Ativa DS-700 Manuale d'uso - Pagina 2

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Example:
4.123.586.4 = 21.1496
4.123.587.1 = 7.6496
[ON/AC] [4] [•] [1] [2] []
4 .1 2x3.58+6.
21.1496
[3] [•] [5] [8] [] [6] [•] [4] [=]
D
[3]
1 2x 3.58+6.4 _
21.1496
D
[3] [3] [3] [3]
4 .1 2x3.58+6.
21.1496
D
[] [7] [•] [1]
1 2x 3.58–7.1 _
21.1496
D
[=]
4 .1 2x3.58–7.
7.6496
D
The replay function is not cleared even when [ON/AC] is
pressed or when power is turned OFF, so contents can be
recalled even after [ON/AC] is pressed.
Replay function is cleared when mode or operation is
switched.
Error Position Display Function
When an ERROR message appears during operation
execution, the error can be cleared by pressing the
[ON/AC] key, and the values or formula can be re-entered
from the beginning. However, by pressing the [3] or [4]
key, the ERROR message is cancelled and the cursor moves
to the point where the error was generated.
Example: 1402.3 is input by mistake
[ON/AC] [1] [4] [] [0] []
Ma ERROR
[2] [.] [3] [=]
[3] (or [4] )
1 4 ÷0x 2.3
0.
D
Correct the input by pressing
[3] [SHIFT] [INS] [1]
1 4 ÷10 x2.3
0.
D
[=]
1 4 ÷10 x2.3
3.22
D
– 20 –
Scientific Function
Trigonometric functions and inverse trigonometric
functions
• Be sure to set the unit of angular measurement before
performing trigonometric
function and inverse
trigonometric function calculations.
• The unit of angular measurement (degrees, radians,
grads) is selected in sub-menu.
• Once a unit of angular measurement is set, it remains in
effect until a new unit is set. Settings are not cleared
when power is switched OFF.
Display
Example
Operation
(Lower)
sin 63 º 52'41"
[MODE][MODE][1]
("DEG" selected)
[sin] 63 [ º ' "] 52 [ º ' "]
= 0.897859012
41 [ º ' "][=]
0.897859012
cos (π/3 rad) = 0.5
[MODE][MODE][2]
("RAD" selected)
[cos][(] [SHIFT][π][]3
[)] [=]
0.5
tan (–35 grad)
[MODE][MODE][3]
= –0.612800788
("GRA" selected)
[tan] [(–)] 35 [=]
–0.612800788
2sin45 º cos65 º
[MODE][MODE][1]
("DEG")
= 0.597672477
2[sin] 45 [cos] 65 [=]
0.597672477
sin
–1
0.5 = 30
[SHIFT][sin
–1
] 0.5 [=]
30.
–1
cos
(√2/2)
[MODE][MODE][2]
("RAD")
= 0.785398163 rad
[SHIFT][cos
–1
][(][√]2 []2
= π/4 rad
[)][=]
0.785398163
[][SHIFT][π][=]
0.25
tan
–1
0.741
[MODE][MODE][1]
("DEG")
= 36.53844577 º
[SHIFT][tan
–1
]0.741[=]
36.53844576
= 36 º 32' 18.4"
←
36 º 32 º 18.4 º
[SHIFT] [
º' "]
If the total number of digits for degrees/minutes/seconds exceed
11 digits, the higher order values are given display priority, and
any lower-order values are not displayed. However, the entire
value is stored within the unit as a decimal value.
