This is the English chapter of the original user manual of the Casio fx-85v.
Scanned, transformed to ASCII via OCR and copied to HTML by F. Seebass, July 2002.
CASIO
fx-85v
Electronic Calculator
User Manual
Dear customer,
Thank you very much for purchasing our electronic calculator.
To fully utilize its features no special training is required, but we suggest you study this operation manual to become familiar with its many abilities. To help ensure its longevity, do not touch the
inside of the calculator, avoid hard knocks and unduly strong key pressing. Extreme cold (below 32°F or 0°C heat (above 104°F or 40°C) and humidity may also affect the functions of the
calculator. Never use volatile fluid such as lacquer thinner, benzine, etc. when cleaning the unit. For servicing contact your retailer or nearby dealer.
Before starting calculation, be sure to press the
-key and to confirm that "0." is shown on the display.
* Special care should be taken not to damage the unit by bending or dropping. For example, do not carry it in your hip pocket.
INDEX
General keys
Memory keys
Special keys
Function keys
Statistical keys 1-1 Modes
1-2 The display 8-1 Four basic calculations (incl. parenthesis calculations)
8-2 Constant calculations
8-3 Memory calculations using the independent memory
8-4 Memory calculations using 6 constant memories
8-5 Fraction calculations
8-6 Percentage calculations 9-1 Sexagesimal <-> Decimal conversion
9-2 Trigonometric/Inverse trigonometric functions
9-3 Hyperbolic functions and inverse hyperbolic functions
9-4 Common & Natural logarithms/Exponentiations (Common antilogarithms, Natural antilogarithms, Powers and Roots)
9-5 Square roots, Cube roots, Squares, Reciprocals & Factorials
9-6 Miscellaneous functions (FIX, SCI, NORM, RND, RAN#, ENG)
9-7 Polar to rectangular co-ordinates conversion
9-8 Rectangular to polar co-ordinates conversion
9-9 Permutations
9-10 Combinations 10-1 Standard deviation
10-2 Regression analysis
Linear regression
Logarithmic regression
Exponential regression
Power regression KEY INDEX
GENERAL KEYS
MEMORY KEYS
SPECIAL KEYS
FUNCTION KEYS
STATISTICAL KEYS
1 / GENERAL GUIDE
1-1 Modes
To put the calculator into a desired operating mode or to select a specific angular unit, press
first then
,
, ... or
.
  |
COMP mode. Carry out ordinary arithmetic and functional calculations. |
  |
LR is displayed. Calculate regression analysis. |
  |
SD is displayed. Calculate standard deviation. |
  |
DEG is displayed. Use degrees as the unit of angle measurement. |
  |
RAD is displayed. Use radians as the unit of angle measurement. |
  |
GRA is displayed. Use grads as the unit of angle measurement. |
![[Mode]](gif/mode.gif) ![[7]](gif/7.gif) |
Press any number from 0 to 7 to indicate how many decimal places you want displayed (FIX is displayed). |
  |
Press any number from 1 (1 digit) to 8 (8 digits) to indicate how many significant digits you want displayed (SCI is displayed). |
  |
Releases instructions entered in ![[Mode]](gif/mode.gif) and  . This operation also changes the range of the exponent display. |
1-2 The display
The display shows input data, interim results and answers to calculations. The mantissa section displays up to 8 digits. The exponent section displays up to ±99.
Exponential Displays
The display can show calculation results only up to 8 digits long. When an intermediate value or a final result is longer, the calculator
automatically switches over to exponential notation. Values greater than 99,999,999 are always displayed exponentially, while the lower limit is selectable. Note the following:
Type |
Lower limit |
Upper limit |
A (Norm 1) |
0.01 |
99,999,999 |
B (Norm 2) |
0.0000001 |
99,999,999 |
Values less than the lower limits or greater than the upper limit shown above are displayed using exponential format. Use the following procedure to switch between the Type A lower limit and the Type
B lower limit:
-
Check the display to see if the FIX or SCI symbols are shown, indicating that the number of significant digits or the number of decimal places have been specified. If either of the symbols is shown,
press

