Linear Regression Calculation

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

Regression is an important part in statistical calculation. Here we develop relationship between two variables on the basis of observed data assuming the relationship to be linear, parabolic,quadratic etc.


Example: On the basis of following data establish regression equation between x and y assuming the relation to be linear.( Let y=A+Bx and Find out A,B,correlation coefficient r). Also calculate  Σx, Σx², Σy, Σy², Σxy, x̅, xσ_n, xσ_n-1,(standard variation), x̅, y bar, yσ_n, yσ_{n-1, estimated value of y for x=18,} estimated value of  x for y=20. (Answers: Σx=100, Σx²=2250, Σy=5043, Σy²=5086451, Σxy=101000, x̅=20, xσ_n=7.071,

Calculation of normal distribution in statistical calculation

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

In statistics often it is necessary to calculate normal distribution.Normal distribution indicates percentage of chance of occurrence of an event based on the observed data.It's one type of probability distribution.

Example: Calculate normalized variate(→t) for x=53 and normal probability distribution P(t) for the following data 55,54,51,55,53,53,54,52.Also calculate Q(t) and R(t) for these data.(Ans: -0.28, 0.387, 0.112, 0.612 respectively)

Some important notes on complex mode and modulas,argument determination

Model : CASIO fx-570MS, CASIO fx-991MS, CASIO  fx-100MS

Note 1: Expression can be stored in CALC memory in complex mode.

Note 2: Variables A,B,C and M can be used in COMPLEX mode. Variables D,E,F,X,Y won't appear in COMPLEX mode.

Note  3: The indicator R↔I in the upper right corner of a calculation result display indicates a complex number result.

Note 4: Direct calculation of (a+ib)ⁿ will show mathematical error.

Example: Compute modulas and argument of the complex number -3+2i. (Ans: 3.606 and 146.31 Degree)

Solution:

(Mode initialization)

How to determine unit vector perpendicular to two coplaner vectors and angle between two vectors

Model : CASIO fx-570MS, CASIO fx-991MS

If you have read the previous post on Determination of Cross Product and Absolute Value of a vector. then determination of angle and unit vector in calculator would be very easy.In order to determine unit vector, cross product of two vector has to be divided with the value of cross product.Again in order to determine angle between two vector, dot product of two vector has to be divided with the value of dot product.The formulas are as follows..

unit vector ẑ = (A*B) / |A*B|
angle θ = (A.B) / AB

How to work with complex numbers in calculator

Model : CASIO fx-570MS, CASIO fx-991MS, CASIO  fx-100MS

The number that has a negative square value is called a complex number. It has a real part and an imaginary part.The imaginary part includes i (=√-1). a+ib is a complex number where a is the real part and ib is the imaginary part.This format is known as rectangular format.Complex numbers are also presented in another format that is known as polar format. r∠θ° is a representation of complex number in polar format.

Example:  Calculate (5+2i)*2∠30°.(Ans: 6.66+8.46i)

Solution:

(Mode initialization)

How to use logical operators in Base Mode

Model : CASIO  fx-991MS, CASIO fx-570MS

Addition,Subtraction,Multiplication, Division are same as arithmetic calculation in Base Mode.Besides this you can use the following logical operators between values in Base-n calculations. The meaning of this operators are as follows..

How to convert decimal number into hexadecimal,binary and octal number.

Model : CASIO  fx-991MS, CASIO fx-570MS
 
Natural number or decimal numbers that we use for our calculation have base 10. There are other format of number like hexadecimal,binary,octal that have base16,2 and 8 respectively. These type of number are often used in programming sector. Base mode of calculator can be used for conversion of such numbers into one another.

Example: Solve (17)₁₀ = (?)₂ = (?)₁₆ = (?)₈.(what is the value of 17 if it is converted in binary (base 2),

How to solve an equation of two degree

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

A two degree equation contains a single variable with maximum power two.it has two roots.It is called quadratic equation. ax²+bx+c=0 is a quadratic equation where x is the variable and a,b,c are constants.This type of equation is solved by a process known as middle term method. But often it's not possible to have the factor. Equation mode of calculator lets you to solve such equations very easily and quickly.

Example: Solve the equation 2x²-3x-1=0.(Ans: 1.78, -0.28)

Determination of Cross Product and Absolute Value of a vector.

Model : CASIO fx-570MS, CASIO fx-991MS

Manual determination of cross product requires determinant which is confusing and may provide unwanted error in result.You can easily create vectors in calculator and perform cross product within a minute.

Example: Find the cross product of vectors A= 3i-2j+5k and B= i+4j-3k. Also find the absolute value of vector A.(Ans: -14i+14j+14k and 6.1644)

Solution:

How to solve basic problems of statistics

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

Statistics is a very important part of mathematics. Mean ( x̅ ), Standard deviation(σ_n, σ_n-1), Σx, Σx² etc can be calculated with calculator for any given data.

Example: The numbers of students of different class of a school are 55,58,51,63,55,59,51,60,53,55.Calculate mean ( x̅ ), Standard Deviation (σ_n, σ_n-1), Σx, Σx² for the these

How to integrate a function (Definite Integral)

Model : CASIO fx-570MS, CASIO fx-991MS

Calculator can easily perform definite integration (integration with limit). Mainly three inputs are required for the operation.They are a function with variable x, lower limit, upper limit.

Example: What is the value of  ∫₂⁵(x³-5x-3)dx ?
              Options: a) 129/12, b) 363/4, c) 65/7, d) 1/2

How to solve equations with two unknowns

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

Solving equations is frequently required in almost every mathematical problems. As number of unknowns is equal to number of equations. So at least two equations are required here.Calculator takes the coefficients of x and y and returns the value of x and y. Calculator can easily solve the following equations with coefficients known.    
                      a₁x+b₁y=c₁
                      a₂x+b₂y=c₂

Constant and Conversion

Model : CASIO  fx-991MS
Often we use different constants such as Plank Constant ( h = 6.63*10^-34 Js ), Mass of Electron ( m_e=9.11*10^-31 kg) etc in calculation. It is difficult to keep in mind such values all the time. Calculator has kept stored such constant values in it's memory.

Example: What are the values of Plank Constant and Charge of an Electron ?(Ans: h=6.63*10^-34 Js and e=1.6*10^-19 C )

How to find the values of a function for different input simultaneously(Calc Memory))

Model : CASIO fx-570MS, CASIO fx-991MS
CALC memory(CALC button) lets you temporarily store a mathematical expression that you need to perform a number of times using different values.Once you store an expression,you can recall it, input values for it's variables and calculate  a result quickly and easily.

You can store a single mathematical expression with up-to 79 steps.CALC memory can only be used in the COMP and COMPLX Mode.

Example: Calculate the result of  y=a²+b²+c²+3abc when
                                                a) a=5,b=2,c=1 (Ans:60)
                                                b) a=3,b=7,c=4 (Ans:326)