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,
xσ_n-1=7.9056, y bar=1008.6, yσ_n=4.029, yσ_{n-1=4.029, A=997.4, B=0.56, correlation coefficient r=0.9826, estimated value of y for x=18 is 1007.48,} estimated value of  x for y=1000is 4.6428)

x	y
10	1003
15	1005
20	1010
25	1011
30	1014

Solution:

(Mode initialization)
MODE >> MODE >> 2(REG) >> 1(Lin)

(Memory clear Important) 
SHIFT >> MODE >> 1(Scl) >> = (Stat clear)

(Input data)
1 >> 0 >> , (Comma) >> 1 >> 0 >> 0 >> 3 >> M+(n=1) >> 1 >> 5 >> , >> 1 >> 0 >> 0 >> 5 >> M+(n=2) >> 2 >> 0 >> , >> 1 >> 0 >> 1 >> 0 >> M+(n=3) >> 2 >> 5 >> , >> 1 >> 0 >> 1 >> 1 >> M+(n=4) >> 3 >> 0 >> , >> 1 >> 0 >> 1 >> 4 >> M+(n=5)


(Calculation of Σx, Σx²)
SHIFT >> 1 >> 1(Σx²) >> =

SHIFT >> 1 >> 2(Σx) >> =

(Calculation of Σy, Σy²,Σxy)
SHIFT >> 1 >> Right button of replay >> 1(Σy²) >> =

SHIFT >> 1 >> Right button of replay >> 2(Σy) >> =

SHIFT >> 1 >> Right button of replay >> 3(Σxy) >> =

 

(Calculation of xσ_n, xσ_n-1, x̅)
SHIFT >> 2 >> 1(x̅) >> =

SHIFT >> 2 >> 2(xσ_n) >> =

SHIFT >> 2 >> 3(xσ_n-1) >> =


(Calculation of yσ_n, yσ_n-1, y bar)
SHIFT >> 2 >> Right button of replay >> 1(y bar) >> =

SHIFT >> 2 >> Right button of replay >> 2(yσ_n) >> =

SHIFT >> 2 >> Right button of replay >> 3(yσ_n-1) >> =

(Calculation of A,B,r)
SHIFT >> 2 >> Right button of replay >> Right button of replay >> 1(A) >> =

SHIFT >> 2 >> Right button of replay >> Right button of replay >> 2(B) >> =

SHIFT >> 2 >> Right button of replay >> Right button of replay >> 3(r) >> =


 
( Calculation of estimated value of y for x=18)
1 >> 8 >> SHIFT >> 2 >> Right button of replay >> Right button of replay >> Right button of replay >> 2 >> =

( Calculation of estimated value of y for x=18)
1 >> 0 >> 0 >> 0 >> SHIFT >> 2 >> Right button of replay >> Right button of replay >> Right button of replay >> 1 >> =


Use the same key operations as linear to recall results for following type of regression,
 

Type	Equation calculator follows
Logarithmic	y =A+B.lnx
Exponential	y =A*eB*x (lny=lnA+Bx)
Power	y =A*xB (lny=lnA+Blnx)
Inverse	y =A+B*1/x