to cancel the specification.
-
Perform the following calculation: 1
200
-
Look at the display to see what the current lower limit is.
If the display reads:
5.-03, the current setting is Type A |
|
If the display reads:
0.005, the current setting is Type B |
|
-
Press

to switch between the Type A and Type B lower limits.
* Note that the lower limit is not changed if you press 
while the number of significant digits (SCI displayed) and/or the number of decimal places (FIX displayed) are specified. The first time you press 
you clear the FIX and SCI specifications, and so you must press 
again to change the lower limit. 2 / ORDER OF OPERATIONS AND LEVELS
Operations are performed in the following order of precedence:
-
Functions
-
x y, x1/y, R->P, P->R, nPr, nCr
-
x,
-
+, -
Operations with the same precedence are performed from left to right, with operations enclosed in parentheses performed first. If parentheses are nested, the operations enclosed in the innermost set
of parentheses are performed first.
* Registers L1 through L6 are provided to store operations of lower precedence (including parenthetical operations). Since six registers are provided, calculations up to six
levels can be retained.
* Since each level can contain up to three open parentheses, parantheses can be nested up to 18 times.
Example (4 levels, 5 nested parentheses)
Operation
Register contents at point A:
x |
4 |
L1 |
[( [( 5 + |
L2 |
4 x |
L3 |
[( [( [( 3 + |
L4 |
2 x |
L5 |
|
L6 |
|
3 / CALCULATION RANGE AND SCIENTIFIC NOTATION
|
|
|
|
|
|
|
-9,9999999x1099 |
|
-10-99 |
0 |
10-99 |
|
9,9999999x1099 |
|
Normal display |
|
Scientific notation |
When the answer exceeds the normal display capacity, it is automatically shown by scientific notation, 8-digit mantissa and exponents of 10 up to ±99.
1 The minus (-) sign for mantissa
2 The mantissa
3 The minus (-) sign for exponent
4 The exponent of ten
The whole display is read: - 1,2345678 x 10-99
* Entry can be made in scientific notation by using the
key after entering the mantissa.
Example: -1.2345678 x 10-3 (= -0.0012345678)
OPERATION |
READ-OUT |
1 2 3 4 5 6 7 8  |
|
 |
|
3  |
|
4 / CORRECTIONS
If you notice an input mistake before you press the arithmetic operation key, simply press
to clear the value and enter it again.
In a series of calculations, you can correct errors in intermediate results by recalculating correctly when the error appears and then continuing with the original series from where you interrupted it.
You can also use the
key to backspace through an entered value until you reach the digit you wish to change and then make any necessary corrections. For example:
To change entry of 123 to 124:
OPERATION |
READ-OUT |
123 |
|
 |
|
4 |
|
If you make a mistake by pressing the wrong key when entering
,
,
,
,
or 
simply press the appropriate key to correct. In this case, the most recently pressed key operation is used, but it retains the order of
precedence of the original operation entered.
5 / OVERFLOW OR ERROR CHECK
Overflow or error is indicated by the "-E-" or "-[-" sign and stops further calculation
Overflow or error occurs:
a) When an answer, whether intermediate or final, or accumulated total in the memory is more than 1 x 10100 ("-E-" sign appears).
b) When function calculations are performed with a number exceeding the input range ("-E-" sign appears).
c) When unreasonable operations are performed in statistical calculations ("-E-" sign appears).
d) When the total number of levels of explicity and/or implicity (with addition-subtraction versus multiplication-division including x y und x1/y) nested
parentheses exceeds 6, or more than 18 pairs of parentheses are used ("-[-" sign appears).
Ex.) You have pressed the
key 18 times continously before designating the sequence 


