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Results:

Mean: 3, Population Standard Deviation: 1,154700538

Example 3:

To calculate the linear regression and logarithmic regression

correlation coefficients for the following paired-variable data and determine
the regression formula for the strongest correlation: (

;

) = (20; 3150),

(110; 7310), (200; 8800), (290; 9310). Specify Fix 3 (three decimal places)
for results.

(SETUP)

(STAT)

(OFF)

(SETUP)

(Fix)

(STAT)

(A+BX)

110

200

290

3150

7310

8800

9310

(STAT/DIST)

(Reg)

(

)

0,923

(STAT/DIST)

(Type)

(ln X)

(STAT/DIST)

(Reg)

(

)

0,998

(STAT/DIST)

(Reg)

(A)

-3857,984

(STAT/DIST)

(Reg)

(B)

2357,532

Linear Regression Correlation Coefficient: 0,923
Logarithmic Regression Correlation Coefficient: 0,998
Logarithmic Regression Formula:

= -3857,984 + 2357,532ln

Calculating Estimated Values

Based on the regression formula obtained by paired-variable statistical
calculation, the estimated value of

can be calculated for a given

-value.

The corresponding

-value (two values,

and

, in the case of quadratic

regression) also can be calculated for a value of

in the regression

formula.

Example 4:

To determine the estimate value for

when

= -130 in the

regression formula produced by logarithmic regression of the data in
Example 3. Specify Fix 3 for the result. (Perform the following operation
after completing the operations in Example 3.)

130

(STAT/DIST)

(Reg)

(

ˆ)

4,861

Important!

• Regression coefficient, correlation coefficient, and estimated value calculations can

take considerable time when there are a large number of data items.

Содержание fx-991ZA Plus

Страница 1: ...EN https edu casio com CASIO Worldwide Education Website https world casio com manual calc Manuals are available in multi languages at User s Guide NATURAL V P A M fx 991ZA PLUS II...

Страница 2: ...c Input Rules 16 Inputting with Natural Display 17 Form Calculation Range 17 Using Values and Expressions as Arguments Natural Display only 18 Overwrite Input Mode Linear Display only 19 Correcting an...

Страница 3: ...ger RanInt 38 Permutation nPr and Combination nCr 39 Rounding Function Rnd 39 Greatest Common Divisor GCD and Least Common Multiple LCM 40 Using CALC 40 Using SOLVE 41 Solution Screen Contents 43 Cont...

Страница 4: ...DIST Mode Calculation Examples 76 Inequality Calculations INEQ 78 Changing the Inequality Type 79 INEQ Mode Calculation Examples 79 Special Solution Display 80 Ratio Calculations 81 Changing the Ratio...

Страница 5: ...contents of this manual are subject to change without notice The displays and illustrations such as key markings shown in this manual are for illustrative purposes only and may differ somewhat from t...

Страница 6: ...attery life may be shorter than normal Do not use a nickel based primary battery with this product Incompatibility between such batteries and product specifications can result in shorter battery life...

Страница 7: ...ay you want press Important If adjusting display contrast does not improve display readability it probably means that battery power is low Replace the battery Key Markings Pressing the or key followed...

Страница 8: ...irection as shown in the illustration nearby In this manual cursor key operation is indicated as and Reading the Display The two line display makes it possible to view both the input expression and it...

Страница 9: ...o assign a value to the variable This indicator appears after you press STO RCL The calculator is standing by for input of a variable name to recall the variable s value This indicator appears after y...

Страница 10: ...lation internally Using Menus Some of the calculator s operations are performed using menus Pressing or for example will display a menu of applicable functions The following are the operations you sho...

Страница 11: ...OMP Complex number calculations CMPLX Statistical and regression calculations STAT Calculations involving specific number systems binary octal decimal hexadecimal BASE N Equation solution EQN Matrix c...

Страница 12: ...hO SETUP MthIO MathO Natural Display MthIO LineO SETUP MthIO LineO Linear Display LineIO SETUP LineIO Natural Display MthIO MathO MthIO LineO causes fractions irrational numbers and other expressions...

Страница 13: ...BASE N MATRIX or VECTOR Mode Specifying the Default Angle Unit To specify this as the default angle unit Perform this key operation Degrees SETUP Deg Radians SETUP Rad Grads SETUP Gra 90 2 radians 100...