2.5(sin
–1
0.8cos
–1
0.9)
2.5[] [(] [SHIFT] [sin
–1
]0.8
= 68 º 13'13.53"
–1
[] [SHIFT] [cos
] 0.9 [)]
68 º 13 º 13.53 º
[=] [SHIFT] [
←
º' "]
– 21 –
Performing Hyperbolic and Inverse Hyperbolic Functions
Display
Example
Operation
(Lower)
sinh3.6= 18.28545536
[hyp][sin] 3.6 [=]
18.28545536
cosh1.23 = 1.856761057
[hyp][cos] 1.23 [=]
1.856761057
tanh2.5= 0.986614298
[hyp][tan] 2.5 [=]
0.986614298
cosh1.5sinh1.5
[hyp][cos] 1.5 [][hyp]
= 0.22313016
[sin] 1.5 [=]
0.22313016
sinh
–1
30 = 4.094622224
[hyp][SHIFT][sin
–1
] 30 [=]
4.094622224
–1
–1
cosh
(20/15)
[hyp][SHIFT][cos
][(] 20
= 0.795365461
[] 15 [)][=]
0.795365461
x = (tanh
–1
0.88) / 4
[hyp][SHIFT][tan
–1
]0.88
= 0.343941914
[]4[=]
0.343941914
sinh
–1
2cosh
–1
1.5
[hyp][SHIFT][sin
–1
]2[]
= 1.389388923
[hyp][SHIFT][cos
–1
]1.5[=]
1.389388923
–1
–1
–1
sinh
(2/3)tanh
(4/5)
[hyp][SHIFT][sin
][(]2[]
= 1.723757406
3[)][][hyp][SHIFT][tan
–1
]
[(]4[]5[)][=]
1.723757406
Logarithmic and Exponential Functions
Display
Example
Operation
(Lower)
log1.23
[log] 1.23 [=]
= 8.990511110
–2
0.089905111
In90 = 4.49980967
[In] 90 [=]
4.49980967
log456In456
[log]456[In]456 [=]
0.434294481
= 0.434294481
10
1.23
= 16.98243652
[SHIFT][10
x
] 1.23 [=]
16.98243652
4.5
x
e
= 90.0171313
[SHIFT][e
]4.5[=]
90.0171313
10
4
• e
–4
1.2 • 10
2.3
[SHIFT][10
x
]4[][SHIFT][e
x
]
= 422.5878667
[(–)]4[]1.2[][SHIFT][10
x
]
2.3[=]
422.5878667
(–3)
4
= 81
[(][(–)] 3 [)] [x
y
] 4 [=]
81.
–3
4
= –81
[(–)] 3 [x
y
] 4 [=]
–81.
2.3
y
5.6
= 52.58143837
5.6 [x
] 2.3 [=]
52.58143837
7
√123 = 1.988647795
7 [SHIFT][
x
√] 123 [=]
1.988647795
(7823)
–12
[(]78[]23[)][x
y
][(–)]12[=]
1.305111829
–21
–21
= 1.30511182910
23
3
√644 = 10
2[]3[]3[SHIFT][
x
√]64
[]4[=]
10.
(5+6.7)
y
23.4
= 3306232
2[]3.4[x
][(]5[]6.7[)][=]
3306232.001
– 22 –
Coordinate Transformation
• This scientific calculator lets you convert between
rectangular coordinates and polar coordinates, i.e., P(x, y)
↔ P(r, )
• Calculation results are stored in variable memory E and
variable memory F. Contents of variable memory E are
displayed initially. To display contents of memory F,
press [RCL] [F].
• With polar coordinates,  can be calculated within a
range of –180 º < ≤180 º .
(Calculated range is the same with radians or grads.)
Display
Example
Operation
(Lower)
x=14 and y=20.7, what
[MODE][MODE][1]
("DEG" selected)
are r and  º ?
[Pol(]14 [ , ]20.7[)][=]
24.98979792(r)
[RCL][F]
55.92839019()
←
55 º 55 º 42.2()
[SHIFT][
º' "]
x=7.5 and y=–10, what
[MODE][MODE][2]
("RAD" selected)
[Pol(]7.5[ , ][(–)]10[)][=]
are r and  rad?
12.5(r)
[RCL][F]
–0.927295218()
r=25 and = 56 º , what
[MODE][MODE][1]
("DEG" selected)
[SHIFT][Rec(]25 [ , ]56[)][=]
are x and y?
13.97982259(x)
[RCL][F]
20.72593931(y)
r=4.5 and =2π/3 rad,
[MODE][MODE][2]
("RAD" selected)
[SHIFT][Rec(]4.5[ , ][(]2[]
what are x and y?
3[][SHIFT][π][)][)][=]
–2.25(x)
[RCL][F]
3.897114317(y)
Permutation and Combination
Total number of permutations nPr = n!/(n
r)!
Total number of combinations nCr = n!/(r!(n
r)!)
Display
Example
Operation
(Lower)
Taking any four out of
10[SHIFT][nPr]4[=]
5040.
ten items and arranging
them in a row, how many
different arrangements
are possible?
P
= 5040
10
4
– 23 –
Display
Example
Operation
(Lower)
Using any four numbers
7[SHIFT][nPr]4[]3[]
360.
from 1 to 7, how many
7[=]
four digit even numbers
can be formed if none of
the four digits consist of
the same number?
