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Results for ols assumptions
Search options not deleted score>= 50
55 votes
3 answers
16k views

Why do we care so much about normally distributed error terms (and homoskedasticity) in line...

I suppose I get frustrated every time I hear someone say that non-normality of residuals and /or heteroskedasticity violates OLS assumptions. … To estimate parameters in an OLS model neither of these assumptions are necessary by the Gauss-Markov theorem. …
Zachary Blumenfeld's user avatar
59 votes
5 answers
108k views

Regression when the OLS residuals are not normally distributed

Here we have several thousand observations and clearly we must reject the normally-distributed-residuals assumption. … What is the most efficient way to model data violating the OLS normality of residuals assumption? Or at least what should be the first step to develop a sound regression analysis methodology? …
Robert Kubrick's user avatar
56 votes
4 answers
80k views

If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equi...

That's why there's an assumption of normality in the DATA. ANOVA is equivalent to linear regression with dummy variables, and uses sums of squares, just like OLS. … That's why there's an assumption of normality of RESIDUALS. It's taken me several years, but I think I've finally grasped those basic facts. …
Chris Beeley's user avatar
  • 5,881
71 votes
5 answers
17k views

What problem do shrinkage methods solve?

But, OLS typically provides unbiased and consistent estimates. … or consistent estimate of something even if these assumptions aren't true. …
Charlie's user avatar
  • 14.3k
52 votes
Accepted

Assumptions of linear models and what to do if the residuals are not normally distributed

Answer 2: You are actually asking about two separate assumptions of ordinary least squares (OLS) regression: One is the assumption of linearity. … Creatively violating OLS assumptions (with the appropriate methods) allows us to ask and answer more interesting questions. …
Alexis's user avatar
  • 30.7k
113 votes
6 answers
51k views

On the importance of the i.i.d. assumption in statistical learning

the i.i.d. assumption and obtain robust results. … regression weights but to adapt the finite-sample behaviour of the OLS estimator to account for the violation of the Gauss-Markov assumptions). …
Quantuple's user avatar
  • 1,566
135 votes
4 answers
142k views

When to use gamma GLMs?

Naively, it seems like the gamma GLM is a relatively assumption-light means of modeling non-negative data, given gamma's flexibility. … Beyond communication to people who "just run OLS"? …
generic_user's user avatar
  • 13.7k
60 votes

How does linear regression use the normal distribution?

Linear regression by itself does not need the normal (gaussian) assumption, the estimators can be calculated (by linear least squares) without any need of such assumption, and makes perfect sense without … EDIT This answer led to a large discussion-in-comments, which again led to my new question: Linear regression: any non-normal distribution giving identity of OLS and MLE? …
kjetil b halvorsen's user avatar
52 votes
Accepted

Theory behind partial least squares regression

Note that: If all PLS1 components are used, then PLS will be equivalent to OLS. … Thus PCR and PLS make the assumption that the truth is likely to have particular preferential alignments with the high spread directions of the predictor-variable (sample) distribution. …
amoeba's user avatar
  • 107k
158 votes

Interpreting plot.lm()

Interpreting [1] is discussed on CV here: Interpreting residuals vs. fitted plot for verifying the assumptions of a linear model. … I explained the assumption of homoscedasticity and the plots that can help you assess it (including scale-location plots [2]) on CV here: What does having constant variance in a linear regression model …
gung - Reinstate Monica's user avatar
87 votes

What is difference-in-differences?

If there is a correlation between the fixed effects and $D_{it}$ then estimating this regression via OLS will be biased given that the fixed effects are not controlled for. … The most important assumption in DiD is the parallel trends assumption (see the figure above). Never trust a study that does not graphically show these trends! …
Andy's user avatar
  • 19.3k
99 votes

What is the difference between estimation and prediction?

OLS prediction consists of observing a new value $Z = Y(x)$ of the dependent variable associated with some value $x$ of the independent variable. … {\alpha}$ and $\hat{\beta}$ are uncertain (because they depend mathematically on the random values $(y_i)$), that $\sigma$ is not known for certain (and therefore has to be estimated), as well as the assumption
whuber's user avatar
  • 334k
85 votes

What do "endogeneity" and "exogeneity" mean substantively?

If you want to think about it that way, using OLS to estimate it amounts to assuming that: $X$ causes $Y$ $\epsilon$ causes $Y$ $\epsilon$ does not cause $X$ $Y$ does not cause $X$ Nothing which causes … Instrumental variables is a way of correcting for the fact that you got the causation wrong (by making another, different, causal assumption). …
Bill's user avatar
  • 8,004
51 votes
Accepted

A more definitive discussion of variable selection

We rarely adjust for anything in such trials per the randomization assumption, with few exceptions (Senn, 2004). … The interpretation of the coefficient from an OLS model Y~X is straightforward: it is a slope, an expected difference in Y comparing groups differing by 1 unit in X. …
AdamO's user avatar
  • 64.8k
114 votes
Accepted

What are the major philosophical, methodological, and terminological differences between eco...

More generally, economists want to make as few assumptions as possible about their models, so as to make sure that their findings do not hinge on something as ridiculous as multivariate normality. … That's why economists run their regression with "robust" standard errors, and statisticians, with the default OLS $s^2 (X'X)^{-1}$ standard errors. …
StasK's user avatar
  • 32.3k

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