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Like the simple linear regression model, the multiple regression model is also based on certain assumptions.
Consider the multiple regression model
The following assumptions are often made:
Assumption 1: For any given set of values of 
and 
, the random error 
has a normal probability distribution with mean equal to 0 and variance equal to 
.
Assumption 2: The errors associated with different sets of values of independent variables are independent.
Assumption 3: The independent variables are not linearly related. If any of them is linearly related, then we can eliminate one of the variables by making substitution and reduce the number of independent variables.
Assumption 4: It is not possible to find a set of numbers 
, such that
The explanatory power of a multiple regression equation
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