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E-26

• The values in the above tables can be used inside of

expressions the same way you use variables.

Linear Regression

• The regression formula for linear regression is:

= A + B

•

Example:

Atmospheric Pressure vs. Temperature

Perform linear regression to de-
termine the regression formula
terms and correlation coefficient
for the data nearby. Next, use
the regression formula to esti-
mate atmospheric pressure at
18

C and temperature at 1000

hPa. Finally, calculate the coeffi-
cient of determination (

) and

sample covariance

In the REG Mode:

(Lin)

(Scl)

(Stat clear)

1003

Each time you press

to register your input,

the number of data input up to that point is

indicated on the display (

value).

1005

1010

1011

1014

Regression Coefficient A =

997.4

Regression Coefficient B =

0.56

Correlation Coefficient

0.982607368

Atmospheric Pressure at 18

C =

1007.48

Temperature at 1000 hPa =

4.642857143

1000

Temperature

Atmospheric

Pressure

1003 hPa

1005 hPa

1010 hPa

1011 hPa

1014 hPa

REG

Содержание FX-820MS

Страница 1: ...http world casio com edu_e fx 820MS User s Guide E ...

Страница 2: ...CASIO ELECTRONICS CO LTD Unit 6 1000 North Circular Road London NW2 7JD U K ...

Страница 3: ...E 1 ...

Страница 4: ...ly Never charge batteries try to take batteries apart or allow batteries to become shorted Never expose batteries to direct heat or dispose of them by incin eration Misuse of batteries can cause them to leak and dam age nearby items and can create the risk of fire and personal injury Always make sure that the battery s positive kand negative l ends are facing correctly when you load it into the ca...

Страница 5: ...ce every three years A dead battery can leak causing damage to and mal function of the calculator Never leave a dead battery in the calculator The battery that comes with this unit discharges slightly during shipment and storage Because of this it may require replacement sooner than the normal expected battery life Low battery power can cause memory contents to become corrupted or lost completely ...

Страница 6: ...where it might be sub jected to twisting or bending Never try to take the calculator apart Never press the keys of the calculator with a ball point pen or other pointed object Use a soft dry cloth to clean the exterior of the cal culator If the calculator becomes very dirty wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent Wring out all excess mo...

Страница 7: ...s 11 kArithmetic Calculations 11 kFraction Operations 11 kPercentage Calculations 13 kDegrees Minutes Seconds Calculations 14 kFIX SCI RND 15 Memory Calculations 16 kAnswer Memory 16 kConsecutive Calculations 16 kIndependent Memory 17 kVariables 17 Scientific Function Calculations 18 kTrigonometric Inverse Trigonometric Functions 18 kHyperbolic Inverse Hyperbolic Functions 19 kCommon and Natural L...

Страница 8: ... kEngineering Notation Calculations 21 Statistical Calculations 22 Standard Deviation 22 Regression Calculations 24 Technical Information 28 kWhen you have a problem 28 kError Messages 28 kOrder of Operations 30 kStacks 31 kInput Ranges 32 Power Supply 34 Specifications 35 ...

Страница 9: ...s indicated in the table below To perform this type of Perform this To enter calculation key operation this mode Basic arithmetic calculations F 1 COMP Standard deviation F 2 SD Regression calculations F 3 REG Pressing the F key more than once displays additional setup screens Setup screens are described in the sec tions of this manual where they are actually used to change the calculator setup In...

Страница 10: ...ample takes up only one step You can input up to 79 steps for a single calculation Whenever you input the 73rd step of any calculation the cursor changes from _ to k to let you know memory is running low If you need to input more than 79 steps you should divide your calculation into two or more parts Pressing the g key recalls the last result obtained which you can use in a subsequent calculation ...

Страница 11: ...r replay memory so you can recall the last calculation even after you press t Replay memory capacity is 128 bytes for storage of both expressions and results Replay memory is cleared by any of the following ac tions When you press the 5 key When you initialize modes and settings by pressing A B 2 or 3 When you change from one calculation mode to another When you turn off the calculator k Error Loc...

Страница 12: ...ntial notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places uNorm 2 With Norm 2 exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places All of the examples in this manual show calculation re sults using the Norm 1 format k Decimal Point and ...

Страница 13: ... the F key to enter the COMP Mode when you want to perform basic calculations COMP F 1 Negative values inside of calculations must be enclosed within parentheses sin 1 23 S R D 1 23 T It is not necessary to enclose a negative exponent within parentheses sin 2 34 10 5 S 2 34 e D 5 Example 1 3 5 10 9 1 5 10 8 3 5 e D 9 Example 2 5 9 7 80 5 R 9 7 T You can skip all T operations before k Fraction Oper...

Страница 14: ...hat mix fraction and decimal val ues are always decimal uDecimal Fraction Conversion Use the operation shown below to convert calculation results between decimal values and fraction values Note that conversion can take as long as two seconds to perform 2 3 4 00 11 4 00 Example 1 2 75 2 Decimal Fraction 2 75 2 75 C A B 3 4 11 4 C C 0 500 1 2 00 1 2 00 1 2 Example 2 0 5 Fraction Decimal 1 C 2 ...

