The
Distribution of Response variable “Y”
The assumption of classical linear regression model, the disturbance is
iid normally with mean zero and fixed variance δ2.
Consider the simple linear regression model;
Y = α + β X + ϵ
ϵ ~ N (0, δ2.)
The distribution of response variable is depending on the distribution of the disturbance term.
E (Y ) = α + β X
The variance of Y:
The Sampling Distribution Regression Parameters
Consider the simple linear regression model;
Y = α + β X + ϵ
ϵ ~ N (0, δ2.)
Then Y follow normal distribution with mean α + β X and
standard deviation δ.
The estimate of the
slope of the above regression model is given by;
The
estimate of the intercept of the regression model;
The Sampling Distribution
of Mean value of Response Variable “Y” for a given value X = X0
Consider the simple linear regression model;
Y = α + β X + ϵ
The predict values
of Y is Y^0 at X = X0 is given by:
Y^0 = α + β X0
Sampling Distribution of individual value of Response
Variable
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