7-9-9 Tests

Linear Regression t Test

Command: LinRegTTest￿

Description: This command treats two groups of data as paired variables (x, y). The method of least squares is used to determine the most appropriate pair for the a, b coefficients of the regression formula y = a + b.x. It also determines the correlation coefficient and t value, and calculates the strength of the relationship between x and y.

 

n

 

 

 

 

 

 

Σ( x – o)( y – p)

 

 

 

 

 

 

a = p – b.o

 

n – 2

b =

i=1

 

t = r

 

 

 

 

 

n

 

1 – r

2

 

Σ(x – o)2

 

 

 

i=1

a : regression constant term (y-intercept)

b : regression coefficient (slope)

n: sample size (n >3)

r: correlation coefficient

r2 : coefficient of determination

Command Syntax

“β & ρ condition”, XList, YList, Freq (or 1)

* “Freq” can be omitted. Doing so sets “1” for “Freq”.

Definition of Terms

β& ρ condition : test conditions (“≠” specifies two-tail test, “<” specifies lower one-tail test, “>” specifies upper one-tail test.)

XList :

x-data list

YList :

y-data list

Freq :

frequency (1 or list name)

Input Example:

LinRegTTest “≠”,list1,list2,1

Calculation Result Output

β≠ 0 & ρ ≠ 0 : test condition

t :

t value

p :

p-value

df :

degrees of freedom

a :

regression constant term (y-intercept)

b :

regression coefficient (slope)

s :

standard error of estimation

r :

correlation coefficient

r2 :

coefficient of determination

20021201