Ativa PET1030 owner manual Logarithmic regression, Exponential regression, Power regression

– 36 –

Example:
4.123.586.4 = 21.1496
4.123.587.1 = 7.6496
[ON/AC] [4] [•] [1] [2] []	4.12x3.58+6.
[3] [•] [5] [8] [] [6] [•] [4] [=]	21.1496
	D
[3]	12x3.58+6.4_
	21.1496
	D
[3] [3] [3] [3]	4.12x3.58+6.
	21.1496
	D
[] [7] [•] [1]	12x3.58–7.1_
	21.1496
	D
[=]	4.12x3.58–7.
	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] )	14⎟ 0x2.			3	0.
				D
Correct the input by pressing
[3] [SHIFT] [INS] [1]	14	⎟	10x2	.3D	0.
[=]	14	⎟	10x2	.33.22
				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 63º52'41"	[MODE][MODE][1]("DEG" selected)
= 0.897859012	[sin] 63 [º ' "] 52 [º ' "]
	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
2sin45ºcos65º	[MODE][MODE][1]("DEG")
= 0.597672477	2[sin] 45 [cos] 65 [=]	0.597672477
sin–10.5 = 30	[SHIFT][sin–1] 0.5 [=]	30.
cos–1(√2/2)	[MODE][MODE][2]("RAD")
= 0.785398163 rad	[SHIFT][cos–1][(][√]2 []2
= π/4 rad	[)][=]	0.785398163
	[][SHIFT][π][=]	0.25
tan–10.741	[MODE][MODE][1]("DEG")
= 36.53844577º	[SHIFT][tan–1]0.741[=]	36.53844576
= 36º32' 18.4"	[SHIFT] [←º' "]	36º32º18.4º

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–10.8cos–10.9)	2.5[] [(] [SHIFT] [sin–1]0.8
= 68º13'13.53"	[] [SHIFT] [cos–1] 0.9 [)]
	[=] [SHIFT] [←º' "]	68º13º13.53º

– 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–130 = 4.094622224	[hyp][SHIFT][sin–1] 30 [=]	4.094622224
cosh–1(20/15)	[hyp][SHIFT][cos–1][(] 20
= 0.795365461	[] 15 [)][=]	0.795365461
x = (tanh–10.88) / 4	[hyp][SHIFT][tan–1]0.88
= 0.343941914	[]4[=]	0.343941914
sinh–12cosh–11.5	[hyp][SHIFT][sin–1]2[]
= 1.389388923	[hyp][SHIFT][cos–1]1.5[=]	1.389388923
sinh–1(2/3)tanh–1(4/5)	[hyp][SHIFT][sin–1][(]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
101.23 = 16.98243652	[SHIFT][10x] 1.23 [=]	16.98243652
e4.5 = 90.0171313	[SHIFT][ex]4.5[=]	90.0171313
104 • e–41.2 • 102.3	[SHIFT][10x]4[][SHIFT][ex]
= 422.5878667	[(–)]4[]1.2[][SHIFT][10x]
	2.3[=]	422.5878667
(–3)4= 81	[(][(–)] 3 [)] [xy] 4 [=]	81.
–34= –81	[(–)] 3 [xy] 4 [=]	–81.
5.62.3 = 52.58143837	5.6 [xy] 2.3 [=]	52.58143837
7√123 = 1.988647795	7 [SHIFT][x√] 123 [=]	1.988647795
(7823)–12	[(]78[]23[)][xy][(–)]12[=]	1.305111829–21
= 1.30511182910–21
233√644 = 10	2[]3[]3[SHIFT][x√]64
	[]4[=]	10.
23.4(5+6.7) = 3306232	2[]3.4[xy][(]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 –180º< ≤180º.

(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()
	[SHIFT][←º' "]	55º55º42.2()
x=7.5 and y=–10, what	[MODE][MODE][2]("RAD" selected)
are r and  rad?	[Pol(]7.5[,][(–)]10[)][=]	12.5(r)
	[RCL][F]	–0.927295218()
r=25 and = 56º, what	[MODE][MODE][1]("DEG" selected)
are x and y?	[SHIFT][Rec(]25 [,]56[)][=]	13.97982259(x)
	[RCL][F]	20.72593931(y)
r=4.5 and =2π/3 rad,	[MODE][MODE][2]("RAD" selected)
what are x and y?	[SHIFT][Rec(]4.5[,][(]2[]
	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?
10P4 = 5040

		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.)
7P437 = 360
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?
10C4 = 210
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.
25C515C5 = 50127

Other Functions (√ , x2, x–1, x!, 3√, Ran#)

