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37
2. Two-variable Statistics and
Linear
Regression
In addition to the statistics for
both
variables
x
and
y
which are the same as those of
x
in
single-variable
statistics,
the sum of the products
of
samples
~xy is
obtained
in two-
variable
statistics. Two-variable
statistics make possible the development of a relation-
ship
(correlation)
between
two sets
of
data.
Each pair of
data
has x and
y
values.
From
these
sets
of data a line of
regression
can be
established.
The relationship of
the
two sets of data by use of the
straight
line method is called Linear
Regression.
In Linear
Regression
there
are three
important values, r,
a,
and
b.
The equation of the
straight line
is
y
=
a
+
bx,
where a
i
s the point
at
which the line
crosses the Y-axis and
b is the slope of
the line.
The correlation
coefficient r
shows the relationship between two sets of
data.
A perfect
correlation
between two values
is an r
equal
to
1
(-1
is a perfect negative
correla-
tion);
in other
words,
by knowing
the
value of one
variable
you can
predict with
100%
accuracy the value of the
other
variable. The
further
the
val
u e
of r
is
from
1, the less
reliable will your predictions
be.
The following table
can
be used as a set of definitions
of
the
values of the correlation coefficient:
Display:
7.
9.
Key
in:
65
00
2
lsHtFTI
~
60
00
2
ffiilll
Correct Data
(CD): The last data entry
in
the
above example is
an error and must be
changed to 60
x
2.
Key in:
Display:
Mean:
@!.Film
53.88888889
Standard
Deviation:
lsHIFTI
~
9.279607271
Variance:
~
86.11111111
Notes:
1.
After all
the
data
have
been
entered,
statistics such as
mean value,
standard
deviation,
etc., may be obtained
in
any
desired
order.
2.
After a mean
value,
standard
deviation,
or
any
other
statistic has
been
obtained as an
intermediate result,
more data
can be
entered and
statistical
calculations
can be performed continuously
on
additional data
entry.
Key
in:
Display
[SHIFT
I
[STAT]
0.
35
~
1.
45
~
2.
55X5
~
7.
65x2
~
9.
As each sample is
entered,
the
number
of data of
that
sample will
appear
at the right
of
the display.
Using as a Calculator
- Quick Links:
- Basic Commands
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