(3/7 of the total number
of permutations will be
even.)
P
37 = 360
7
4
If any four items are
10[nCr]4[=]
210.
removed from a total
of 10 items, how many
different combinations
of four items are
possible?
C
= 210
10
4
If 5 class officers are
25[nCr]5[]15[nCr]5[=]
50127.
being selected for a
class of 15 boys and
10 girls, how many
combinations are
possible? At least one
girl must be included
in each group.
C
C
= 50127
25
5
15
5
Other Functions (√ , x
2
, x
–1
, x!,
3
√, Ran#)
Display
Example
Operation
(Lower)
√2√5 = 3.65028154
[√]2[][√]5[=]
3.65028154
2
2
3
2
4
2
5
2
= 54
2[x
2
][]3[x
2
][]4[x
2
]
54.
2
[]5[x
][=]
(3)
2
= 9
[(][(–)]3[)][x
2
][=]
9.
1/(1/3–1/4) = 12
[(]3[x
–1
][]4[x
–1
][)][x
–1
][=]
12.
8! = 40320
8[SHIFT][x!][=]
40320.
3
√(364249) = 42
[
3
√][(]36[]42[]49[)][=]
42.
Random number
[SHIFT][Ran#][=]
0.792
generation (number is
(random)
in the range of 0.000 to
0.999)
– 24 –
Display
Example
Operation
(Lower)
2
√(1–sin
40)
[MODE][MODE][1]
("DEG" selected)
= 0.766044443
[√][(]1[][(][sin]40[)][x
2
]
[)][=]
0.766044443
–1
[SHIFT][cos
][Ans][=]
40.
1/2!1/4!1/6!1/8!
2[SHIFT][x!][x
–1
][]
= 0.543080357
4[SHIFT][x!][x
–1
][]
–1
6[SHIFT][x!][x
][]
8[SHIFT][x!][x
–1
][=]
0.543080357
Fractions
Fractions are input and displayed in the order of integer,
numerator and denominator. Values are automatically
displayed in decimal format whenever the total number of
digits of a fractional value (interger + numerator +
denominator + separator marks) exceeds 10.
Display
Example
Operation
(Lower)
2
1
13
b
b
/
3
/
= 3
/
2[a
/
]5[]3[a
/
]1
5
4
20
c
c
b
[a
/
]4[=]
3
13
20.
c
⎦
⎦
b
[a
/
c
](conversion to decimal)
3.65
Fractions can be converted
to decimals, and then
converted back to fractions.
456
11
b
b
3
/
= 8
/
3[a
/
]456[a
/
]78[=]
8
11
13.
78
13
c
c
⎦
⎦
d
[SHIFT][
/
]
115
13.
c
⎦
1
1
b
b
/
2578
/
4572
1[a
/
c
]2578[]1[a
/
c
]
–04
= 0.00060662
4572[=]
6.066202547
When the total number
of characters, including
integer, numerator,
denominator and
delimiter mark exceeds
10, the input fraction is
automatically displayed
in decimal format.
1
b
/
0.5 = 0.25
1[a
/
]2[].5[=]
0.25
2
c
1
4
5
1
b
b
/
(–
/
)–
/
= –1
/
1[a
/
]3[][(–)]4[a
/
]5
3
5
6
10
c
c
b
[]5[a
/
]6[=]
–1
1
10.
c
⎦
⎦
1
1
1
1
b
b
/
/
/
/
1[a
/
]2[]1[a
/
]3[]
2
3
4
5
c
c
13
b
b
=
/
1[a
/
]4[]1[a
/
]5[=]
13
60.
60
c
c
⎦
1
1
b
b
(
/
)/
=
/
[(]1[a
/
]2[)][a
/
]3[=]
1
6.
2
3
6
c
c
⎦
1
1
1
5
b
b
/(
/
3
/
4
) = 1
/
7
1[a
/
c
][(]1[a
/
c
]3[]
b
1[a
/
]4[)][=]
1
5
7.
c
⎦
⎦
– 25 –
Degree, Radian, Gradient Interconversion
Degree, radian and gradient can be converted to each
other with the use of [SHIFT][DRG>]. Once [SHIFT]
[DRG>] have been keyed in, the "DRG" selection menu
will be shown as follows.
