27 questions linked to/from Linear regression prediction interval
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### Can I calculate prediction intervals in scikit-learn for a linear model without bootstrapping? [duplicate]

I'd like to produce 95% prediction intervals along with predictions from my model. I'm using a moderately large dataset and making thousands of predictions, so I was wondering if there was some way ...
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### Variance of a predicted $y$ when $x_0$ is given? [duplicate]

I cannot figure out why the variance of a prediction of $y$, when given $x_0$ is $$\sigma^2\bigg(1+\frac 1 n +\frac{(x_0-\bar x)^2}{Sxx}\bigg)$$ Isn't this the variance of a prediction error? ...
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### How to obtain the equation of a predictive interval around the regression line in R? [duplicate]

I have a some data set on which I fit a linear regression model using the lm function in R. I can also visually obtain the prediction Interval around that regression line using predict. My question is ...
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### What is the difference between estimation and prediction?

For example, I have historical loss data and I am calculating extreme quantiles (Value-at-Risk or Probable Maximum Loss). The results obtained is for estimating the loss or predicting them? Where can ...
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### Understanding shape and calculation of confidence bands in linear regression

I am trying to understand the origin of the curved shaped of confidence bands associated with an OLS linear regression and how it relates to the confidence intervals of the regression parameters (...
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### Obtaining a formula for prediction limits in a linear model (i.e.: prediction intervals)

Let's take the following example: set.seed(342) x1 <- runif(100) x2 <- runif(100) y <- x1+x2 + 2*x1*x2 + rnorm(100) fit <- lm(y~x1*x2) This creates a ...
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### Why does the standard error of the intercept increase the further $\bar x$ is from 0?

The standard error of the intercept term ($\hat{\beta}_0$) in $y=\beta_1x+\beta_0+\varepsilon$ is given by SE(\hat{\beta}_0)^2 = \sigma^2\left[\frac{1}{n}+\frac{\bar{x}^2}{\sum_{i=1}^n(x_i-\bar{x})^...
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### Prediction and Tolerance Intervals

I have a couple of questions for prediction and tolerance intervals. Let's agree on the definition of the tolerance intervals first: We are given a confidence level, say 90%, the percentage of the ...
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### Gaussian process prediction interval

How can the prediction interval of a Gaussian process be evaluated? I don't know how to estimate this interval though I can find a 95 % confidence interval for the mean line.