Linked Questions

0
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0answers
9 views

extrapolation from interpolating polynomial [duplicate]

given data points (1,2), (2,4), and (3,6). using lagrange interpolation, I get the polynomial as f(x) = 2x. Now can I use this polynomial to find f (18) [note that 18 lies outside the range of x's of ...
84
votes
14answers
62k views

What is the meaning of "All models are wrong, but some are useful"

"Essentially, all models are wrong, but some are useful." --- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339. What ...
47
votes
6answers
49k views

Best method for short time-series

I have a question related to modeling short time-series. It is not a question if to model them, but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$...
47
votes
4answers
95k views

Difference between forecast and prediction?

I was wondering what difference and relation are between forecast and prediction? Especially in time series and regression? For example, am I correct that: In time series, forecasting seems to mean ...
33
votes
5answers
9k views

Extrapolation v. Interpolation

What is the difference between extrapolation and interpolation, and what is the most precise way of using these terms? For example, I have seen a statement in a paper using interpolation as: "The ...
40
votes
3answers
6k views

Why law of large numbers does not apply in the case of Apple share price?

Here is the article in NY times called "Apple confronts the law of large numbers". It tries to explain Apple share price rise using law of large numbers. What statistical (or mathematical) errors does ...
36
votes
3answers
12k views

Why is the mean function in Gaussian Process uninteresting?

I have just started reading about GPs and analogous to the regular Gaussian distribution it is characterized by a mean function and the covariance function or the kernel. I was at a talk and the ...
2
votes
3answers
18k views

Predicting future values with a regression model

I have a set of predictor variables and a target variable. I am really confused with regards to what method to use for forecasting the target variable. For example, my data set has monthly customer ...
11
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2answers
739 views

How to make predictions with non-parametric regression?

Let's say I have a dataset to which I have estimated a relationship using non-parametric regression, specifically Kernel (obviously in this hypothetical example it's probably overfit slightly). The ...
2
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3answers
8k views

What are the theoretical reasons for why extrapolation "less reliable" than interpolation?

Extrapolation is in general "unreliable". (See "What is wrong with extrapolation?") But it is also commonly said that extrapolation is "less reliable" than interpolation. But why should we ...
1
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1answer
7k views

Difference between non-linear curve fitting and interpolation

I understand the difference between linear curve fitting and interpolation. In interpolation, the targeted function should pass through all given data points whereas in linear curve fitting we find ...
21
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1answer
1k views

Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max)

EDIT: As this question has been inflated, a summary: finding different meaningful and interpretable datasets with the same mixed statistics (mean, median, midrange and their associated dispersions, ...
6
votes
2answers
2k views

Which gamma regression model to use for extrapolation?

I'm looking for a regression model which would satify these requirements: My target variable follows the exponential distribution, so to my understanding I should use gamma loss function. I have ...
8
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1answer
2k views

Difference between extrapolation and interpolation in higher dimensions

The most common distinction I've seen made between interpolation and extrapolation is that interpolation is within the range of the data, whereas extrapolation is outside the range of the data. This ...
3
votes
1answer
840 views

Is the correlation coefficient useful for measuring linearity with only 10 observations?

I need to measure the linearity between two variables but I only have 10 samples. Is it relevant to use correlation in this case? If not, what else could I use?

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