D
R
G
1
2
3
Example
Operation
Display
Define degree first
[MODE][MODE][1]
("DEG" selected)
r
Change 20 radian to
20[SHIFT][DRG>][2][=]
20
degree
1145.91559
To perform the following
10[SHIFT][DRG>][2]
calculation :-
[]25.5[SHIFT][DRG>][3]
10 radians+25.5 gradients
[=]
10
r
25.5
g
The answer is expressed
595.9077951
in degree.
Degrees, Minutes, Seconds Calculations
You can perform sexagesimal calculations using degrees
(hours), minutes and seconds. And convert between
sexagesimal and decimal values.
Example
Operation
Display
2 º 15 º 28.8
To express 2.258 degrees
2.258[º' "][=]
in deg/min/sec.
To perform the calculation:
12[º' "]34[º' "]56[º' "][]
12 º 34'56"3.45
43 º 24 º 31.2
3.45[=]
– 26 –
Statistical Calculations
This unit can be used to make statistical calculations
including standard deviation in the "SD" mode, and
regression calculation in the "REG" mode.
Standard Deviation
In the "SD" mode, calculations including 2 types of
standard deviation formulas, mean, number of data, sum
of data, and sum of square can be performed.
Data input
1. Press [MODE] [2] to specify SD mode.
2. Press [SHIFT] [Scl] [=] to clear the statistical memories.
3. Input data, pressing [DT] key (= [M+]) each time a new
piece of data is entered.
Example Data: 10, 20, 30
Key operation: 10 [DT] 20 [DT] 30 [DT]
• When multiples of the same data are input, two different
entry methods are possible.
Example 1 Data: 10, 20, 20, 30
Key operation: 10 [DT] 20 [DT] [DT] 30 [DT]
The previously entered data is entered again each time
the DT is pressed without entering data (in this case 20
is re-entered).
Example 2
Data: 10, 20, 20, 20, 20, 20, 20, 30
Key operation: 10 [DT] 20 [SHIFT] [;] 6 [DT] 30 [DT]
By pressing [SHIFT] and then entering a semicolon
followed by value that represents the number of items the
data is repeated (6, in this case) and the [DT] key, the
multiple data entries (for 20, in this case) are made
automatically.
Deleting input data
There are various ways to delete value data, depending on
how and where it was entered.
Example 1 40 [DT] 20 [DT] 30 [DT] 50 [DT]
To delete 50, press [SHIFT] [CL].
Example 2 40 [DT] 20 [DT] 30 [DT] 50 [DT]
To delete 20, press 20 [SHIFT] [CL].
Example 3 30 [DT] 50 [DT] 120 [SHIFT] [;]
To delete 120 [SHIFT] [;] , press [ON/AC].
Example 4 30 [DT] 50 [DT] 120 [SHIFT] [;] 31
To delete 120 [SHIFT] [;] 31, press [AC].
– 27 –
Example 5 30 [DT] 50 [DT] 120 [SHIFT] [;] 31 [DT]
To delete 120 [SHIFT] [;] 31 [DT], press [SHIFT] [CL].
Example 6 50 [DT] 120 [SHIFT] [;] 31 [DT] 40 [DT] 30 [DT]
To delete 120 [SHIFT] [;] 31 [DT], press 120 [SHIFT] [;] 31
[SHIFT] [CL].
Example 7 [√] 10 [DT] [√] 20 [DT] [√] 30 [DT]
To delete [√] 20 [DT], press [√] 20 [=] [Ans] [SHIFT] [CL].
Example 8 [√] 10 [DT] [√] 20 [DT] [√] 30 [DT]
To delete [√] 20 [DT], press [√] 20 [SHIFT] [;] [(–)] 1 [DT].
Performing calculations
The following procedures are used to perform the various
standard deviation calculations.
Key operation
Result
Population standard deviation, xσ
[SHIFT][xσ
]
n
n
Sample standard deviation, xσ
[SHIFT][xσ
]
n–1
n–1
Mean, x
[SHIFT][x]
[RCL][A]
Sum of square of data, ∑x
2
[RCL][B]
Sum of data, ∑x
Number of data, n
[RCL][C]
Standard deviation and mean calculations are performed
as shown below:
n
2
Population standard deviation σ
= √(∑(x
i
x)
/
)
n
where i = 1 to
n
n
Sample standard deviation σ
= √(∑(x
x)
2
/(
-
))
i
1
n–1
where i = 1 to
n
Mean x = (∑x)/
n
Example
Operation
Display
Data 55, 54, 51, 55, 53,
[MODE][2]
0.
(SD Mode)
53, 54, 52
[SHIFT][Scl][=]
0.
