Hello
in a simple linear regression we have
Y=b0 +b1X +ε where ε is a random variable
but when we use a sample
we have
Yi = b0 + b1Xi + εi, i = 1, …, n where εi are random variable too
I’m a little bit lost ε is a random variable and its occurrence εi are random variable too?
and why E(ε)=0 would imply E(εi) for each i?
Suppose that you have three data points:
The regression equation is:
y = 2.0_x_ + 0.0 + ε
In this case:
Yes, as S2000 says, those " i " means the data observations, they can be temporal data or cross-sectional data. For example, set X variable as consumption. So Xi is the " i-th " observation of the sample you got about consumption:
X1 = 50 dollar consumption of Harrogath on August, 2015
X2 = 75 dollar consumption of S2000Magician on August, 2015
…
Xn = 62 dollar consumption of Javad05 on August, 2015
This is cross-sectional data of X variable.
Time-series data of variable X would be:
X1 = 62 dollar consumption of Javad05 on August, 2015
X2 = 70 dollar consumption of Javad05 on September, 2015
…
Xn = 128 dollar consumption of Javad05 on January, 2038
Regards
Based on the equation, shouldn’t the signs be flipped on the above ε’s?
(1) = 2.0(1) + 0.0 + ε1
ε1_=-1_
(6) = 2.0(2) + 0.0 + ε2
ε2_=+2_
…
Absolutely correct.
Mea culpa.
I’ve corrected it.
Thank you guys
but I was not asking about that !
if you look to the assumption of linear regression (6)
-The variance of the error term is the same for all observations: E(ε2i)=σ2ε , i = 1, …, n.
-The error term, ε, is uncorrelated across observations. Consequently, E(εiεj) = 0 for all i not equal to j you can see that εi are not only value but random variable on their own so do I have to dwell on that or move on thank you
The outcome of the roll of a die is a random variable, but once you roll the die, it takes on a specific value.
So it goes with linear regression: the error term is a random variable, but once you run the regression with a specific data set, each random error term then takes on a specific value.