.
To release these overflow checks:
a), b), c) |
Press the key. |
d) |
Press the key. Or press the key, and the intermediate result just before the overflow occurs is displayed and the subsequent calculation is possible. |
Memory protection:
The content of the memory is protected against overflow or error and the accumulated total is recalled pressing the
key after the overflow check is released by the
key.
6 / POWER SOURCE
The CASIO C-POWER system makes it possible to operate calculators any place even in complete darkness, you don't have to worry about the light conditions.
* This unit protects memory no matter what the light conditions.
* This unit uses two power sources: an amorphous silicon solar cell, and a lithium battery (GR927).
* A weakened lithium battery is indicated when memory contents spontaneously clear or when display darkens under poor light conditions and cannot be restored by pressing the
key. Anytime such symptoms occur, the unit should be taken to your retailer or nearby dealer for battery replacement.
* Lithium battery replacement should only be performed by your retailer or an authorized dealer.
* To ensure proper operation the lithium battery should be replaced once every six years no matter how much the unit is used.
Auto power-off function
This unit automatically switches OFF if not operated for approximately 6 minutes. Power can be restored by pressing the
key. Memory contents and mode setting are retained even when power is switched off.
7 / SPECIFICATIONS
BASIC OPERATIONS
4 basic calculations, constants for + / - / x /
/
xy,x1/y, parenthesis calculations and memory calculations. BUILT-IN FUNCTIONS
Trigonometric/inverse trigonometric functions (with angle in degrees,
radians or grads), hyperbolic/inverse hyperbolic functions, common/natural logarithms, exponential functions (common antilogarithms, natural antilogarithms), powers, roots, square roots, cube roots,
squares, reciprocals, factorials, conversion of coordinate system (R->P, P->R), permutations, combinations, random number,
, fractions, percentages and logical operations. STATISTICAL FUNCTIONS
Standard deviation, linear regression, logarithmic regression,
exponential regression, and power regression. MEMORY
1 independent memory and 6 constant memories. CAPACITY
Entry/basic calculations
8-digit mantissa, or 8-digit mantissa
plus 2-digit exponent up to 10±99 Fraction calculations
Total of integer, numerator and denominator must be within 8 digits (includes division marks).
Scientific functions |
Input range |
sinx/cosx/tanx |
|x| < 9 x 109 degrees
|x| < 5 x 107 rad
|x| < 1010 gra |
sin-1x/cos-1x |
|x| <= 1 |
tan-1x |
|x| < 10100 |
sinhx/coshx |
|x| <= 230,2585 |
tanhx |
|x| < 10100 |
sinh-1x |
|x| < 5 x 1099 |
cosh-1x |
1 <= x < 5 x 1099 |
tanh-1x |
|x| < 1 |
logx/lnx |
10-99 <= x <= 10100 |
ex |
-10100 < x <= 230,2585 |
10x |
-10100 < x < 100 |
x y |
x > 0: -10100 < y logx < 100
x = 0: y > 0
x < 0: y: integer or 1/2n+1 (n integer) |
x1/y |
x > 0: y 0 -10100 < 1/y logx < 100
x = 0: y > 0
x < 0: y: odd number or 1/n (n integer) |
 |
0 <= x < 10100 |
x2 |
|x| < 1050 |
 |
|x| < 10100 |
1/x |
|x| < 10100 (x 0) |
x! |
0 <= x <= 69 (x: integer) |
nPr / nCr |
0 <= 0 r <= n, n < 1010 (n, r: integer)
* Certain combinations or permutations may cause errors due to overflow during internal calculations. |
REC -> POL |
< 10100 |
POL -> REC |
|x| < 9 x 109 degrees
|x| < 5 x 107 rad
|x| < 1010 gra
0 <= r <= 10100 |
° ' " |
up to second |
 |
8 digits |
* Errors are cumulative with such internal continous calculations as xy,x1/yx!,
so accuracy rnay be adversely affected.
* Output accuracy
± 1 in the 8th digit.
DECIMAL POINT
Full floating with underflow. EXPONENTIAL DISPLAY
Norm 1 - 10-2 > |x|, |x| >= 108
Norm 2 - 10-7 > |x|, |x| >= 108 READ-OUT
Liquid crystal display, suppressing unnecessary O's (zeros). POWER SOURCE
Power
source: Amorphous silicon solar cell, lithium battery (GR927)
Lithium battery life: 6 years with GR927 (1-hour daily use). AMBIENT TEMPERATURE RANGE
O °C bis 40 °C (32 °F - 104 °F) DIMENSIONS
17.5mmH x 73mmW x 140mmD
(3/4"H x 27/8"W x 51/2"D) - fx-85V
8.5mmH x 73mmW x 140mmD
(5/16"H x 27/8"W x 51/2"D) - fx-911V WEIGHT
64 g (2.3 oz) - fx-85V
59 g (2.1 oz) - fx-911V 8 / NORMAL CALCULATIONS
* You can perform normal calculations in the COMP mode (
).
* Calculations can be performed in the same sequence as the written formula (true algebraic logic).
* Nesting of up to 18 parentheses at 6 levels is allowed. 8-1 Four basic calculations (incl. parenthesis calculations)
EXAMPLE OPERATION |
READ-OUT |
23 + 4.5 -53 = |
|
23 4 5 53  |
|
56 x (-12) (-2.5) = |
|
56 12 ![[+/-]](gif/sign.gif) 2 5   |
|
2 3 x (1 x 1020) = |
|
2 3 1 20  |
|
7 x 8 - 4 x 5 (= 56 - 20 ) = |
|
7 8 4 5  |
|
1 + 2 - 3 x 4 5 + 6 = |
|
1 2 3 4 5 6  |
|
|
|
4 5 6    |
|
* The number of levels of the
key can be displayed.
2 x { 7 + 6 x (5 + 4) } = |
|
2   |
|
7 6   |
|
5 4    |
|
* It is unnecessary to press the
key before the
key.
10 - { 7 x (3 + 6 ) } = |
|
10  7  3 6  |
|
Another operation: 10 
7 
3
6

