HP (Hewlett-Packard) 50g ユーザーズマニュアル

Page 18-50

Therefore, the F test statistics is  F

o

 = s

M

2

/s

m

2

=0.36/0.25=1.44

The P-value is  P-value = P(F>F

o

) = P(F>1.44) = UTPF(

ν

N

,

 ν

D

,F

o

) =

UTPF(20,30,1.44) = 0.1788…

Since 0.1788… > 0.05, i.e., P-value > 

α, therefore, we cannot reject the null 

hypothesis that H

o

:

σ

1

2

=

σ

2

2

.

In this section we elaborate the ideas of linear regression presented earlier in 
the chapter and present a procedure for hypothesis testing of regression 
parameters.

Let x = independent, non-random variable, and Y = dependent, random 
variable.  The regression curve of Y on x is defined as the relationship between 
x and the mean of the corresponding distribution of the Y’s.
Assume that the regression curve of Y on x is linear, i.e., mean distribution of 
Y’s is given by 

Α + Βx.   Y differs from the mean (Α + Β⋅x) by a value ε, thus

Y = 

Α + Β⋅x + ε, where ε is a random variable.

To visually check whether the data follows a linear trend, draw a scattergram or 
scatter plot.

Suppose that we have n paired observations (x

i

, y

i

); we predict y by means of

∧

y = a + b

⋅x, where a and b are constant.

Define the prediction error as, e

i

 = y

i

 - 

∧

y

i

 = y

i

 - (a + b

⋅x

i

).

The method of least squares requires us to choose a, b so as to minimize the 
sum of squared errors (SSE)

the conditions 

      

2

1

1

2

)]

(

[

i

n

i

i

n

i

i

bx

a

y

e

SSE

+

−

=

=

∑

∑

=

=

0

)

(

=

SSE

a

∂

∂

0

)

(

=

SSE

b

∂

∂