Страница 14: ...ulation results Calculation results are rounded off to the specified digit before being displayed Example LineIO 1 7 1 4286 10 1 Sci 5 1 429 10 1 Sci 4 1 428571429 10 1 Sci 0 Norm Selecting one of the...

Страница 15: ...this key operation Show FREQ Column SETUP STAT ON Hide FREQ Column SETUP STAT OFF Specifying the Table Format Specifies whether to use function f x only or the two functions f x and g x in the TABLE...

Страница 16: ...turns the calculation mode to COMP and returns all other settings including setup menu settings to their initial defaults CLR Setup Yes This setting Is initialized to this Calculation Mode COMP Displa...

Страница 17: ...tely before sin or other function that includes parentheses immediately before the Ran random number function or immediately before a variable A B C D E F M X Y scientific constants or e 3 The closing...

Страница 18: ...ght of an input expression to be greater than one display line The maximum allowable height of an input expression is two display screens 31 dots 2 Further input will become impossible if the height o...

Страница 19: ...ent of a function After you have input 7 6 for example you can make it the argument of resulting in 7 6 Example To input 1 7 6 and then change it to 1 7 6 MthIO MathO 1 7 6 INS As shown above the valu...

Страница 20: ...Display to Natural Display will automatically switch to the insert mode Correcting and Clearing an Expression To delete a single character or function Move the cursor so it is directly to the right of...

Страница 21: ...raction form and decimal form its form and decimal form or its form and decimal form Example 1 6 1 6 0 5235987756 MthIO MathO 6 1 6 0 5235987756 Example 2 2 2 3 6 2 3 5 913591358 MthIO MathO 2 2 3 6 2...

Страница 22: ...ion result in decimal form a calculation that results in a form or form expression a division calculation Pressing after that will switch to the fraction form or form of the calculation result The for...

Страница 23: ...of 880 is 660 75 660 880 75 Example 3 Increase 2500 by 15 2875 2500 2500 15 2875 Example 4 Decrease 3500 by 25 2625 3500 3500 25 2625 Degree Minute Second Sexagesimal Calculations You can perform calc...

Страница 24: ...ou can use the colon character to connect two or more expressions and execute them in sequence from left to right when you press Example 3 3 3 3 3 3 3 3 6 9 Using Engineering Notation A simple key ope...

Страница 25: ...to X If a R calculation is part of a multi step calculation only the quotient is passed on to the next operation Example 10 17 R 6 10 2 12 Operation of the and keys is disabled while a remainder divi...

Страница 26: ...n result display Pressing FACT or Pressing any of the following keys or Using the setup menu to change the angle unit setting Deg Rad Gra or the display digits setting Fix Sci Norm Note You will not b...

Страница 27: ...3 2 14 Continuing 7 5 Using Memory Functions Answer Memory Ans Previous Answer Memory PreAns The last calculation result obtained is stored in Ans answer memory The calculation result obtained prior t...

Страница 28: ...tions shown below 123 456 579 Continuing 789 Using PreAns Memory Example For Tk 2 Tk 1 Tk Fibonacci sequence determine the sequence from T1 to T5 Note however that T1 1 and T2 1 T1 1 1 Ans T1 1 T2 1 1...

Страница 29: ...of variable A by 10 Continuing A 10 80 To recall the contents of variable A Continuing A 8 To clear the contents of variable A 0 STO A 0 Independent Memory M You can add calculation results to or sub...

Страница 30: ...independent memory and variable contents are retained even if you press change the calculation mode or turn off the calculator PreAns memory contents are retained even if you press and turn off the ca...

Страница 31: ...ess Pi Natural Logarithm Base e is displayed as 3 141592654 but 3 14159265358980 is used for internal calculations e is displayed as 2 718281828 but e 2 71828182845904 is used for internal calculation...

Страница 32: ...Note that the input method is different depending upon whether you are using Natural Display or Linear Display Example To calculate e5 2 to three significant digits Sci 3 SETUP Sci MthIO MathO 5 2 2...

Страница 33: ...50 100 Power Functions and Power Root Functions Note that the input methods for and are different depending upon whether you are using Natural Display or Linear Display Example 1 1 2 103 1200 MthIO Ma...