Страница 15: ... of times until you reach the setup screen shown below 1 D i s p Display the selection screen 1 Press the number key 1 or 2 that corresponds to the setting you want to use 1 ab c Mixed fraction 2 d c Improper fraction An error occurs if you try to input a mixed fraction while the d c display format is selected k Percentage Calculations Example 1 To calculate 12 of 1500 180 1500 12 A v Example 2 To...

Страница 16: ...stores a result to Answer Memory before the key is pressed Example 6 If 300 grams are added to a test sample originally weighing 500 grams what is the percentage increase in weight 160 300 500 A v Example 7 What is the percentage change when a value is increased from 40 to 46 How about to 48 15 20 46 40 A v e e e e e e 8 k Degrees Minutes Seconds Calculations You can perform sexagesimal calculatio...

Страница 17: ...s the number key 1 2 or 3 that corresponds to the setup item you want to change 1 Fix Number of decimal places 2 Sci Number of significant digits 3 Norm Exponential display format 28 57100 400 00000 Internal calculation continues using 12 digits 400 00 Example 1 200 7 14 200 7 14 F 1 Fix 3 200 7 14 400 00000 FIX Specifies three decimal places The following performs the same calculation using the s...

Страница 18: ...ter A through F or M X or Y You can recall Answer Memory contents by pressing g Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent Answer Memory contents are not updated if the opera tion performed by any of the above key operations re sults in an error k Consecutive Calculations You can use the calculation result that is currently on the display and also stor...

Страница 19: ...9 32 23 9 A j 3 53 6 47 53 6 45 2 90 45 2 A Total 11 0 3 k Variables There are nine variables A through F M X andY which can be used to store data constants results and other values Use the following operation to delete data assigned to a particular variable 0 A j 1 This operation de letes the data assigned to variable A Perform the following key operation when you want to clear the values assigne...

Страница 20: ... ing the next calculation π 3 14159265359 k Trigonometric Inverse Trigonometric Functions To change the default angle unit degrees radians grads press the F key a number of times until you reach the angle unit setup screen shown below 1 2 3 Deg Rad Gr a Press the number key 1 2 or 3 that corresponds to the angle unit you want to use 90 radians 100 grads Example 1 sin 63 52 41 0 897859012 q 1 Deg S...

Страница 21: ...tilogarithms Example 1 log 1 23 0 089905111 R 1 23 Example 2 In 90 loge 90 4 49980967 T 90 ln e 1 T p P Example 3 e10 22026 46579 A U 10 Example 4 101 5 31 6227766 A Q 1 5 Example 5 24 16 2 W 4 k Square Roots Cube Roots Roots Squares Cubes Reciprocals Factorials Random Numbers π and Permutation Combination Example 1 2 3 5 5 287196909 L 2 L 3 L 5 Example 3 cos 1 q 2 Rad A V R L 2 2 T g A x 0 25 π r...

Страница 22: ...lts differ each time Example 9 3π 9 424777961 3 A x Example 10 To determine how many different 4 digit values can be produced using the numbers 1 through 7 Numbers cannot be duplicated within the same 4 digit value 1234 is allowed but 1123 is not 840 7 A m 4 Example 11 To determine how many different 4 mem ber groups can be organized in a group of 10 individuals 210 10 n 4 k Angle Unit Conversion ...

Страница 23: ...P 60 T y 1 732050808 0 o Press 0 n to display the value of x or 0 o to dis play the value of y Example 2 To convert rectangular coordinates 1 3 to polar coordinates r Rad r 2 f 1 P L 3 T θ 1 047197551 0 o Press 0 n to display the value of r or 0 o to dis play the value of k Engineering Notation Calculations Example 1 To convert 56 088 meters to kilometers 56 088 103 56088 J Example 2 To convert 0 ...

Страница 24: ... which you can recall using the key opera tions noted nearby To recall this type of value Perform this key operation Σx2 A U 1 Σx A U 2 n A U 3 o A X 1 σn A X 2 σn 1 A X 3 Example To calculate σn 1 σn o n Σx and Σx2 for the following data 55 54 51 55 53 53 54 52 In the SD Mode A B 1 Scl Stat clear 55 S Each time you press S to register your input the number of data input up to that point is indica...

Страница 25: ...value with the new one This also means that if you want to perform some other operation calculation recall of statistical calculation results etc you should always press the t key first to exit data display Pressing the S key instead of after changing a value on the display registers the value you input as a new data item and leaves the old value as it is You can delete a data value displayed usin...

Страница 26: ...ger after perform either the following operations Changing to another mode Changing the regression type Lin Log Exp Pwr Inv Quad Regression Calculations Use the F key to enter the REG Mode when you want to perform statistical calculations using regression REG F 3 Entering the REG Mode displays screens like the ones shown below REG 1 2 3 L i n Log Exp 1 2 3 Pw r Inv Quad r e Press the number key 1 ...