		Display
Example	Operation	(Lower)
√2√5 = 3.65028154	[√]2[][√]5[=]	3.65028154
22324252 = 54	2[x2][]3[x2][]4[x2]	54.
	[]5[x2][=]
(3)2 = 9	[(][(–)]3[)][x2][=]	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)
√(1–sin240)	[MODE][MODE][1]("DEG" selected)
= 0.766044443	[√][(]1[][(][sin]40[)][x2]
	[)][=]	0.766044443
	[SHIFT][cos–1][Ans][=]	40.
1/2!1/4!1/6!1/8!	2[SHIFT][x!][x–1][]
= 0.543080357	4[SHIFT][x!][x–1][]
	6[SHIFT][x!][x–1][]
	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)
2/531/4 = 313/20	2[ab/c]5[]3[ab/c]1
	[ab/c]4[=]	3⎦13⎦20.
	[ab/c](conversion to decimal)	3.65
	Fractions can be converted
	to decimals, and then
	converted back to fractions.
3456/78 = 811/13	3[ab/c]456[ab/c]78[=]	8⎦11⎦13.
	[SHIFT][d/c]	115⎦13.
1/25781/4572	1[ab/c]2578[]1[ab/c]
= 0.00060662	4572[=]	6.066202547–04
	When the total number
	of characters, including
	integer, numerator,
	denominator and
	delimiter mark exceeds
	10, the input fraction is
	automatically displayed
	in decimal format.
1/20.5 = 0.25	1[ab/c]2[].5[=]	0.25
1/3(–4/5)–5/6= –11/10	1[ab/c]3[][(–)]4[ab/c]5
	[]5[ab/c]6[=]	–1⎦1⎦10.
1/21/31/41/5	1[ab/c]2[]1[ab/c]3[]
= 13/60	1[ab/c]4[]1[ab/c]5[=]	13⎦60.
(1/2)/3 = 1/6	[(]1[ab/c]2[)][ab/c]3[=]	1⎦6.
1/(1/31/4) = 15/7	1[ab/c][(]1[ab/c]3[]
	1[ab/c]4[)][=]	1⎦5⎦7.
	– 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)
Change 20 radian to		20[SHIFT][DRG>][2][=]	20r
degree			1145.91559
To perform the following		10[SHIFT][DRG>][2]
calculation :-		[]25.5[SHIFT][DRG>][3]
10 radians+25.5 gradients		[=]	10r25.5g
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
To express 2.258 degrees	2.258[º' "][=]	2º15º28.8
in deg/min/sec.
To perform the calculation:	12[º' "]34[º' "]56[º' "][]
12º34'56"3.45	3.45[=]	43º24º31.2

– 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].

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
[SHIFT][xσn]	Population standard deviation, xσn
[SHIFT][xσn–1]	Sample standard deviation, xσn–1
[SHIFT][x]	Mean, x
[RCL][A]	Sum of square of data, ∑x2
[RCL][B]	Sum of data, ∑x
[RCL][C]	Number of data, n

Standard deviation and mean calculations are performed as shown below:

Population standard deviation σn = √(∑(xix)2/n) where i = 1 to n

Sample standard deviation σn–1= √(∑(xix)2/(n-1)) where i = 1 to n

Mean x = (∑x)/n

Example	Operation	Display
Data 55, 54, 51, 55, 53,	[MODE][2] (SD Mode)	0.
53, 54, 52	[SHIFT][Scl][=] (Memory cleared)	0.
	55[DT]54[DT]51[DT]
	55[DT]53[DT][DT]54[DT]
	52[DT]	52.
What is deviation of the	[RCL][C](Number of data)	8.
unbiased variance, and	[RCL][B](Sumof data)	427.
the mean of the above	[RCL][A](Sum of square of data)	22805.
data?	[SHIFT][x][=](Mean)	53.375
	[SHIFT][xσn][=](Population SD)	1.316956719
	[SHIFT][xσn–1][=](Sample SD)	1.407885953
	[SHIFT][xσn–1]
	[x2][=](Sample variance)	1.982142857

– 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:

COMP SD REG

1 2 3

and then select one of the following regression types:-

Lin Log Exp

1 2 3

Lin: linear regression

Log: logarithmic regression

Exp: exponential regression

press [4] for the other three regression types:-

Pwr Inv Quad

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
[SHIFT][r][=]	Correlation coefficient r
[SHIFT][x][=]	Estimated value of x
[SHIFT][y][=]	Estimated value of y
[SHIFT][yσn]	Population standard deviation, yσn
[SHIFT][yσn–1]	Sample standard deviation, yσn–1
[SHIFT][y]	Mean, y
[SHIFT][xσn]	Population standard deviation, xσn
[SHIFT][xσn–1]	Sample standard deviation, xσn–1
[SHIFT][x]	Mean, x
[RCL][A]	Sum of square of data, ∑x2
[RCL][B]	Sum of data, ∑x
[RCL][C]	Number of data, n
[RCL][D]	Sum of square of data, ∑y2
[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∑x2(∑x )2)

r = ( n∑xy∑x∑y ) / √ (( n∑x2(∑x )2)( n∑y2(∑y )2)) y = A + Bx

x = ( yA) / B

Example		Operation	Display
Temperature and length		[MODE][3][1]	0.
of a steel bar		("REG" then select linear regression)
Temp	Length	[SHIFT][Scl][=] (Memory cleared)	0.
10ºC	1003mm	10[,]1003[DT]	10.
15ºC	1005mm	15[,]1005[DT]	15.
20ºC	1010mm	20[,]1010[DT]	20.
25ºC	1011mm	25[,]1011[DT]	25.
30ºC	1014mm	30[,]1014[DT]	30.
Using this table, the		[SHIFT][A][=](Constant term A)	997.4
regression formula and		[SHIFT][B][=]	0.56
correlation coefficient		(Regression coefficient B)
can be obtained. Based		[SHIFT][r][=]	0.982607368
on the coefficient		(Correlation coefficient r)
formula, the length of		18[SHIFT][y](Length at 18ºC)	1007.48
the steel bar at 18ºC		1000[SHIFT][x](Temp at 1000mm)	4.642857143
and the temperature		[SHIFT][r][x2][=]	0.965517241
at 1000mm can be		(Critical coefficient)
estimated. Furthermore		[(][RCL][F][–][RCL][C][]
the critical coefficient		[SHIFT][x][][SHIFT][y][)][]
(r2) and covariance can		[(][RCL][C][–]1[)][=](Covariance)	35.
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][=] (Memory cleared)	0.
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
data, the regression		118[,]48.9[DT]	118.
formula and correlation		[SHIFT][A][=](Constant term A)	–111.1283975
coefficient are obtained.		[SHIFT][B][=](Regression coefficient B)	34.02014748
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
∑x2	∑(Inx)2
∑xy	∑y•Inx

Exponential regression

Exponential regression calculations are carried out using

the following formula:

y = A•eB•x (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 regression formula y = A•eB•x (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
∑y2	∑(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][=] (Memory cleared)	0.
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
data, the regression		35.1[,]5.2[DT]	35.1
formula and correlation		[SHIFT][A][=](Constant term A)	30.49758742
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](y when xi=16)	13.87915739
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:

y = A•xB (lny = lnA + Blnx)

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

If we assume that lny = y, lnA =a' and ln x = x, the power regression formula y = A•xB (lny = lnA + Blnx) becomes the linear regression formula y = a' + bx if we store In(x) and In(y) instead of x and y themselves. Therefore, the 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
∑x2	∑(Inx)2
∑y	∑Iny
∑y2	∑(Iny)2
∑xy	∑Inx•Iny

Example		Operation	Display
xi	yi	[MODE][3][4][1]	0.
28	2410	("REG" then select Pwr regression)
30	3033	[SHIFT][Scl][=] (Memory cleared)	0.
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
data, the regression		38[,]5717[DT]	38.
formula and correlation		[SHIFT][A][=](Constant term A)	0.238801069
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.

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)
∑x2	∑(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][=] (Memory cleared)	0.
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
data, the regression		6[,]6[DT]	6.
formula and correlation		[SHIFT][A][=](Constant term A)	7.272727272
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

Quadratic Regression

Quadratic regression calculations are carried out using the following formula:

y = A + Bx + Cx2

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.

The regression formula is y = A + Bx + Cx2 where A, B, C are regression coefficients.

C = [(n∑x2(∑x)2) (n∑x2y∑x2∑y )(n∑x3∑x2∑x) (n∑xy ∑x∑y)][(n∑x2(∑x)2) (n∑x4(∑x2)2)(n∑x3∑x2∑x)2] B = [n∑xy∑x∑yC (n∑x3∑x2∑x)](n∑x2(∑x)2)

A = (∑yB∑xC∑x2) / n

To read the value of ∑x3, ∑x4 or ∑x2y, you can recall 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]	103.
regression of the above
data, the regression		118[,]48[DT]	118.
formula and correlation		[SHIFT][A][=](Constant term A)	–35.59856935
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](x1 when yi=20)	47.14556728
		[SHIFT][x](x2 when yi=20)	175.5872105
		– 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: 0º ~ 40ºC (32ºF ~ 104ºF)

– 38 –

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