(Memory cleared)
55[DT]54[DT]51[DT]
55[DT]53[DT][DT]54[DT]
52[DT]
52.
What is deviation of the
[RCL][C]
8.
(Number of data)
unbiased variance, and
[RCL][B]
427.
(Sumof data)
the mean of the above
[RCL][A]
22805.
(Sum of square of data)
data?
[SHIFT][x][=]
53.375
(Mean)
[SHIFT][xσ
][=]
1.316956719
n
(Population SD)
[SHIFT][xσ
][=]
1.407885953
n–1
(Sample SD)
[SHIFT][xσ
]
n–1
[x
2
][=]
1.982142857
(Sample variance)
– 28 –
Regression Calculation
In the REG mode, calculations including linear regression,
logarithmic regression, exponential regression, power
regression, inverse regression and quadratic regression
can be performed.
Press [MODE] [3] to enter the "REG" mode:
CO MP S D RE G
1
2
3
and then select one of the following regression types:-
Li n Lo g Ex p
1
2
3
Lin: linear regression
Log: logarithmic regression
Exp: exponential regression
press [4] for the other three regression types:-
Pw r In v Qu a d
1
2
3
Pwr: power regression
Inv: inverse regression
Quad: quadratic regression
Linear regression
Linear regression calculations are carried out using the
following formula:
y = A + Bx.
Data input
Press [MODE] [3] [1] to specify linear regression under
the "REG" mode.
Press [Shift] [Scl] [=] to clear the statistical memories.
Input data in the following format: <x data> [,] <y data>
[DT]
• When multiples of the same data are input, two different
entry methods are possible:
Example 1 Data: 10/20, 20/30, 20/30, 40/50
Key operation: 10 [,] 20 [DT]
20 [,] 30 [DT] [DT]
40 [,] 50 [DT]
The previously entered data is entered again each time
the [DT] key is pressed (in this case 20/30 is re-entered).
– 29 –
Example 2 Data: 10/20, 20/30, 20/30, 20/30, 20/30, 20/30,
40/50
Key operation: 10 [,] 20 [DT]
20 [,] 30 [SHIFT] [;] 5 [DT]
40 [,] 50 [DT]
By pressing [SHIFT] and then entering a semicolon
followed by a value that represents the number of times
the data is repeated (5, in this case) and the [DT] key, the
multiple data entries (for 20/30, in this case) are made
automatically.
Deleting input data
There are various ways to delete value data, depending on
how and where it was entered.
Example 1
10 [,] 40 [DT]
20 [,] 20 [DT]
30 [,] 30 [DT]
40 [,] 50
To delete 40 [,] 50, press [ON/AC]
Example 2
10 [,] 40 [DT]
20 [,] 20 [DT]
30 [,] 30 [DT]
40 [,] 50 [DT]
To delete 40 [,] 50 [DT], press [SHIFT][CL]
Example 3
To delete 20 [,] 20 [DT], press 20 [,] 20 [SHIFT][CL]
Example 4
[√] 10 [,] 40 [DT]
[√] 40 [,] 50 [DT]
To delete[√]10[,]40[DT],
press [√]10[=][Ans][,]40[SHIFT][CL]
– 30 –
Key Operations to recall regression calculation results
Key operation
Result
[SHIFT][A][=]
Constant term of regression A
[SHIFT][B][=]
Regression coefficient B
[SHIFT][C][=]
Regression coefficient C
Correlation coefficient r
[SHIFT][r][=]
Estimated value of x
[SHIFT][x][=]
Estimated value of y
[SHIFT][y][=]
Population standard deviation, yσ
[SHIFT][yσ
]
n
n
Sample standard deviation, yσ
[SHIFT][yσ
]
n–1
n–1
Mean, y
[SHIFT][y]
Population standard deviation, xσ
[SHIFT][xσ
]
n
n
Sample standard deviation, xσ
[SHIFT][xσ
]
n–1
n–1
Mean, x
[SHIFT][x]
[RCL][A]
Sum of square of data, ∑x
2
[RCL][B]
Sum of data, ∑x
n
[RCL][C]
Number of data,
[RCL][D]
Sum of square of data, ∑y
2
[RCL][E]
Sum of data, ∑y
[RCL][F]
Sum of data, ∑xy
Performing calculations
The following procedures are used to perform the various
linear regression calculations.
