Error variable

Statistics MOC #input Statistics permanent

16.3 Error Variable: required conditions

Required Conditions for the Error Variable

1. The probability distribution of ε is normal.
2. The mean of the distribution is 0; that is, E (ε) = 0.
3. The standard deviation of ε is ${\sigma }_{ϵ}$, which is a constant regardless of the value of x.
4. The value of ε associated with any particular value of y is independent of ε associated with any other value of y. From 1, 2, 3, we can know: For each value of x, y is a normally distributed random variable whose means is $E(y)={\beta }_0+{\beta }_{1}x$ whose standard deviation is ${\sigma }_{ϵ}$ That is, no matter how the x is , the standard deviation of y is the same.