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Assumptions of linear models and what to do if the residuals are not ...
Check different kind of models. Another model might be better to explain your data (for example, nonlinear regression, etc). You would still have to check that the assumptions of this "new model" are not violated. Your data may not contain enough covariates (dependent variables) to explain the response (outcome).
Linear regression what does the F statistic, R squared and residual ...
The Fstatistic is the division of the model mean square and the residual mean square. Software like Stata, after fitting a regression model, also provide the pvalue associated with the Fstatistic. This allows you to test the null hypothesis that your model's coefficients are zero.
What to do when a linear regression gives negative estimates which are ...
$\begingroup$ Your model is misspecified; you need a different kind of model. If your data cannot go below 0, and your model can, your model does not reflect the reality of your data. The difference may not be a big enough deal to worry about in some context, but it sounds like that isn't the case here. $\endgroup$ –
What happens when I include a squared variable in my regression ...
Well, first of, the dummy variable is interpreted as a change in intercept. That is, your coefficient β3 β 3 gives you the difference in the intercept when D = 1 D = 1, i.e. when D = 1 D = 1, the intercept is β0 +β3 β 0 + β 3. That interpretation doesn't change when adding the squared x1 x 1. Now, the point of adding a squared to the ...
Linear regression, conditional expectations and expected values
It is my understanding that the linear regression model. is predicted via a conditional expectation E(YX)=b+Xb+e. The fundamental equation of a simple linear regression analysis is: E(Y  X) = β0 + β1X, This equation meaning is that the average value of Y is linear on the values of X. One can also notice that the expected value is also ...
How are the standard errors of coefficients calculated in a regression?
The linear model is written as $$ \left \begin{array}{l} \mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{\epsilon} \\ \mathbf{\epsilon} \sim N(0, \sigma^2 \mathbf{I}), \end{array} \right.$$ where $\mathbf{y}$ denotes the vector of responses, $\mathbf{\beta}$ is the vector of fixed effects parameters, $\mathbf{X}$ is the corresponding design ...
regression  What is the difference between deterministic and ...
with E(x) = αt E (x) = α t and Var(x) = tσ2 V a r (x) = t σ 2. So a simple linear model is regarded as a deterministic model while a AR (1) model is regarded as stocahstic model. According to a Youtube Video by Ben Lambert  Deterministic vs Stochastic, the reason of AR (1) to be called as stochastic model is because the variance of it ...
regression  What is wrong with extrapolation?  Cross Validated
A regression model is often used for extrapolation, i.e. predicting the response to an input which lies outside of the range of the values of the predictor variable used to fit the model. The danger associated with extrapolation is illustrated in the following figure.
What does having "constant variance" in a linear regression model mean?
The simple linear regression model is this: $$ Y=\beta_0+\beta_1X+\varepsilon \\ \text{where } \varepsilon\sim\mathcal N(0, \sigma^2_\varepsilon) $$ What's important to note here is that this model explicitly states once you've estimated the meaningful information in the data (that's the " $\beta_0+\beta_1X$ ") there is nothing left over but ...
How do I perform a regression on nonnormal data which remain non ...
Least squares regression is the BLUE estimator (Best Linear, Unbiased Estimator) regardless of the distributions. See the GaussMarkov Theorem (e.g. wikipedia) A normal distribution is only used to show that the estimator is also the maximum likelihood estimator.