The regression formula is y = A + Bx. The constant term of
regression A, regression coefficient B, correlation r,
estimated value of x, and estimated value of y are
calculated as shown below:
A = ( ∑y∑x )/n
B = ( n∑xy∑x∑y ) / ( n∑x
2
2
(∑x )
)
r = ( n∑xy∑x∑y ) / √ (( n∑x
)( n∑y
2
(∑x )
2
2
(∑y )
2
))
y = A + Bx
x = ( yA) / B
– 31 –
Example
Operation
Display
Temperature and length
[MODE][3][1]
0.
of a steel bar
("REG" then select linear regression)
Temp
Length
[SHIFT][Scl][=]
0.
(Memory cleared)
10[ , ]1003[DT]
10ºC
1003mm
10.
15[ , ]1005[DT]
15ºC
1005mm
15.
20[ , ]1010[DT]
20ºC
1010mm
20.
25[ , ]1011[DT]
25ºC
1011mm
25.
30[ , ]1014[DT]
30ºC
1014mm
30.
Using this table, the
[SHIFT][A][=]
997.4
(Constant term A)
regression formula and
[SHIFT][B][=]
0.56
(Regression coefficient B)
correlation coefficient
can be obtained. Based
[SHIFT][r][=]
0.982607368
(Correlation coefficient r)
on the coefficient
formula, the length of
18[SHIFT][y]
1007.48
(Length at 18ºC)
the steel bar at 18ºC
1000[SHIFT][x]
4.642857143
(Temp at 1000mm)
and the temperature
[SHIFT][r][x
2
][=]
0.965517241
(Critical coefficient)
at 1000mm can be
estimated. Furthermore
[(][RCL][F][–][RCL][C][]
the critical coefficient
[SHIFT][x][][SHIFT][y][)][]
r
2
(
) and covariance can
[(][RCL][C][–]1[)][=]
35.
(Covariance)
also be calculated.
Logarithmic regression
Logarithmic regression calculations are carried out using
the following formula:
y = A + B•lnx
Data input
Press [MODE] [3] [2] to specify logarithmic regression
under "REG" mode.
Press [SHIFT] [Scl] [=] to clear the statistical memories.
Input data in the following format: <x data>, <y data>
[DT]
• To make multiple entries of the same data, follow
procedures described for linear regression.
Deleting input data
To delete input data, follow the procedures described for
linear regression.
– 32 –
Performing calculations
The logarithmic regression formula y = A + B•lnx. As x is
input, In(x) will be stored instead of x itself. Hence, we can
treat the logarithmic regression formula same as the
linear regression formula. Therefore, the formulas for
constant term A, regression coefficient B and correlation
coefficient r are identical for logarithmic and linear
regression.
Example
Operation
Display
xi
yi
[MODE][3][2]
0.
29
1.6
("REG" then select LOG regression)
50
23.5
[SHIFT][Scl][=]
0.
(Memory cleared)
74
38
29[ , ]1.6[DT]
29.
103
46.4
50[ , ]23.5[DT]
50.
118
48.9
74[ , ]38[DT]
74.
The logarithmic
103[ , ]46.4[DT]
103.
regression of the above
118[ , ]48.9[DT]
data, the regression
118.
formula and correlation
[SHIFT][A][=]
–111.1283975
(Constant term A)
coefficient are obtained.
[SHIFT][B][=]
34.02014748
(Regression coefficient B)
Furthermore, respective
[SHIFT][r][=]
(Correlation coefficient r)
0.994013946
estimated values y and
80[SHIFT][y]
(y when xi=80)
37.94879482
x can be obtained for
xi = 80 and yi = 73 using
73[SHIFT][x]
(x when yi=73)
224.1541314
the regression formula.
A number of logarithmic regression calculation results
differ from those produced by linear regression. Note the
following:
Linear regression Logarithmic regression
∑x
∑Inx
2
2
∑x
∑(Inx)
∑xy
∑y•Inx
Exponential regression
Exponential regression calculations are carried out using
the following formula:
e
B•x
y = A•
(ln y = ln A +Bx)
Data input
Press [MODE] [3] [3] to specify exponential regression
under the "REG" mode.
Press [SHIFT] [Scl] [=] to clear the statistical memories.
Input data in the following format: <x data>,<y data> [DT]
• To make multiple entries of the same data, follow
procedures described for linear regression.
Deleting input data
To delete input data, follow the procedures described for
linear regression.
