4

Usually predictive power refers to the model, rather than the data. I've occasionally seen some people use it in the way that the author of your book uses it (see this for example). In the context of your book, yes, predictive power refers to whether input can be mapped to target output $X\rightarrow Y$. We can infer a dataset's "predictive power" ...


3

The term "linearity" is context-dependent, so a linear regression model is not necessarily the same as a linear function. A linear function is classified as such via the superposition principle, requiring both additivity and homogenity. We can generalize linear maps with to multivariate functions simply: Additivity: $f(\vec{x}_1+\vec{x}_2)=f(\vec{...


3

I agree that if scaling is used on the training data, it should also be used on the test data. However, from what I see in the pcr documentation there is not scale option in the function. This seems to be confirmed by running the code from the example in the documentation: https://www.rdocumentation.org/packages/analogue/versions/0.17-5/topics/pcr > ...


2

Decision Tree Regressor won't predict values outside the range of values they are given in the train set. If your extreme values are -4 and +10 the predicted values will be between -4 and +10. The reason for that is that a decision tree splits the training data in groups. The prediction associated with a node is then the mean value of the training data of ...


2

In many cases, at the end of a neural network you could find a Softmax layer, which outputs probabilities, so they add up to 1. It seems exactly what you're looking for. Please find more information about softmax function here or here. Hope it helps.


1

I support your "proof is in the pudding" sentiment. Some of those hyperparameters are not that extreme, in my experience. Boosted trees very often perform best with weak individual learners; your max_depth is right in line with what I'm used to seeing as best. The score regularization penalties (alpha, lambda) don't play as important a role in my ...


1

It depends of your point of view: when one speaks about linear you usually refer the variables linked by the linear relationship. The model with x as input and Y as target is not linear however the model with input $\log(x)$ and target $\log(Y)$ is linear: $$ \tilde{Y} = \tilde{\beta} + \beta_1\tilde{x} + \tilde{e} $$ with $\tilde{Y}=\log(Y)$, $\tilde{\...


1

There is regression by neural networks. For example, have a look at this analysis (Deep Regression), RBF neural networks, and General regression neural networks. Also, linear regression can be implemented using a neural network. If using neural networks for interpolation, this may work very good. However, if regression is used to extrapolate, results may be ...


1

You can use a Sigmoid function on the Force values(Scaled to [0-10] based on a max value) The Threshold should become 5 after scaling. def predict_proba(y_pred): y_pred = y_pred*10/100000 # scaled to [0-10] thresold = 5 proba = np.exp(y_pred - threshold)/(1 + np.exp(y_pred - threshold)) return proba predict_proba(100000), predict_proba(...


1

The regression tasks are not very different from classification and the behavior you faced with is probably due to a bug in the code. If your training set is small and the network is comparably large, it should overfit on it (correlation with inputs doesn't matter, there was a paper https://arxiv.org/pdf/1611.03530.pdf that shows you can randomly shuffle ...


1

The general answer is how the model will be used deal. Either way may be optimal for the case. For example - If the model groups applicants into good credit risk and bad credit risk, that might be fine to say model score > x = good risk and model score <= x = bad risk. But maybe there will be differential action based on the model score - like giving a ...


1

Rather than asking about the predictive power of a dataset, I think it's intuitive to ask about the predictive power of a model. My reasoning is as follows; A dataset can be univariate, bivariate or multivariate types. The dataset can contain only numerical features or categorical features or both. Suppose there is a univariate dataset with a negative skewed ...


1

ANOVA is a linear regression...a regression on categorical variables. Regressions can have any mix of continuous and categorical variables. Some, like ANOVA and ANCOVA, have special names that you may want to use when you're communicating with people who have less training in statistics and don't know how to unify them with linear regression.


1

I think your input features are lacking. Firstly, The budget allocation is not simply done based on the previous year turnover and size of the company, there are myriad other factors involved which directly correlate towards a budget allocated to any department. Secondly where is the relation of profit vs budget allocation? For maximizing profit according to ...


1

Please bear in mind that excel does not handle missing values well. If your data column has some blank cells in it, if you filter them out, the r2 can change (subtly). Excel is fine for an overview but use a more robust method in case you want to get formal figures for publication.


1

you can print the coefficients with: coef(fm$finalModel,model No. e.g.1)


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