prediction intervals and confidence intervals


i have really hard time understanding what prediction interval is and how is it different from confidence interval. Really appreciate if anyone could help clarifying it.

thanks in advance!

For all intents and purposes, they’re the same thing: an interval in which we expect a value to lie (with a given probability).

The technical difference is that we use prediction intervals for the dependent variable in a simple regression model, and the formula for the variance of the prediction interval is ugly.

I would be careful with this wording-- can you give an example of what you mean by it? A given confidence interval doesn’t have a probability associated with it (i.e. it doesn’t tell you how likely the interval is to contain the value; that would be a credible interval). The level of confidence refers to the methodology’s long-run performance.

I would say they’re identical in that they’re both confidence intervals (convention is to say prediction interval with one to avoid confusion due to a small difference), but they’re different in the parameter each attempts to pin down, and therefore, the variances (standard errors) used in the calculation are different.

Ok with all honesty, the test does not get into this detail. Don’t waste your time differentiating the two, if you just want to pass the test. Seriously.

Prediction interval is the interval in which the predicted value of a variable lie. In simple linear regression ,the y^ -predicted value also has a standard error as its an estimated value. Just remember that the regression equation used to estimate the Y^ values is also derived from estimated regression co-efficients( b0 - intercept term and bi-slope co-efficient)… The way these both terms have a standard error and hence confidence intervals, the same way predicted value Y^ can also have an interval. Concept is the same. Correct me if i m wrong.

Did you take the exams to have meaningless letters behind your name, or did you take the exams to actually learn something? While some of the discussion might be beyond the scope of the exam, it can’t hurt candidates to have a deeper understanding (especially if they ask about something). Afterall, most people “just want to pass” and most people end up retaking some part of the exam…

A prediction interval is an interval in which the actual, not predicted, value (for a single observation) is estimated to lie with a given level of confidence.

At a broad level, they’re identical, as they’re both confidence intervals. The calculations and parameters of interest are different between a confidence interval for a mean and a prediction interval for Y.

You can also use prediction intervals in multiple regression, but the formula is easier for them to show you in simple linear regression.

I don’t need to tell you the reason of why I took the test. Maybe I was just bored

But let’s face it, wIthin 99.99999% confidence interval (beyond the 6 sigma), people on AF just want to pass this test and get it over with. If you want to drill down the detail, perhaps grad school would be a better option.

I was just saying…to pass the test, you don’t need to differentiate the two. perhaps I should not have put “seriously” at the end. Not trying to start a keyboard war, but to help others save time for those financial accounting formula.

I most certainly didn’t imply that you need to tell me or anyone your reason…It was more of a rhetorical question. My participation was largely due to personal interest with full knowledge that it will not, in all foreseeable circumstances, help my career. My point in asking was to point out that some people do actually want to learn. Networking and relevant experience is probably a better way to improve your career than 3 exams (unless your employer pushes the exams).

It might be a reasonable assumption, but the OP knows his or her own goals and decided to ask the question anyway. The responses were geared towards a correct answer. I agree that grad school might be a good idea, depending on the circumstances.

I also didn’t have any intention to start anything but a discussion. Again, it comes back to the point that the OP asked for more detail. Telling someone they don’t need to know it (without providing any answers) doesn’t help the candidate learn. At the end of the day, a question correct is a question correct, irrespective of which section it comes from.

I strongly disagree to be honest. The people I know are studying it for pass AND LEARN.

YOu can have your CFA charterholder but if you do not focus on learning and understanding the stuff

1- You have more chances to fail

2- and most important, when you get the job of your life you will no have a fu**** clue of what to do. Well I think you will not pass the interview mate… the CFA is good for your CV but then you have to SHOW YOUR KNOWLEDGE AND YOUR SKILLS.

Nobody will give you a good job just for the CFA, they will test you.

It seems this discussion has gone off-track. If anyone is still looking for an answer to the original question, which is:

What is the difference between CONFIDENCE INTERVAL and PREDICTION INTERVAL?

It’s a CONCEPTUAL difference. It’s not absolute, and it very much depends on judgment and methodologies.

From what I learned in the CFAI curriculum:

PREDICTION intervals are typically used to estimate an EXPECTED value of a dependent variable in a context of regression.

CONFIDENCE intervals are typically used to estimate the RISK of investments. It’s more typically used in calculating risk rather than to predict expacted values.

Re: my previous post (#7).

How does the difference between a CI and PI depend on someone’s judgement? The parameter each attempts to locate is different-- that’s objective. The overall concepts for the CI and PI are also nearly identical-- the practical and theoretical interpretation of each is highly similar.

Prediction intervals do not jive with the answer you provided. In statistics, an expected value is a mean value. The prediction interval isn’t used for a mean, it’s used to (more or less) predict the next single observation of the DV (rather than the expected value of y, which is the same as the mean value of y, E[Y|X]). Can you give an example what you mean by saying that CIs are used to estimate risk in this context?