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We can't include it in the regression as is, but you could create a dummy variable for all but one value of kettlehole and put those in your regression to effectively obtain the desired relationship within … In so doing, you've effectively run a Fixed Effects Regression. Entity fixed effects can control for variables that are constant over time but differ across entities (i.e. kettleholes). …

.)=0 it means that you are assuming that the true population regression is: which, when y is binary, is equivalent to assuming that: which, in words, means you are assuming that the P(y=1|x) is a …

It is a logistic regression. All coefficients are statistically significant at the 5% level. I calculated the VIF for the set of predictors in the multiple regression model. …

The Penn State STAT200 course states that assuming that the errors are independent is equivalent to assuming that residuals $\hat{\epsilon}$ and predicted values $\hat{y}$ are not related, which I tak …

In this article Chen & Pearl make the following 2 statements: "Identification techniques are available for models in which X is far from satisfying $E(u_i|X_i)=0$" in response to Stock & Watson's sen …

Having consulted a number of sources, I still can't find a complete proof that Regression Sum of Squares ($SS_{regression}$) and ($SS_{residual}$) are independent random variables. …

Then you build a sample using this DGP and run a regression on this sample (can be linear regression or Huber or any other type). … This clarification of how regression simulation works should answer all your questions. …

Keeping in mind the widespread misunderstanding that linear regression can only model linear relationships/missing the fact that linear regression refers to linearity in parameters and can accommodate … That is, (3.36) is simply a multiple linear regression model with $X_1=horsepower$ and $X_2=horsepower^2$. …

Second, run the regression, as usual. Now you know what to condition on. The coefficients you'll get would be the direct effects, as mapped out in your causal map. …

When the range of the residuals - as you saw it, or to use another measure of spread, the variance of residuals - changes over time, this is a symptom that goes by the name of heteroskedasticity, from …

No. If your regressors are perfectly collinear, OLS estimation is impossible. In contrast, the more multicollinear (high collinearity but not perfect) your regressors the more inefficient your estimat …

In the section on Ridge Regression (source: Elements of Statistical Learning by Hastie, Tibshirani, Friedman) : When there are many correlated variables in a linear regression model, their coefficients … We will now look at Ridge Regression, Lasso Regression, and Elastic Net, which implement three different ways to constrain the weights. …

The next step is to regress one series on the other one, and save the residuals from this regression. This residual is itself a time series. … stationary (use the same tests as you did above), then you conclude that the 2 variables are cointegrated, with the cointegration coefficient estimated to be the beta hat on the independent variable in the regression …

Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression? …

interesting, controlling for a variable by its inclusion in a regression is insightful but not a very intuitive answer. … Edit: To put some numbers behind it, with the completely made up data below, I obtain the following regression results: On the left are the results of the simple regression of weight on education (after …