Casio fx-50F Sx2y.Sxx – Sxy.Sxx2, Sxx.Sx2x2 – (Sxx2)2, = Σxi, = Σxi, – b +, – b –, Command, Command, Command, Formula Table, Linear Regression, Calculation Formula, a, b, r

ARegression Coefficient and Estimated Value CalculationFormula Table

The following table shows the calculation formulas used by the regression coefficient and estimated value commands for each regression calculation type.

Linear Regression

Command				Calculation Formula
Regression Formula	a =		Σyi – b.Σxi
Constant Term a			n
Regression Coefficient b	b =	n.Σxiyi – Σxi.Σyi
			n.Σxi2 – (Σxi)2
Correlation Coefficient r	r =			n.Σxiyi – Σxi.Σyi
			{n.Σxi2 – (Σxi)2}{n.Σyi2 – (Σyi)2}
Estimated Value m	m =	y – a
			b
Estimated Value ţ	n = a + bx

Quadratic Regression

Command

Calculation Formula

Regression Formula

Σyi

Σxi

Σxi2

Constant Term a

a =

– b (

n

)– c (

n

)

n

Regression Coefficient b

b =

Sxy.Sx2x2 – Sx2y.Sxx2

Sxx.Sx2x2 – (Sxx2)2

Regression Coefficient c

c =

Sx2y.Sxx – Sxy.Sxx2

Sxx.Sx2x2 – (Sxx2)2

However,

2

3

(Σxi.Σxi2)

(Σxi)

2

Sxx

= Σxi

–

2

n

Sxx = Σxi

–

(Σxi2)2

n

2

2

Σxi

4

(Σxi.Σyi)

Sx

x

=

–

Sxy = Σxiyi

–

n

2

n

2

2

(Σxi .Σyi)

Sx

y

= Σxi

yi

–

n

Command

Calculation Formula

– b +

Estimated Value m1

m1 =

b2 – 4c(a – y)

2c

– b –

Estimated Value m2

m2 =

b2 – 4c(a – y)

2c

Estimated Value n

n = a + bx + cx2

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