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POPredict.lm() in R - how to get nonconstant prediction bands around fitted values
 

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  1. POPredict.lm() in R - how to get nonconstant prediction bands around fitted values
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    <p>So I am currently trying to draw the confidence interval for a linear model. I found out I should use predict.lm() for this, but I have a few problems really understanding the function and I do not like using functions without knowing what's happening. I found several how-to's on this subject, but only with the corresponding R-code, no real explanation. This is the function itself:</p> <pre><code>## S3 method for class 'lm' predict(object, newdata, se.fit = FALSE, scale = NULL, df = Inf, interval = c("none", "confidence", "prediction"), level = 0.95, type = c("response", "terms"), terms = NULL, na.action = na.pass, pred.var = res.var/weights, weights = 1, ...) </code></pre> <p>Now, what I've trouble understanding:</p> <pre><code> 1) newdata An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used. </code></pre> <ul> <li><p>Everyone seems to use newdata for this, but I cannot quite understand why. For calculating the confidence interval I obviously need the data which this interval is for (like the # of observations, mean of x etc), so cannot be what is meant by it. But then: What is does it mean?</p> <p><code>2) interval<br> Type of interval calculation.</code></p></li> <li><p>okay.. but what is "none" for?</p> <p><code>3a) type<br> Type of prediction (response or model term).</code></p> <p><code>3b) terms<br> If type="terms", which terms (default is all terms)</code></p></li> <li><p>3a: Can I by that get the confidence interval for one specific variable in my model? And if so, what is 3b for then? If I can specify the term in 3a, it wouldn't make sense to do it in 3b again.. so I guess I'm wrong again, but I cannot figure out why.</p></li> </ul> <p>I guess some of you might think: Why don't just try this out? And I would (even if it would maybe not solve everything here), but I right now don't know how to. As I do not now what the newdata is for, I don't know how to use it and if I try, I do not get the right confidence interval. Somehow it is very important how you choose that data, but I just don't understand!</p> <p>EDIT: I want to add that my intention is to understand how predict.lm works. By that I mean I don't understand if it works the way I think it does. That is it calculates y-hat (predicted values) and than uses adds/subtracts for each the upr/lwr-bounds of the interval to calculate several datapoints(looking like a confidence-line then) ?? Then I would undestand why it is necessary to have the same lenght in the newdata as in the linear model.</p>
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      1. POPredict.lm() in R - how to get nonconstant prediction bands around fitted values
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    1. COThe Details section of the documentation discusses the `newdata` argument at some length. What part of that discussion remains confusing?
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    2. COI guess this is what confuses me: "predict.lm produces predicted values, obtained by evaluating the regression function in the frame newdata" (in the general explanation) and "If newdata is omitted the predictions are based on the data used for the fit." for newdata. Why would I try to get confidence intervals which are not connected in my actual regression? This is how I understand this sentence, so this is what confuses me. Then it explains how missing values are handled in that case, but I struggle with the first part already!
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    3. COYou might be interested in _prediction_ intervals for new observations.
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