When the error terms have a constant variance?

Homoskedasticity occurs when the variance of the error term in a regression model is constant. If the variance of the error term is homoskedastic, the model was well-defined.

What does the standard error of estimate see measure and what can this tell us about how well your linear regression can model data?

The standard error of the regression (S), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable.

What is variance of estimator?

Variance. The variance of is simply the expected value of the squared sampling deviations; that is, . It is used to indicate how far, on average, the collection of estimates are from the expected value of the estimates. (Note the difference between MSE and variance.)

What is meant by the variance of the OLS estimator?

The variance of a random variable X is defined as the expected value of the square of the deviation of different values of X from the mean X̅. It shows how spread the distribution of a random variable is.

What is the variance of the error term?

Residual Variance (also called unexplained variance or error variance) is the variance of any error (residual). The exact definition depends on what type of analysis you’re performing. For example, in regression analysis, random fluctuations cause variation around the “true” regression line (Rethemeyer, n.d.).

Why is variance constant?

It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the red lines (a proxy of its variance) are the same.

What does standard error of estimate mean?

Standard error is the estimated standard deviation of an estimate. It measures the uncertainty associated with the estimate. Compared with the standard deviations of the underlying distribution, which are usually unknown, standard errors can be calculated from observed data.

What is Sigma hat squared?

The square root of (sigma hat)^2 is called the standard error of the regression . It is just the standard deviation of the residuals e_i. There are two important theorems about the properties of the OLS estimators.