Страница 34: ...be ignored To input 222 input 2 press the key and then press MthIO MathO x2 x3 x 1 can be used in complex number calculations Integration Calculations Function for performing numerical integration us...

Страница 35: ...f x and the region of integration calculation error that exceeds the tolerance may be generated causing the calculator to display an error message The content of f x positive negative values within t...

Страница 36: ...d then combine the results Differential Calculations Function for approximation of the derivative based on the central difference method Natural Display input syntax is d dx f x x a while Linear Displ...

Страница 37: ...en tol input is omitted the tol value will be adjusted automatically to determine the solution Non consecutive points abrupt fluctuation extremely large or small points inflection points and the inclu...

Страница 38: ...inates Rec 2 Polar Coordinates Pol Specify the angle unit before performing calculations The calculation result for r and and for x and y are each assigned respectively to variables X and Y Calculatio...

Страница 39: ...generates a pseudo random number in the range of 0 000 to 0 999 The result is displayed as a fraction when Natural Display is selected Generate three 3 digit random numbers The random 3 digit decimal...

Страница 40: ...1 or Norm 2 the argument is rounded off to 10 digits With Fix and Sci the argument is rounded off to the specified digit When Fix 3 is the display digits setting for example the result of 10 3 is disp...

Страница 41: ...ve calculation expressions that contain variables which you can then recall and execute in the COMP Mode and the CMPLX Mode The following describes the types of expressions you can save with CALC Expr...

Страница 42: ...r coordinates r Angle Unit Deg CMPLX A B i CMPLX r 3 1 2 30 or 1 3 2 60 To exit CALC Note During the time from when you press until you exit CALC by pressing you should use Linear Display input proced...

Страница 43: ...OLVE solves for Y for example when an equation is input as Y X 5 Y Important If an equation contains input functions that include an open parenthesis such as sin and log do not omit the closing parent...

Страница 44: ...ue to limitations in Newton s method solutions tend to be difficult to obtain for equations like the following y sin x y ex y x Solution Screen Contents Solutions are always displayed in decimal form...

Страница 45: ...built in scientific constants that can be used in any mode besides BASE N Each scientific constant is displayed as a unique symbol such as which can be used inside of calculations To input a scientifi...

Страница 46: ...lear magneton 08 B Bohr magneton 09 Planck constant rationalized 10 fine structure constant 11 re classical electron radius 12 C Compton wavelength 13 p proton gyromagnetic ratio 14 Cp proton Compton...

Страница 47: ...temperature 39 G Newtonian constant of gravitation 40 atm standard atmosphere The values are based on CODATA 2014 recommended values Metric Conversion The calculator s built in metric conversion comm...

Страница 48: ...re m2 12 m2 acre 13 gal US 14 gal US 15 gal UK 16 gal UK 17 pc km 18 km pc 19 km h m s 20 m s km h 21 oz g 22 g oz 23 lb kg 24 kg lb 25 atm Pa 26 Pa atm 27 mmHg Pa 28 Pa mmHg 29 hp kW 30 kW hp 31 kgf...

Страница 49: ...6i 2i 3 i Complex number format a bi 2 6 i 2 i 3 i Example 2 2 45 2 2i MthIO MathO Angle unit Deg Complex number format a bi 2 45 2 2i Example 3 2 2i 2 45 MthIO MathO Angle unit Deg Complex number for...

Страница 50: ...CMPLX arg 1 i 45 Using a Command to Specify the Calculation Result Format Either of two special commands r or a bi can be input at the end of a calculation to specify the display format of the calcul...

Страница 51: ...Bx e X Paired variable X Y ab exponential regression y ABx A B X Paired variable X Y power regression y AxB A X B Paired variable X Y inverse regression y A B x 1 X Pressing any of the above keys to d...

Страница 52: ...stics Editor is deleted whenever you exit the STAT Mode switch between the single variable and a paired variable statistical calculation type or change the Stat Format setting on the setup menu The fo...

Страница 53: ...Screen Using the Statistics Menu While the Statistics Calculation Screen is on the display press STAT DIST to display the Statistics Menu The content to the Statistics Menu depends on whether the cur...

Страница 54: ...Regression Calculation A BX Is Selected and Commands when Quadratic Regression Calculation _ CX2 Is Selected MinMax Display the MinMax sub menu of commands for obtaining maximum and minimum values Sin...