8-2 Constant calculations
* The "K" sign appears when a number is set as a constant..
17 + 17 + 17 + 17 = |
|
17    |
34. |
|
 |
51. |
|
 |
68. |
|
|
2.89 |
|
1.73 = |
 |
|
4.913 |
|
1.74 = |
 |
|
8.3521 |
|
|
18. |
|
3 x 6 x (-5) = |
4  |
|
72. |
|
|
5   |
|
-90. |
|
56
4 x (2 + 3) |
= |
23
4 x (2 + 3) |
= |
|
|
4  2 3    |
20. |
|
56  |
2.8 |
|
23  |
1.15 |
|
8-3 Memory calculations using the independent memory
* When a new number is entered into the independent memory by the
key, the previous number stored is automatically cleared and the new number is put in the independent memory.
* The "M" sign appears when a number is stored in the memory .
* The contents accumulated into the independent memory are preserved even after the power switch is tuned off.
To clear the contents press ![[0]](gif/0.gif)
or ![[AC]](gif/ac.gif)
in sequence.
53 + 6 = 59
23 - 8 = 15
56 x 2 = 112
+ ) 99
4 = 24.75
210.75
53 6   |
59. |
|
23 8  |
15. |
|
56 2  |
112. |
|
99 4  |
24.75 |
|
 |
210.75 |
|
7 + 7 - 7 + (2 x 3) + (2 x 3) + (2 x 3) - (2 x 3) = |
|
7    2 3       |
19. |
|
12 x 3 = 36
- ) 45 x 3 = 135
78 x 3 = 234
135
3  12   |
 36. |
|
45   |
 135. |
|
78  |
 234. |
|
 |
 135. |
|
8-4 Memory calculations using 6 constant memories
* When a new number is entered into a constant memory by operating ENTRY
(
to
), the previous number stored is automatically cleared and the new number is put in the constant memory.
* The contents stored in the constant memories are preserved even after the power switch is turned off. To clear the contents press 

