Re: random generation

Dear nitish,
tou can do it easily with Statistica by supposing this model:

you have two groups (called group 1 and group 2) and you observe the
relation between the response variable and the predictor, in each of
this group. You can imagine that you observe weight (Y), height (X) for
a group of men (group 1) and female (group 2). You suppose this 2
models:

M(1): group 1 : Y = (b_0 + b_2) + (b_1 + b_3) * X + e
M(2): group 2: Y = b_0 + b_1 * X + e

you want to verifiy H_0: b_1 + b_3 = b_1, that is b_3=0.


So you can consider the model with a dummy variable Z: Z=1 if the unit
is in the group 1, Z=0 if the unit is in the group 2, and so you can
use the model:

M(1+2) : Y = b_0 + b_1*X + b_2*Z + b_3*X*Z + e


You can see that if:
Z=1 then M(1+2) = M(1)
Z=0 then M(1+2) = M(2).

Now you can do the analysis with Statistica in this way:

1- creating a new spread*** with 3 variables:
v1= Z (1 if group1, 0 if group 2)
v2= X
v3= Z*X (you can do it by writing "=v1*v2" into Variable
Specifications Editor > Long Name (label or formula) )
v4= Y.
2 - now you have to use the module Statistics > Multiple regression
3 - to choose v4 as dipendent variable, from v1 to v3 as independent
variables.
4 - ok > ok > Regression summary

With the output of the linear regression you obtain the p-value for
each parameter from b_0 to b_3.

If the p-value of b_3 is more than, for example, 0.05 (Alpha for
highlighting effects) you accept H_0.

To verify the hypothesis of the same intercept:

H_0: b_0+b_2 = b_0

in the same way you have to verify H_0 : b_2=0 in the model M(1+2).

Finally, it's important to know that these tests are based on the
hypothesis of normality that should be tested....



Michele De Meo
Statistician
http://crea.html.it/sito/micheledemeo

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