What happens if linear regression assumptions are violated?

If the X or Y populations from which data to be analyzed by linear regression were sampled violate one or more of the linear regression assumptions, the results of the analysis may be incorrect or misleading. For example, if the assumption of independence is violated, then linear regression is not appropriate.

What does blue stand for in regression analysis?

BLUE is an acronym for the following: Best Linear Unbiased Estimator. In this context, the definition of “best” refers to the minimum variance or the narrowest sampling distribution.

What does it mean when estimators are said to be blue?

OLS estimators are BLUE (i.e. they are linear, unbiased and have the least variance among the class of all linear and unbiased estimators). Amidst all this, one should not forget the Gauss-Markov Theorem (i.e. the estimators of OLS model are BLUE) holds only if the assumptions of OLS are satisfied.

Should regression estimates be blue?

Instead, a variation called general least squares (GLS) will be BLUE. The Gauss-Markov Theorem states that if a linear regression model fulfils the assumptions of the classical linear regression model the ordinary least squares estimator is the best linear unbiased estimator (BLUE).

When assumptions are violated what do we use?

As we have already discussed, to use a one-sample t-test, you need to make sure that the data in the sample is normal or at least reasonably symmetric. In particular, you need to make sure that the presence of outliers does not distort the results.

What does y-intercept mean in linear regression?

The y-intercept is the place where the regression line y = mx + b crosses the y-axis (where x = 0), and is denoted by b. Sometimes the y-intercept can be interpreted in a meaningful way, and sometimes not. This uncertainty differs from slope, which is always interpretable.

What is a best linear unbiased estimator Blue )? Explain?

Best Linear Unbiased Estimator (BLUE) of t′β: The best linear unbiased estimator of t′β is (i) a linear function of the observed vector Y, that is, a function of the form a′Y + a0 where a is an n × 1 vector of constants and a0 is a scalar and. (ii) the unbiased estimator of t′β with the smallest variance.

What assumptions must be met for OLS to be blue?

The Use of OLS Assumptions If the OLS assumptions 1 to 5 hold, then according to Gauss-Markov Theorem, OLS estimator is Best Linear Unbiased Estimator (BLUE). These are desirable properties of OLS estimators and require separate discussion in detail.