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You have the deciles of you distribution of interest, don't you? Use those! Of course you may compute any kind of strange measure on them, even an approximation of skewness using means of decile bins, …

Yes, it is possible to do regression on your data. … It's very important that you are aware of the shortcomings of doing regression on aggregated data. …

I can't comment, so I'll answer: in ordinary linear regression the response variable need not to be continuous, your assumption is not: $$ y = β_0 + β_1x $$ but is: $$ E[y] = β_0 + β_1x. $$ Ordinary … linear regression derives from the minimization of the squared residuals, which is a method believed to be appropriate for continuous and discrete variables (see Gauss-Markof theorem). …

If the model manages to set apart successes and unsuccesses completely, AUC will be 1. you have very little data and many predictors, and some of them are very effective in predicting outcome, so no s …

I don't think it is the same. If you say that $\hat \beta$ is statistically significant, that's a short way to say that it's significantly different from 0, and "different from 0" is not the same as " …

@PeterFlom answer is very good and explains very well the general phenomenon known as Simpson's paradox. However, he forgot to mention one important thing, that is actually fundamental to our job: to …

No, actually it's very easy. you should compare the formula of $s^2$ (only $s$ is given in your exercize) to the one of SSE. The solution is: In your text it is reported rounded to unit.

Usual approach in statistics is to consider the errors $\epsilon_i= y_i-E[y_i|x]$ homoscedastic with variance $\sigma^2$. This assumption, joint with independence one, results in least squares as the …

Fitting the model on the residuals from your control variables is the same as fitting the model all together after orthogonalizing the study variables with respect to controls (it's the same model, bu …

Why is this If you are not good with thinking of $SS_Y$ as a pie being divided among explanatory variables, you must know that this happens because least squares regression maps a target variable $Y$ to …

The exponential curve model you described can be achieved tranforming x: x1 = exp(-x) mod = lm(y~x1) This method is the most reasonable if you expect errors around the model underlying data to be …

In linear model, $\epsilon$ always results to be orthogonal to de predictors, then $Cov(y, \epsilon) = Var(\epsilon)$. Their correlation depends on the proportion of y which is explained by the model, …

This always happens when logistic regression is used in a deterministic setting and no misclassifications happen. …

So you have set the rest of the model and you only want to test $x_2$ effect each time? Also, you are interested in an inferential statistical approach (which is, using hypothesis testing)? If so, th …

One other example of a distribution used in bayesian statistics even if data is not really believed to follow it, is asymmetric Laplace, for quantile regression. …