Страница 55: ...o obtain this minX Minimum value maxX Maximum value Q1 First quartile med Median Q3 Third quartile Commands when Linear Regression Calculation A BX Is Selected Sum Sub menu STAT DIST Sum Select this m...

Страница 56: ...a y Population standard deviation of the Y data sy Sample standard deviation of the Y data Reg Sub menu STAT DIST Reg Select this menu item When you want to obtain this A Regression coefficient consta...

Страница 57: ...ts x 1 Estimated value of x1 x 2 Estimated value of x2 y Estimated value of y Note x x 1 x 2 and y are not variables They are commands of the type that take an argument immediately before them See Cal...

Страница 58: ...ent 0 998 Logarithmic Regression Formula y 3857 984 2357 532lnx Calculating Estimated Values Based on the regression formula obtained by paired variable statistical calculation the estimated value of...

Страница 59: ...ow t This function is preceded by the argument X and determines the normalized variate X t X x x Example 5 For the single variable data xn freqn 0 1 1 2 2 1 3 2 4 2 5 2 6 3 7 4 9 2 10 1 to determine t...

Страница 60: ...le 2 Continuing from above switch to the hexadecimal mode and calculate 1F16 116 HEX 1 F 1 Example 3 Continuing from above switch to the octal mode and calculate 78 18 OCT 7 1 Note Use the following k...

Страница 61: ...number mode of that value The special commands are d decimal h hexadecimal b binary and o octal Example To calculate 1010 1016 102 108 and display the result as a decimal value DEC BASE d 10 BASE h 10...

Страница 62: ...exclusive logical sum which returns the result of a bitwise XOR xnor Logical operator xnor exclusive negative logical sum which returns the result of a bitwise XNOR Not Not function which returns the...

Страница 63: ...alue to binary takes the two s complement and then converts back to the original number base For decimal base 10 values the calculator merely adds a minus sign Equation Calculations EQN You can use th...

Страница 64: ...s of will display another solution Pressing while the final solution is displayed will return to the Coefficient Editor You can scroll between the solutions using the and keys To return to the Coeffic...

Страница 65: ...mple 3 2x2 3x 6 0 MthIO MathO EQN aX2 bX c 0 2 3 6 X1 3 57 4 X2 3 57 X Value Minimum 3 4 Y Value Minimum 57 8 The local minimum value is displayed when a 0 The local maximum value is displayed when a...

Страница 66: ...tB 1 Press MATRIX to enter the MATRIX Mode 2 Press MatA 2 2 This will display the Matrix Editor for input of the elements of the 2 2 matrix you specified for MatA 1 A stands for MatA 3 Input the eleme...

Страница 67: ...ATRIX MatAns Pressing any one of the following keys while the MatAns screen is displayed will switch automatically to the calculation screen x3 The calculation screen will show the MatAns variable fol...

Страница 68: ...y If you want to copy MatA for example perform the following key operation MATRIX Data MatA If you want to copy MatAns contents perform the following to display the MatAns screen MATRIX MatAns 2 Press...

Страница 69: ...uaring and x3 to specify cubing MATRIX MatA MATRIX MatA x3 Example 9 Determine the MatA row echelon form MATRIX Ref MATRIX MatA Example 10 Determine the MatA reduced row echelon form MATRIX Rref MATRI...

Страница 70: ...r limit of X Default 1 End Input the upper limit of X Default 5 Note Make sure that the End value is always greater than the Start value Step Input the increment step Default 1 Note The Step specifies...

Страница 71: ...r viewing values only Table contents cannot be edited The numerical table generation operation causes the contents of variable X to be changed The maximum number of rows in the generated numerical tab...

Страница 72: ...Mode 2 Press VctA 2 This will display the Vector Editor for input of the 2 dimensional vector for VctA 1 A stands for VctA 3 Input the elements of VctA 1 2 4 Perform the following key operation VECTOR...

Страница 73: ...nput with the Vector Editor To assign new data to a vector variable 1 Press VECTOR Dim and then on the menu that appears select the vector variable to which you want to assign data 2 On the next menu...

Страница 74: ...d VctC 2 1 2 from Example 2 Example 3 3 VctA Vector scalar multiplication 3 VctA VctB Calculation example using VctAns 3 VECTOR VctA VECTOR VctB Example 4 VctA VctB Vector dot product VECTOR VctA VECT...