Страница 27: ...A U r 1 Σy A U r 2 Σxy A U r 3 o A X 1 xσn A X 2 xσn 1 A X 3 p A X r 1 yσn A X r 2 yσn 1 A X r 3 Regression coefficient A A X r r 1 Regression coefficient B A X r r 2 Regression calculation other than quadratic regression Correlation coefficient r A X r r 3 m A X r r r 1 n A X r r r 2 The following table shows the key operations you should use to recall results in the case of quadratic regression ...

Страница 28: ...ally calculate the coeffi cient of determination r2 and sample covariance In the REG Mode 1 Lin A B 1 Scl Stat clear 10 P1003 S Each time you press S to register your input the number of data input up to that point is indicated on the display n value 15 P 1005 S 20 P1010 S 25 P 1011 S 30 P 1014 S Regression Coefficient A 997 4 A X r r 1 Regression Coefficient B 0 56 A X r r 2 Correlation Coefficie...

Страница 29: ...ower Regression y Aⴢ xB In y In A BIn x Inverse Regression y A B ⴢ1 x xi yi 29 1 6 50 23 5 74 38 0 103 46 4 118 48 0 uQuadratic Regression The regression formula for quadratic regression is y A Bx Cx2 Example Perform quadratic regression to de termine the regression formula terms for the data nearby Next use the regression formula to estimate the values for n estimated value of y for xi 16 and m e...

Страница 30: ...nformation k When you have a problem If calculation results are not what you expect or if an error occurs perform the following steps 1 Press A B 2 Mode to initialize all modes and settings 2 Check the formula you are working with to confirm it is correct 3 Enter the correct mode and try performing the calcula tion again If the above steps do not correct the problem press the 5 key The calculator ...

Страница 31: ...using Stack ERROR Cause The capacity of the numeric stack or operator stack is exceeded Action Simplify the calculation The numeric stack has 10 lev els and the operator stack has 24 levels Divide your calculation into two or more separate parts Syntax ERROR Cause An attempt to perform an illegal mathematical opera tion Action Press e or r to display the calculation with the cur sor located at the...

Страница 32: ...e is entered 3 log In ex 10x sin cos tan sin 1 cos 1 tan 1 sinh cosh tanh sinh 1 cosh 1 tanh 1 7 Abbreviated multiplication format in front ofType B func tions 2 3 Alog2 etc 8 Permutation and combination nPr nCr 9 0 Operations of the same precedence are performed from right to left ex In 120 ex In 120 Other operations are performed from left to right Operations enclosed in parentheses are performe...

Страница 33: ...and the command stack has 24 levels A stack error Stack ERROR occurs whenever you try to perform a calculation that is so com plex that the capacity of a stack is exceeded Example 1 2 3 4 5 1 2 3 4 5 6 7 Numeric Stack Command Stack 1 2 3 4 5 2 3 4 5 4 1 2 3 4 5 6 7 Calculations are performed in sequence according to Order of Operations Commands and values are de leted from the stack as the calcula...

Страница 34: ... Same as sinx except when x 2n 1 π 2 GRA Same as sinx except when x 2n 1 100 sin 1 x 0 x 1 cos 1 x tan 1 x 0 x 9 999999999 1099 sinhx 0 x 230 2585092 coshx sinh 1 x 0 x 4 999999999 1099 cosh 1x 1 x 4 999999999 1099 tanhx 0 x 9 999999999 1099 tanh 1 x 0 x 9 999999999 10 1 logx lnx 0 x 9 999999999 1099 10 x 9 999999999 1099 x 99 99999999 ex 9 999999999 1099 x 230 2585092 x 0 x 1 10100 x2 x 1 1050 1 ...

Страница 35: ...is an integer However 1 10100 1 x log y 100 ab c x 1 1050 y 1 1050 SD n 1 10100 REG x n y n o p n G 0 x n 1 y n 1 A B r n G 0 1 Total of integer numerator and denominator must be 10 digits or less including division marks 1 2n 1 1 n For a single calculation calculation error is 1 at the 10th digit In the case of exponential display calculation er ror is 1 at the last significant digit Errors are c...

Страница 36: ...be replaced Display figures are dim and difficult to read in areas where there is little light available Nothing appears on the display when you press the 5 key u To replace the battery 1 Remove the screw that holds the battery cover in place and then remove the battery cover 2 Remove the old battery 3 Wipe off the sides of new battery with a dry soft cloth Load it into the unit with the positive ...

Страница 37: ... press 5 to turn power back on Specifications Power Supply Solar cell and a single G13 Type button battery LR44 Battery Life Approximately 3 years 1 hour use per day Dimensions 12 0 H 89 0 W 173 0 D mm 1 2 H 31 2 W 613 16 D Weight 120 g 4 23 oz including battery Power Consumption 0 0002 W Operating Temperature 0 C to 40 C 32 F to 104 F ...

Страница 38: ...SA0205 A Printed in China CASIO COMPUTER CO LTD 6 2 Hon machi 1 chome Shibuya ku Tokyo 151 8543 Japan ...

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