(to
) or 

(to
) in sequence.
193.2 23 = |
|
193 2   23  |
|
193.2 28 = |
|
1 28  |
|
193.2 42 = |
|
1 42 |
|
* Another operation by using the independent memory:
193
2 
23
, 
28
, 
42
* Calculations in constant memory registers can also be performed by using the
,
,
and
keys:
7 x 8 x 9 = 504
4 x 5 x 6 = 120
3 x 6 x 9 = 162
14 19 24 786 (Total)
7   8  9     |
504. |
|
4    5    6      |
120. |
|
3    6    9      |
162. |
|
  |
14. |
|
  |
19. |
|
  |
24. |
|
 |
786. |
|
12 x (2.3 + 3.4) - 5 =
30 x (2.3 + 3.4 + 4.5) - 15 x 4.5 = |
|
12  2 3 3 4    5  |
|
30 4 5       15     |
|
The keys 

are pressed to exchange the displayed number (4.5) with the contents of constant memory 1.
8-5 Fraction calculations
* Total of integer, numerator and denominator must be within 8 digits (includes division marks).
* A fraction can be transferred to the memory.
* When a fraction is extracted, the answer is displayed as a decimal.
* A press of
key after the
converts the fraction answer to the decimal scale.
4 |
5
6 |
x (3 |
1
4 |
+ 1 |
2
3 |
) 7 |
8
9 |
= |
(1.5 x 107) - {(2.5 x 106) x |
3
100 |
} = |
* During a fraction calculation, a figure is reduced to the lowest terms by pressing a function command key (
,
,
oder
) or the
if the figure is reducible:
3 |
456
78 |
= 8 |
11
13 |
(Reduction) |
* By pressing 
continuously, the displayed value will be converted to the improper fraction.
Continuing from above:
* The answer in a calculation performed between a fraction and a decimal is displayed as a decimal:
8-6 Percentage calculations
12% of 1500:
Percentage of 660 against 880:
15% add-on of 2500:
25% discount of 3500:
300cc is added to a solution of 500cc. What is the percent of the new volume to the initial one?
If you made $80 last week and $100 this week, what is the percent increase?
12% of 1200:
18% of 1200:
23% of 1200:
1200  12   |
144. |
|
18   |
216. |
|
23   |
276. |
|
26% of 2200:
26% of 3300:
26% of 3800:
26  2200   |
572. |
|
3300   |
858. |
|
3800   |
988. |
|
Percentage of 30 against 192?:
Percentage of 156 against 192?:
* 600 grams was added to 1200 grams. What percent is the total to the initial weight?
* 510 grams was added to 1200 grams. What percent is the total to the initial weight?
* How many percent down is 138 grams to 150 grams?
* How many percent down is 129 grams to 150 grams?
9 / FUNCTION CALCULATIONS
Scientific function keys can be utilized as subroutines of four basic calculations (including parentheses calculations).
* This calculator computes as
= 3,1415927 und e= 2,7182818.
* In some scientific functions, the display disappears mometarily while complicated fomulas are being processed. So do not enter numerals or press the function key until the previous answer is
displayed.
* For each input range of the scientific functions, see the specifications. 9-1 Sexagesimal <-> Decimal conversion
The
key converts the sexagesimal figure (degree, minute and second) to decimal notation. Operation of 
converts the decimal notation to the sexagesimal notation.
14°25'36" =
9-2 Trigonometric/Inverse trigonometric functions
sin ( |
6 |
rad) = |
cos 63°52'41" =
tan (-35 gra) =
2 x sin 45° x cos 65° =
"DEG" 30   |
|
sec ( |
3 |
rad) = |
|
|
cos ( |
3 |
rad) |
|
|
= |
"DEG" 30   |
|
cos-1 |
2 |
= |
tan-1 (0.6104) =
9-3 Hyperbolic functions and inverse hyperbolic functions
sinh 3.6 =
tanh 2.5 =
cosh 1.5 - sinh 1.5 =
1 5     |
2.3524096 |
|
    |
0.223130 |
|
 |
-1.5 |
|
sinh-1 30 =
Solve tanh (4x) = 0.88:
9-4 Common & Natural logarithms/ Exponentiations (Common antilogarithms, Natural antilogarithms, Powers and Roots)
log 1.23 (= log101.23) =
1 23 |
|
Solve 4x = 64:
x log 4 = log 64
ln 90 (= loge 90) =
90  |
|
log 456
ln 456 =
100.4 + 5 e-3 =
5.62.3 =
1231/7 (=
) =
(78 - 23)-12 =
312 + e10 =
log sin 40° + log cos 35° =
(The Antilogarithm................................0.5265407)
9-5 Square roots, Cube roots, Squares, Reciprocals & Factorials
+
x
=
+
=
123 + 302 =
8! (= 1 x 2 x 3 x ..... x 7 x 8) =
8   |
|
9-6 Miscellaneous functions (FIX, SCI, NORM, RND, RAN#, ENG)
1.234 + 1.234 =
"FIX2" (

