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3

No, because variables can be correlated. For an exemple you can take a degenerate problem where you have the same variable twice. Their IV will be the same by construction, however their coefficient could vary wildly as long as their sum is constant and equal to the coefficient you would get with one variable. So even with high IV you can get pretty much ...


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Two things: 1) You should not assign a specific $i$ value to a regression coefficient. The same estimated coefficient applies to all $i$'s, so you should write it as $\beta_1$, not $\beta_i$. 2) An easier to read interpretation would be: "If a firm's cost increases by 1 unit between two consecutive periods, the firm's revenue is expected to increase by $\...


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If I understand correctly, you are interested in estimating some overall population effect. Instead of first doing a regression and then trying to do subsequent weighted tests, there is a more efficient way to use your data to achieve your objective. A mixed-model (a.k.a. hierarchical or mixed-effects model) allows you to estimate your overall population ...


2

I struggled with this same problem--decomposing variance in high-dimensional prediction problems without limiting myself to fitting many, many linear regression models--and came up with the following solution: Shapley Decomposition of R-Squared in Machine Learning Models (with an R implementation). I would say that the trick in an applied setting is to ...


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If your variables measure different things on different scales (e.g., age of a person and weight loss/gain after treatment), you should standardize the data. If your variables measure similar things on the same scale (e.g., number of bugs on 10 different plots in some field), you might not need to standardize. But this case happens rarely. In any case, ...


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I may try to loosely help you to formalize these ideas by one example. Suppose you want to model monthly sales as function of two guys: time measured in months passed month name First, without month name. You model Y (sales volume) ~ time + some positive number (+ error). It can be that the sales grow steadily for 5 years, and you beta coefficient for ...


1

The "base" level (often called the 'reference level') should not have been left out of the model. It is represented by the intercept. The other levels are typically specified in your output, but those coefficients are not actually the values for those levels, instead they are the differences between the values for the indicated level and the base level. ...


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I think OP may be more concerned with an intuitive understanding of a standard error than of its calculation. Consider a population. In the population, there is a population slope $\beta_1$ and a population intercept $\beta_0$ that govern the relationship between $X$ and $Y$. If you draw a sample from that population, using the formulas described in @...


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Both models you mention fit into the framework of the varying coefficient models described originally by Hastie and Tibshirani (1993). From a functional data perspective, the second model you reference is called a functional current regression model. The first model is just a special case of the concurrent model where the coefficient functions are constant. ...


0

To add to the other answer, we have $P(Y=1|x_1,..,x_p)=sigmoid(b_0+b_1x_1+...+beta_px_p).$ the inverse of sigmoid is log odds (aka logit). Note that $$log(odds(Y=1))=b_0+b_1x_1+...+b_px_p$$ and hence for coefficient $b_i$ you have that the log odds changes by $b_i$ With an increase in $x_i$ of one unit holding all other variables constant (which is only ...


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If you scale each feature to have the same standard deviation (i.e. divide each column of the model matrix by its standard deviation), then the magnitude (absolute value) of the coefficients is a direct measure of the importance of the corresponding features. See Schielzeth 2010 Methods in Ecology and Evolution "Simple means to improve the interpretability ...


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