– 33 –
Performing calculations
If we assume that lny = y and lnA = a', the exponential
e
B•x
regression formula y = A•
(ln y = ln A +Bx) becomes
the linear regression formula y =a' + bx if we store In(y)
instead of y itself. Therefore, the formulas for constant
term A, regression coefficient B and correlation coefficient
r are identical for exponential and linear regression.
A number of exponential regression calculation results
differ from those produced by linear regression. Note the
following:
Linear regression Exponential regression
∑y
∑Iny
∑y
2
∑(Iny)
2
∑xy
∑x•Iny
Example
Operation
Display
xi
yi
[MODE][3][3]
0.
6.9
21.4
("REG" then select Exp regression)
12.9
15.7
[SHIFT][Scl][=]
0.
(Memory cleared)
19.8
12.1
6.9[ , ]21.4[DT]
6.9
26.7
8.5
12.9[ , ]15.7[DT]
12.9
35.1
5.2
19.8[ , ]12.1[DT]
19.8
Through exponential
26.7[ , ]8.5[DT]
26.7
regression of the above
35.1[ , ]5.2[DT]
data, the regression
35.1
formula and correlation
[SHIFT][A][=]
30.49758742
(Constant term A)
coefficient are obtained.
[SHIFT][B][=]
–0.049203708
Furthermore, the
(Regression coefficient B)
regression formula is
[SHIFT][r][=]
–0.997247351
used to obtain the
(Correlation coefficient r)
respective estimated
values of y and x, when
16[SHIFT][y]
13.87915739
(y when xi=16)
xi = 16 and yi = 20.
20[SHIFT][x]
(x when yi=20)
8.574868045
Power regression
Power regression calculations are carried out using the
following formula:
x
x
y = A•
B
(lny = lnA + Bln
)
Data input
Press [MODE] [3] [4] [1] to specify "power regression".
Press [SHIFT] [Scl] [=] to clear the statistical memories.
Input data in the following format: <x data>,<y data> [DT]
• To make multiple entries of the same data, follow
procedures described for linear regression.
Deleting input data
To delete input data, follow the procedures described for
linear regression
– 34 –
Performing calculations
x
x
If we assume that lny = y, lnA =a' and ln
=
, the power
x
x
regression formula y = A•
B
(lny = lnA + Bln
) becomes
x
x
the linear regression formula y = a' + b
if we store In(
)
x
and y themselves. Therefore, the
and In(y) instead of
formulas for constant term A, regression coefficient B and
correlation coefficient r are identical the power and linear
regression.
A number of power regression calculation results differ
from those produced by linear regression. Note the
following:
Linear regression Power regression
∑x
∑Inx
∑x
2
∑(Inx)
2
∑y
∑Iny
2
2
∑y
∑(Iny)
∑xy
∑Inx•Iny
Example
Operation
Display
xi
yi
[MODE][3][4][1]
0.
28
2410
("REG" then select Pwr regression)
30
3033
[SHIFT][Scl][=]
0.
(Memory cleared)
33
3895
28[ , ]2410[DT]
28.
35
4491
30[ , ]3033[DT]
30.
38
5717
33[ , ]3895[DT]
33.
Through power
35[ , ]4491[DT]
35.
regression of the above
38[ , ]5717[DT]
data, the regression
38.
formula and correlation
[SHIFT][A][=]
0.238801069
(Constant term A)
coefficient are obtained.
[SHIFT][B][=]
2.771866156
Furthermore, the
(Regression coefficient B)
regression formula is
[SHIFT][r][=]
0.998906255
used to obtain the
(Correlation coefficient r)
respective estimated
values of y and x, when
40[SHIFT][y]
(y when xi=40)
6587.674587
xi = 40 and yi = 1000.
1000[SHIFT][x]
(x when yi=1000)
20.26225681
Inverse regression
Power regression calculations are carried out using the
following formula:
y = A + ( B/x )
Data input
Press [MODE] [3] [4] [2] to specify "inverse regression".
Press [SHIFT] [Scl] [=] to clear the statistical memories.
Input data in the following format: <x data>,<y data> [DT]
• To make multiple entries of the same data, follow
procedures described for linear regression.
– 35 –
Deleting input data
To delete input data, follow the procedures described for
linear regression
Performing calculations
If 1/x is stored instead of x itself, the inverse regression
formula y = A + ( B/x ) becomes the linear regression
formula y = a + bx. Therefore, the formulas for constant
term A, regression coefficient B and correlation coefficient
r are identical the power and linear regression.
