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# Tag Info

## Hot answers tagged fitting

24 votes
Accepted

### What does interpolating the training set actually mean?

Your question already got two nice answers, but I feel that some more context is needed. First, we are talking here about overparametrized models and the double descent phenomenon. By overparametrized ...
• 140k
17 votes

### Why does linear regression use a cost function based on the vertical distance between the hypothesis and the input data point?

When you have noise in both the dependent variable (vertical errors) and the independent variable (horizontal errors), the least squares objective function can be modified to incorporate these ...
• 37.8k
14 votes
Accepted

### Why is the arithmetic mean smaller than the distribution mean in a log-normal distribution?

The two estimators you are comparing are the method of moments estimator (1.) and the MLE (2.), see here. Both are consistent (so for large $N$, they are in a certain sense likely to be close to the ...
• 34.3k
14 votes

### Confidence intervals around functions of estimated parameters

Usually we take normality assumption for linear regression models. That is, $y_i\sim N(\beta^Tx_i,\sigma^2)$. From this assumption we derive the asymptotic distribution of $\hat{\beta}$, which is also ...
• 4,017
13 votes
Accepted

### Algorithms for weighted maximum likelihood parameter estimation

There are a number of ways to handle importance weights. Note that "weights" as a general term can be ambiguous. R's glm method, for instance, takes a weight parameter that is interpreted differently. ...
• 1,614
13 votes

### What does interpolating the training set actually mean?

In layman's terms, an interpolator will literally 'join the dots'. Here's a simple graphical summary of what interpolation can do and why it can be awful. I'd like to stress that interpolation does ...
• 2,927
12 votes

### Understanding the Cullen and Frey plot

This plot used to be commonly called a Pearson plot (it also had several other names), though sometimes with skewness rather than its square being plotted. It was used long before Cullen and Frey ...
• 287k
12 votes

### What I should do if no distribution fits my dataset?

If you have 26K data, any test on a given distribution will fail. Because for that much data, the testing can detect tiny difference and report it is not coming from that distribution. I would ...
• 37.2k
12 votes
Accepted

### Confidence intervals around functions of estimated parameters

Two common approaches for this problem are to calculate the non-linear combination of the coefficients directly from the regression or to bootstrap it. The variance in the former is based on the "...
• 37.8k
12 votes
Accepted

### What is the meaning of "loc" and "scale" for the distributions in scipy.stats?

Background The SciPy distribution objects are, by default, the standardized version of a distribution. In practice, this means that some "special" location occurs at $x=0$, while something ...
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10 votes
Accepted

### Discrete probability distribution with two 'tails'

There's an infinite number of such distributions -- one need merely a way to get a probability for each value of $i$ and one has just such a distribution. It's a simple matter to spend a leisurely ...
• 287k
10 votes

### Why does linear regression use a cost function based on the vertical distance between the hypothesis and the input data point?

One reason is that $$\sum_{i=1}^N(y_i-h_\theta(x_i))^2$$ is relatively easy to compute and optimize, while the proposed cost $$\sum_{i=1}^N \min_{x,y}\big[(y_i-h_\theta(x))^2+(x_i-x)^2\big]$$ has a ...
• 468
10 votes
Accepted

### Formal definition of the qqline used in a Q-Q plot

Sort of "both" - the line depends both on the observed quantiles (which define the y-axis of the QQ plot) and the expected/theoretical/reference quantiles (which the define the x-axis). The ...
• 45.1k
10 votes
Accepted

### How can I fit a spline to data that contains values and 1st/2nd derivatives?

We will describe how a spline can be used through Kalman Filtering (KF) techniques in relation with a State-Space Model (SSM). The fact that some spline models can be represented by SSM and computed ...
• 5,636
10 votes
Accepted

### How does logistic growth rate coincide with the slope of the line in the exponential phase of the growth?

Let's do the calculations to see what the answers are. By changing the units of measurement of $x$ to the origin $x_0$ we may assume $x_0=0$ (to simplify the work and the notation) and--therefore--the ...
• 330k
10 votes

• 330k
8 votes
Accepted

• 3,987
7 votes

### How to choose and perform a goodness-of-fit test?

Great question! (Almost a professional statistician here!) Let's see if I can try to answer your question. Whuber gave a comment on what the typical strategy that someone might follow. I'll try to ...
7 votes

### What does interpolating the training set actually mean?

Apart from literal meaning of interpolation, this is related to something called deep learning models totally memorize the training data. Hence, both ...
• 2,590

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