Casio FX-795P - Linear regression constant term; Linear regression coefficient; Correlation coefficient; Estimated value of x

38
CHAPTER 2 Manual Operations
Oe
Exercise:
The
table
below
shows
the
ratios
of
advertising
expenditure
(advertising
expendi-
ture/operating
expenses)
and
the
ratios
of
operating
profit
(operating
profit/sales
amount)
in
seven
chain
supermarkets
last
year.
Was
advertising
effective?
sor] 1 [2|3) 4/5 /6|7
Ratio of adver'sing | 9.8| 2.1 | 2.5 | 1.8| 3.1) 4.0 | 1.0
Ratio of operating | 2.5 | 3.4| 3.7 | 3.2| 4.3] 6.3 | 2.3
Approach:
Draw up a scatter diagram based on the table.
y
e+
5+
ad
Ratio of operating profit
al
ol*
1+
—t ttt
123 4 xn
Ratio of advertising expenditure
The
scatter
diagram
suggests
that
profit
increased
with
advertising
expenditure.
The
line
connecting.the
plotted
points
in
the
diagram
is
called
the
regression
curve.
In
this
case,
it
is
almost
linear
and
is
therefore
called
linear
regression.
This
linear
regression
is
expressed
by
y=
a
+
b-x
where
a
is
called
the
linear
regression
constant
term
and
b
the
linear
regression
coefficient.
The
correlation
coefficient
(r)
is
known
to
be
within
the
range
of
-1
¢r<l.
Correlationship
is
positive
when
0
<r
<
1,
negative
when
-1
¢r
<0,
and
no
correlationship when r= 0.
Now input data' on the seven stores and obtain statistics.
r
25 Statistical Calculations
Operation:
cam
Gar |r) ea eee
0.802.5m
2.103.48)
(Statistical memories cleared)
(Input all the paired data.)
Next,
output
paired-variable
statistics
by
using
STAT
LIST
2.
(Mean
of
x)
fans)
(oar
ust]
D
(exe
(Mean
of
y)
;
ex)
(Standard
deviation
of
x)
Ea
(Standard
deviation
of
y)
&)
(Sample
standard
deviation
of
x)
bq
(Sample
standard
deviation
of
y)
fa)
(Linear
regression
constant
term)
ex
(Linear
regression
coefficient)
x)
(Correlation
coefficient)
ea
It
is
evident
from
the
value
of
r
that
x
and
y
have
a
positive
correlation.
Then,
what
advertising
expenditure
ratio
should
be
adopted
to
bring
the
operating
profit
ratio
to
5.7%?
What
operating
profit
ratio
will
result
when
the
advertising
expenditure
ratio
is
4.5%?
Now
estimate
such
values.
(Estimated value of x) Gr} EX 5 7 be 2, 281
(Estimated
value
of
y)
MS4.563
(6,4
It
is
estimated
from
the
above
answers
that
the
advertising
expenditure
ratio
needed
to
bring
the
operating
profit
ratio
to
5.7%
is
3.96%,
and.
that
when
the
advertising
expenditure
ratio
is
4.5%,
an
operating
profit
ratio
of
6.32%
will
result.
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39