A number of inverse regression calculation results differ
from those produced by linear regression. Note the
following:
Linear regression Inverse regression
∑x
∑(1/x)
∑x
2
∑(1/x)
2
∑xy
∑(y/x)
Example
Operation
Display
xi
yi
[MODE][3][4][2]
0.
2
2
("REG" then select Inv regression)
3
3
[SHIFT][Scl][=]
0.
(Memory cleared)
4
4
2[ , ]2[DT]
2.
5
5
3[ , ]3[DT]
3.
6
6
4[ , ]4[DT]
4.
Through inverse
5[ , ]5[DT]
5.
regression of the above
6[ , ]6[DT]
data, the regression
6.
formula and correlation
[SHIFT][A][=]
7.272727272
(Constant term A)
coefficient are obtained.
[SHIFT][B][=]
–11.28526646
Furthermore, the
(Regression coefficient B)
regression formula is
[SHIFT][r][=]
–0.950169098
used to obtain the
(Correlation coefficient r)
respective estimated
values of y and x, when
10[SHIFT][y]
(y when xi=10)
6.144200627
xi = 10 and yi = 9.
9[SHIFT][x]
(x when yi=9)
–6.533575316
– 36 –
Quadratic Regression
Quadratic regression calculations are carried out using the
following formula:
y = A + Bx + Cx
2
Data input
Press [MODE] [3] [4] [3] to specify quadratic regression
under the "REG" mode.
Press [SHIFT] [Scl] [=] to clear the statistical memories.
Input data in this format: <x data>,<y data> [DT]
• To make multiple entries of the same data, follow
procedures described for linear regression.
Deleting input data
To delete input data, follow the procedures described for
linear regression.
Performing calculations
The following procedures are used to perform the various
linear regression calculations.
2
The regression formula is y = A + Bx + Cx
where A, B, C are
regression coefficients.
y∑x
C = [(n∑x
2
(∑x)
2
) (n∑x
2
2
∑y )(n∑x
3
∑x
2
∑x) (n∑xy
2
2
4
2
2
3
2
2
∑x∑y)][(n∑x
(∑x)
) (n∑x
(∑x
)
)(n∑x
∑x
∑x)
]
B = [n∑xy∑x∑yC (n∑x
3
∑x
2
∑x)](n∑x
2
(∑x)
2
)
A = (∑yB∑xC∑x
2
) / n
y, you can recall
To read the value of ∑x
3
, ∑x
4
or ∑x
2
memory [RCL] M, Y and X respectively.
Example
Operation
Display
xi
yi
[MODE][3][4][3]
29
1.6
("REG" then select Quad regression)
50
23.5
[SHIFT][Scl][=]
0.
74
38
29[ , ]1.6[DT]
29.
103
46.4
50[ , ]23.5[DT]
50.
118
48
74[ , ]38[DT]
74.
Through power
103[ , ]46.4[DT]
regression of the above
103.
118[ , ]48[DT]
data, the regression
118.
formula and correlation
[SHIFT][A][=]
–35.59856935
(Constant term A)
coefficient are obtained.
[SHIFT][B][=]
1.495939414
Furthermore, the
(Regression coefficient B)
regression formula is
[SHIFT][C][=]
–6.716296671
–03
used to obtain the
(Regression coefficient C)
respective estimated
values of y and x, when
16[SHIFT][y]
(y when xi=16)
–13.38291067
xi = 16 and yi = 20.
20[SHIFT][x]
when yi=20)
47.14556728
(x
1
[SHIFT][x]
when yi=20)
175.5872105
(x
2
– 37 –
Replacing the Battery
Dim figures on the display of the calculator indicate that
battery power is low. Continued use of the calculator
when the battery is low can result in improper operation.
Replace the battery as soon as possible when display
figures become dim.
To replace the battery:-
• Remove the screws that hold the back cover in place and
then remove the back cover,
• Remove the old battery,
• Wipe off the side of the new battery with a dry, soft cloth.
Load it into the unit with the positive(+) side facing up.
• Replace the battery cover and secure it in place with the
screws.
• Press [ON/AC] to turn power on.
Auto Power Off
Calculator power automatically turns off if you do not
perform any operation for about six minutes. When this
happens, press [ON/AC] to turn power back on.
Specifications
Power supply: AG13 x 2 batteries
Operating temperature: 0 º ~ 40 º C (32 º F ~ 104 º F)
– 38 –