Страница 75: ...alculation type To select this type of calculation Press this key Normal probability density Normal PD Normal cumulative distribution Normal CD Inverse normal cumulative distribution Inverse Normal Bi...

Страница 76: ...lation variables that accept input values Normal PD x Normal CD Lower Upper Inverse Normal Area Tail setting always left Binomial PD Binomial CD x or List N p Poisson PD Poisson CD x or List x data st...

Страница 77: ...then press To delete data Move the cursor to the sample data you want to delete and then press To insert sample data Move the cursor to the position where you want to insert the sample data press STA...

Страница 78: ...To calculate binomial probability for the sample data 10 11 12 13 14 when N 15 and p 0 6 DIST Binomial PD Display the List Screen List To specify data using parameter format press Var 10 11 12 13 14...

Страница 79: ...e corresponding sample data is outside the allowable range Inequality Calculations INEQ You can use the following procedure to solve a quadratic inequality or cubic inequality 1 Press INEQ to enter th...

Страница 80: ...the Coefficient Editor while the solutions are displayed press Note Values cannot be converted to engineering notation on the solution screen Changing the Inequality Type Press INEQ and then select an...

Страница 81: ...0 2 3 Example 4 3x3 3x2 x 0 MthIO MathO INEQ aX3 bX2 cX d aX3 bX2 cX d 0 3 3 1 Note Solutions are displayed as shown here when Linear Display is selected Special Solution Display All Real Numbers app...

Страница 82: ...o 10 digits for each of the required values a b c d To solve 3 8 X 12 for X for example press in step 1 and then input the following for the coefficients a 3 b 8 d 12 3 8 12 To change a coefficient va...

Страница 83: ...e and select the ratio expression type you want from the menu that appears Changing the ratio expression type causes the values of all Coefficient Editor coefficients to change to zero RATIO Mode Calc...

Страница 84: ...e calculation screen The cursor will be positioned at the location where the error occurred ready for input Make the necessary corrections to the calculation and execute it again Example When you inpu...

Страница 85: ...eric stack or the command stack to be exceeded The calculation you are performing has caused the capacity of the matrix or vector stack to be exceeded Action Simplify the calculation expression so it...

Страница 86: ...t include an X variable when you do not specify the solution variable Specify a variable that is included in the equation you input as the solution variable Can t Solve Error SOLVE feature only Cause...

Страница 87: ...above steps do not correct your problem press the key This will cause the calculator to perform a routine that checks whether calculation functions are operating correctly If the calculator discovers...

Страница 88: ...not skip the above step Calculation Priority Sequence The priority sequence of input calculations is evaluated in accordance with the rules below When the priority of two expressions is the same the...

Страница 89: ...he value being squared must be enclosed in parentheses 2 Since x2 has a higher priority than the negative sign inputting 2 would result in the squaring of 2 and then appending a negative sign to the r...

Страница 90: ...cosx Deg 0 x 9 109 Rad 0 x 157079632 7 Gra 0 x 1 1010 tanx Deg Same as sinx except when x 2n 1 90 Rad Same as sinx except when x 2n 1 2 Gra Same as sinx except when x 2n 1 100 sin 1 x cos 1 x 0 x 1 ta...

Страница 91: ...me as sinx a b c a b c 1 10100 0 b c The display seconds value is subject to an error of 1 at the second decimal place x 1 10100 Decimal Sexagesimal Conversions 0 0 0 x 9999999 59 59 xy x 0 1 10100 yl...

Страница 92: ...at can be displayed in form when using Natural Display is x 106 Note however that internal calculation error can make it impossible to display some calculation results in form It also can cause calcul...

Страница 93: ...tor ID number 24 character string QR Code for accessing the Worldwide Education Service https wes casio com calc 3 Access the above site 4 Follow the instructions on the display to verify the authenti...

Страница 94: ...formed Use this memory to carry the result of one calculation on to the next PreAns Memory Stores the result of calculation before the last one PreAns memory can be used only in the COMP Mode Independ...

Страница 95: ...ay cause unwanted values or expressions to be included as part of the argument Example sin 30 15 Angle Unit Deg Older S V P A M Model 30 15 15 5 Natural Textbook Display Model LineIO 30 15 15 5 Failur...

Страница 96: ...2020 CASIO COMPUTER CO LTD...

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