)
1.234 + 1.234 =
"FIX2"
1
3 + 1
3 =
"SCI2" (

)
1
3 + 1
3 =
"SCI2"
1
1000 = 0.001
= 1 x 10-3
123 m x 456 = 56088 m = 56.088 km
7.8 g
96 = 0.08125 g = 81.25 mg
Generate a random number between 0.000 and 0.999.
  |
(Example) |
9-7 Polar to rectangular co-ordinates conversion
Formula: x= rcos ß,
y=rsinß
Ex.)
Find the value of x and y when the point P is shown as ß = 60° and length r = 2 in the polar co-ordinates:
"DEG"
9-8 Rectangular to polar co-ordinates conversion
Formula: r=
, ß= tan-1(y/x) (-180°<ß<= 180°)
Ex.)
Find the length r and angle ß in radian when the point P is shown as x = 1 und y =
in the rectangular co-ordinate:
"RAD"
9-9 Permutations
Input range: n>= r(n, r: natural Numbers)
Formula: nPr = |
n!
(n - r)! |
Ex.)
How many numbers of 4 figures can be obtained when permuting 4 different numbers among 7 (1 to 7)?
9-10 Combinations
Input range: n>= r(n, r: natural Numbers)
Formula: nCr = |
n!
r! (n - r)! |
Ex.)
How many groups of 4 members can be obtained when there are ten in class?
10 / STATISTICAL CALCULATIONS
* Be sure to press 
in sequence prior to starting a statistical calculation. 10-1 Standard deviation
* Set the
function mode to "SD" by pressing 
.
Ex.)
Find
,
,
, n,
and
based on the data 55, 54, 51, 55, 53, 53, 54, 52.
"SD"
(Sample standard deviation)
(Population standard deviation)
(Arithmetical mean)
(Number of data)
(Sum of value)
(Sum of square value)
Calculate the unbiased variance and the deviation between each data item and the average.
(Subsequently)
   |
(Unbiased variance) |
   55  |
(55 - ) |
54  |
(54 - ) |
51 |
(51 - ) |
.
.
.
. |
.
.
.
. |
Note:
The sample standard deviation
is defined as:
The population standard deviation
is defined as:
and the arithmetical mean
is defined as:
* Pressing
,
,
,
,
or
key need not be done sequentially.
Ex.)
Find n,
und
, based on the data: 1.2, -0.9, -1.5, 2.7, -0.6, 0.5, 0.5, 0.5, 0.5, 1.3, 1.3, 1.3, 0.8, 0.8, 0.8, 0.8, 0.8.
"SD"
1) (Mistake)
2 5  |
|
1') (To correct)
2) (Mistake)
3) (Mistake)
3') (To correct)
2') (To correct)
4) (Mistake)
1 4  |
|
4') (To correct)
5) (Mistake)
6  |
|
5') (To correct)
10-2 Regression analysis
Set the function mode to "LR" by pressing 
. Linear regression
Formula:
Ex.)
Results from measuring the length and temperature of a steel bar.
temp./°C |
length/mm |
10
15
20
25
30 |
1003
1005
1010
1008
1014 |
Find the constant term (A), regression coefficient (B), correlation coefficient (r) and estimated values (
,
) using the above figures as a basis.
 10  |
|
1003  |
|
15 1005  |
|
20 1010  |
|
25 1008  |
|
30 1014  |
|
  |
(A) |
  |
(B) |
  |
(r) |
(When the temp. is 18 °C)
18  |
(mm) |
(When the length is 1000 mm)
1000   |
(°C) |
Note:
,
, n,
,
,
,
,
,
,
,
,
, A, B and r are respectively obtained by pressing a numeral key (
to
) after the
- or
-key.
* Correction of data entry
Ex.)
xi |
2 |
3 |
2 |
3 |
2 |
4 |
yi |
3 |
4 |
4 |
5 |
5 |
5 |
"LR"
1) (Mistake)
1') (To correct)
2) (Mistake)
3  |
|
2') (To correct)
2  |
|
4  |
|
3) (Mistake)
1  |
|
5  |
|
3') (To correct)
4) (Mistake)
4  |
|
4  |
|
5) (Mistake)
6  |
|
5') (To correct)
4') (To correct)
These ways of correction can also be applied to logarithmic, exponential or power regression.
Logarithmic regression
Formula:
* Input data items are the logarithm of x (ln x), and y which is the same as in linear regression.
* Operation for calculating and correcting regression coefficients are basically the same as in linear regression. Operate the sequence x
to obtain estimator
and y


