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Why Is expected value of error zero?
The error term accounts for the variation in the dependent variable that the independent variables do not explain. Random chance should determine the values of the error term. For your model to be unbiased, the average value of the error term must equal zero.
Why is a regression line often referred to as the Line of conditional means?
If you look at any textbook on linear regression, you will find that it says the following: “Linear regression estimates the conditional mean of the response variable.” This means that, for a given value of the predictor variable X , linear regression will give you the mean value of the response variable Y .
Why is the expected value of the error when?
The stochastic assumptions on the error term, (not on the residuals) E ( u) = 0 or E ( u ∣ X) = 0 assumption (depending on whether you treat the regressors as deterministic or stochastic) are in fact justified by the same action that guarantees that the OLS residuals will be zero: by including in the regression a constant term (“intercept”).
How to test for zero mean in regression?
You can easily test these results. For the zero mean assumption, you can apply t-test to show that the residual mean does not significantly differ from zero while for the covariance condition, you can simply check correlation coefficients between the residuals and features, for each feature. Hope this helps!
Is there a linear relationship between errors and independent variables?
This is, as the name implies, a very strong assumption and generally not possible. Therefore, we apply a softer version of it as: These conditions implies that the error mean is zero and there is no linear relationship between the errors and the independent variables, respectively.
Is the expected value of Y the same in both specifications?
The expected value of y in these two different specifications is the same -and it is the expected value of y that we are essentially estimating in an OLS regression (see this post ).