 ## Top new questions this week:

### Interpreting log-log regression with log(1+x) as independent variable

Is interpreting log-log regression with log(1+x) as independent variable the same as having log(x) as independent variable? 1% increase in x results in beta% change in y? What is x has both negative ...

regression data-transformation interpretation regression-coefficients logarithm asked by user359025 Score of 9 answered by whuber Score of 14

### Objective criteria for assumption violations that do not utilize p-values?

Suppose we have a standard regression model and want to identify whether we have violated the assumptions of the model. Traditionally, we might utilize a significance test to determine whether (for ...

hypothesis-testing references linear-model assumptions diagnostic asked by dfife Score of 8 answered by Christian Hennig Score of 9

### Is the sum of two singular covariance matrices also singular?

I have two sample covariance matrices, computed from $n$ samples, less than $p$ variables: they are singular then. I know that the sum of two covariance matrices is also a covariance matrix. My ...

covariance-matrix sum singular asked by Larel5000 Score of 8 answered by Sextus Empiricus Score of 8

### Finding the MVUE of the center of a circle of unknown location

Is there a known analytic solution for finding the minimum variance unbiased estimator of a disk of an unknown location given that a sample of $n$ points was drawn uniformly and randomly from the disk ...

self-study uniform-distribution unbiased-estimator asked by Dave Harris Score of 6 answered by Xi'an Score of 3

### Linear regression's (OLS) coefficient interpretation with heteroscedasticity

To use OLS for inference, is it necessary in all cases that the premise of homoscedasticity is met? I need to check the influence of some features (eg age, income...) on a variable y (whether or not I ...

regression least-squares interpretation regression-coefficients heteroscedasticity asked by Alysson Score of 5 answered by Noah Score of 11

### How to properly explain a delta between 0.10 to 0.05 in proportions

Assuming I have proportions for clicks to impressions of 0.10 for p1 and 0.05 for p2. This is equivalent to 10% and 5% click through rate. One way is to say that p1 is 5% higher but can we even say ...

proportion differences asked by Roger Steinberg Score of 4 answered by Andrew A Score of 10

### Subclassification on a propensity and prognostic score grid with k × k subclasses, using R MatchIt

I would like to perform a joint subclassification of some data on the propensity and prognostic scores as described in this paper "On the joint use of propensity and prognostic scores in ...

r propensity-scores stratification asked by John Preston Score of 4 answered by Noah Score of 3

## Greatest hits from previous weeks:

### Narrow confidence interval -- higher accuracy?

I have two questions about confidence intervals: Apparently a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our ...

confidence-interval asked by upabove Score of 19 answered by John Score of 19

### When (and why) should you take the log of a distribution (of numbers)?

Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company... Now someone (or some formula) comes along and says "let's take/use ...

distributions data-transformation logarithm asked by PhD Score of 224 answered by IrishStat Score of 120

### Examples for teaching: Correlation does not mean causation

There is an old saying: "Correlation does not mean causation". When I teach, I tend to use the following standard examples to illustrate this point: number of storks and birth rate in Denmark; number ...

correlation teaching asked by csgillespie Score of 83 answered by Paul Score of 43

### How does Keras 'Embedding' layer work?

Need to understand the working of 'Embedding' layer in Keras library. I execute the following code in Python ...

text-mining word-embeddings keras asked by prashanth Score of 174 answered by Daniel López Score of 226

### Pearson's or Spearman's correlation with non-normal data

I get this question frequently enough in my statistics consulting work, that I thought I'd post it here. I have an answer, which is posted below, but I was keen to hear what others have to say. ...

correlation normality-assumption pearson-r spearman-rho asked by Jeromy Anglim Score of 144

### What does the hidden layer in a neural network compute?

I'm sure many people will respond with links to 'let me google that for you', so I want to say that I've tried to figure this out so please forgive my lack of understanding here, but I cannot figure ...

machine-learning neural-networks nonlinear-regression asked by FAtBalloon Score of 202 answered by David J. Harris Score of 248

### What does AUC stand for and what is it?

Searched high and low and have not been able to find out what AUC, as in related to prediction, stands for or means.

classification prediction roc auc abbreviation asked by josh Score of 275 answered by Franck Dernoncourt Score of 361

## Can you answer these questions?

### Difference in clustering standard errors of coeftest and sum

Suppose I have a panel data and would like to look at time fixed effects, i.e. effects constant across "state" but varying over time. My understanding was always, that the estimated ...

panel-data clustered-standard-errors asked by math Score of 1

### forward stepwise AIC approach

I am learning about performing stepwise model selection by AIC and I have 2 questions here: 1.Regarding to stepwise AIC, what is contribution (effectiveness) of the number of parameters in the model ...

feature-selection aic stepwise-regression asked by tcxrp Score of 1

### No gradient for one parameter on the first iteration of gradient descent

Say we have a dataset $D$ of 2-tuples $(x, y)$ where $y$ is the target variable and a function $f_\theta$:  D = \{(1, 3), (2, 5), (3, 8), (4, 6), (5, 9)\},\quad f_\theta(x) = \theta_0 + \theta_1 x. \$... asked by Saucy Goat Score of 1 answered by shimao Score of 0 