for estimator
.
Note that
,
and
are obtained instead of
,
and
respectively.
Ex.)
xi |
29 |
50 |
74 |
103 |
118 |
yi |
1.6 |
23.5 |
38.0 |
46.4 |
48.9 |
Find Sie A, B, r,
and
using the above figures as a basis..
"LR"
 29   |
|
1 6  |
|
50  23 5  |
|
74  38  |
|
103  46 4  |
|
118  48 9  |
|
  |
(A) |
  |
(B) |
  |
(r) |
(When xi is 80)
(When yi is 73)
Exponential regression
Formula:
* Input data items are the logarithm of y (ln y), and x which is the same as in linear regression.
* Operation for correction is basically the same as in linear regression. Operate 


to obtain coefficient A, x

for estimator
, and y

for estimator
.
Note that
,
and
are obtained instead of
,
and
.
Ex.)
xi |
6.9 |
12.9 |
19.8 |
26.7 |
35.1 |
yi |
21.4 |
15.7 |
12.1 |
8.5 |
5.2 |
Find A, B, r,
and
using the above figures as a basis.
"LR"
 6 9  |
|
21 4   |
|
12 9 15 7   |
|
19 8 12 1   |
|
26 7 8 5   |
|
35 1 5 2   |
|
    |
(A) |
  |
(B) |
  |
(r) |
(When xi is16)
(When yi is 20)
Power regression
Formula:
* Input data items are lnx und lny.
* Operation for correcting is basically the same as in linear regression. Operate 


to obtain coefficient A, x


for estimator
and y 



for estimator
. Note that
,
,
,
and
are obtained instead of
,
,
,
and
respectively.
Ex.)
xi |
28 |
30 |
33 |
35 |
38 |
yi |
2410 |
3033 |
3895 |
4491 |
5717 |
Find A, B, r,
und
using the above figures as a basis.
"LR"
 28   |
|
2410   |
|
30  3033  |
|
33  3895   |
|
35  4491   |
|
38  5717   |
|
    |
(A) |
  |
(B) |
  |
(r) |
(When xi is 40)
(When yi is 1000)