x
values that are within a “workable” scope.
o
For example, say the equation of the regression line is
ˆ
2
30
y
x
=
+
where
x
is the age of a
man and
y
is his height. We can use this equation to predict his height as long as the man
is growing at a certain age. That is, we probably can use still use this equation for any
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 Spring '11
 HaHe
 Correlation, Standard Deviation, regression line

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