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11 votes
Accepted

Prediction bands for weighted linear regression

Let's assume the data come from the following heteroskedastic normal simple linear regression model, wherein the unit weights $w_i>0$ are known (even for future observations): $$ y_i = \alpha+\...
Johan de Aguas's user avatar
7 votes

Intercept significant, but confidence intervals around its standardized β include 0

This is unsurprising: The intercept $p$-value tests whether the outcome differs significantly from $0$ when all explanatory variables equal $0$. Using scale on ...
Frans Rodenburg's user avatar
7 votes

confidence interval and rejection

Yes, you should consider providing both the p-value for your chosen null and a confidence interval. The mathematical link between hypothesis testing and confidence intervals should not drive your ...
Graham Bornholt's user avatar
6 votes

confidence intervals for proportions containing a theoretically impossible value (zero)

Stepping back from the complex discussion of statistical frameworks, the way I see your problem is: you want an interval-estimate of some probability, ie an interval estimate of some parameter ...
Guillaume Dehaene's user avatar
6 votes

confidence interval and rejection

YES I would consider this a best-practice. While you are correct to recognize the relationship between hypothesis testing and confidence intervals, the confidence interval gives a range of "...
Dave's user avatar
  • 64.8k
4 votes

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

The misinterpretation of confidence intervals is related to what Blitzstein and Hwang (in their probability textbook) call "sympathetic magic". Sympathetic magic is an anthropology term for ...
Abhishek Divekar's user avatar
4 votes
Accepted

Predicting cost for several options and then choosing the cheapest option

So I am assuming that you are interested in total( ie sum) cost saving . this can be analysed as the average over orders of (cheapest predicted cost - actual cost) saving = (actual cost - model cost )...
seanv507's user avatar
  • 7,268
4 votes

confidence intervals for proportions containing a theoretically impossible value (zero)

The obvious solution when you have prior information is to take a Bayesian approach. Perhaps your prior knowledge can be represented via a beta-distribution, in which case things are super-simple from ...
Björn's user avatar
  • 33.5k
4 votes
Accepted

confidence intervals for proportions containing a theoretically impossible value (zero)

It is not a problem. Confidence intervals display the range of values of estimates/hypotheses that are supported by the data. Or alternatively the values outside the interval are values that are ...
Sextus Empiricus's user avatar
3 votes
Accepted

How to generate 95% prediction interval around predictions from ML model?

THIS SEEMS TO BE AN OPEN PROBLEM. Let's look at some possible solutions and their drawbacks. First, you propose this Yhat +- 1.96 * std(residuals). Let's put that ...
Dave's user avatar
  • 64.8k
3 votes

Confidence intervals vs. standard deviation

My answer focuses on the distinction between estimation and prediction. With the interval (mean) +/- 2*(std deviation), you predict that about 95% of the data will fall in this interval (with the ...
Russ Lenth's user avatar
  • 20.7k
2 votes

Why is AIC not reported with a confidence interval?

While I can sympathize with the wish for an uncertainty measure for AIC, the larger issue is that AIC like model likelihood ratio $\chi^2$ is proportional to the sample size. So as $N$ gets larger, ...
Frank Harrell's user avatar
2 votes
Accepted

Worst-case analysis using confidence intervals

Your intuition that you are double counting the uncertainty is indeed correct. What you are looking for is a Tolerance Interval, that is a confidence interval for a proportion. Let's assume that your ...
jginestet's user avatar
  • 1,782
1 vote

How to generate 95% prediction interval around predictions from ML model?

Simple linear regression is parametric, since you model $Y = \beta X + \epsilon$ with the assumption of $\epsilon \sim N(0, \sigma^2)$. The prediction interval for a new $\hat y_h$ is bigger than the ...
qwr's user avatar
  • 548
1 vote

Confidence intervals when using stratified proportionate random sampling

With proportionate stratification, if you ignore the strata you will still get an unbiased estimate of $p$, but your confidence interval will (in general) be too wide. For binary data it's not likely ...
Thomas Lumley's user avatar
1 vote

Are all values within a 95% confidence interval equally likely?

Although the phrase “all values within the CI equally likely” is unclear in its meaning, it would seem to imply that our confidences in equal-length segments of the CI should be the same irrespective ...
Graham Bornholt's user avatar

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