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### Why is a prediction interval wider than a confidence interval for values of the predictor? [duplicate]

I have this graph that depicts PI being larger than CI for values of 14.5 and 24 for the independent/predictor variable. CI take into account regression coefficients, which are estimates. The PI has ...
109 views

### What is the difference between model prediction and model estimation? [duplicate]

Could you please explain for me what's the difference between model prediction and model estimation ? What is the difference between a prediction interval and an estimation interval?
170k views

### Difference between confidence intervals and prediction intervals

For a prediction interval in linear regression you still use $\hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x$ to generate the interval. You also use this to generate a confidence interval of $E[Y|x_0]$....
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### Linear regression prediction interval

If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between ...
2k views

### Why do you have to provide a variogram model when you are kriging?

I am very new to spatial statistics and watching lots of tutorials, But I don't really get why you have to provide a variogram model when you krige. I am using the gstat package in R, and this is ...
1k views

### Can we make probabilistic statements with prediction intervals?

I've read through the many excellent discussions on the site regarding interpretation of confidence intervals and prediction intervals, but one concept is still a bit puzzling: Consider the OLS ...
316 views

### What is the relationship between minimizing prediction error versus parameter estimation error?

With the advent of statistical learning techniques, people are talking a lot about prediction error, while in classical statistics, one is focusing on parameter estimation error. What is the ...
781 views

### What is the objective of maximum likelihood estimation?

I was reading in "Using Maximum Likelihood Estimation" from "Econometrics for Dummies", and here's what the author had to say: "The objective of maximum likelihood (ML) estimation is to choose values ...
2k views

### Confidence interval vs. prediction interval misunderstanding

Problem I have a time series data set with about 50 observations. I'd like to compute an interval that may contain the next/future value in the time series (the 51st data point). I tried using a 90% ...
423 views

### Prediction interval for the predicted probability obtained using a logistic regression for new subject

I am trying to calculate the prediction interval for the predicted probability for a new subject using a logistic regression, and I wonder if we can use the same formulas that is used for linear ...
115 views

### Can someone explain to me the frequentist definition of inference by Efron and Hastie using a real example?

Problem Can someone help explain the concept of inference as explained by Bradeley Efron and Trevor Hastie in their book Computer Age Statistical Inference?In Chapter 2, beginning on page 13 they ...
146 views

### Comparing sample variances of the same population

If s1 is the variance of a small sample, and s2 is the variance of a larger sample from the same population. Is s1 an unbiased estimator for s2? I am thinking since a sample variance is an unbiased ...
34 views

### predict y variable that is only available as a sum by group

I would like to fit a model in order to predict a y variable, however in the training data the y variable is only available for groups of items (the x variables are available for each individual iteam)...
I'm trying to understand how a frequentist would approach statements like "having observed X, the probability of Y happening is Z". For concreteness, let's say we conducted $n_1$ identical, ...
Say we observe data $D$, which comes from a probability distribution $P[D|\theta]$, where $\theta$ are the unknown model parameters. Given this information, what is the probability distribution of the ...