Extrapolation

#1
Hi all,
First time poster, and I have what might be an odd question. In a typical regression analysis (y = mx + b), we have a set of known x’s and known y’s. If we try to predict y using a value outside the range of known x’s, the result is considered an extrapolated value. However, what if we predict y with a value of x that is within the known range, but because of a quirk in the regression line, the predicted value of y is outside the range of the known y values? Is this also considered an extrapolated value?

Thanks much.

JC
 

hlsmith

Not a robit
#2
Sounds like interpolation. That is when you estimate a value within the range of your data, but you just did not have an observation for it in the dataset. For example, I want to estimate the weight of someone that is 60 inches and my dataset includes: 56, 54, 58, 62, 63, 66.

Welcome to the forum!
 
#3
OK, but let’s say the corresponding weights for your subjects at those heights range from 100 to 150 pounds. And let’s say you want to predict the weight of someone at 65 inches (within the range of your sample), and because of way the regression line falls, it predicts a weight of 153 pounds. This value is outside the weight range of your samples. Should that be considered extrapolated, even though the predictor value (65) was within?

Thanks for your help!
 

hlsmith

Not a robit
#4
It is my belief that if the value of X is within the sample space of other values it is still just interpolation. If you have a particular example that you think is really wonky, post it and we can see.
 

hlsmith

Not a robit
#5
I was just thinking about your last post. If you have a high estimate, that may be a sign of a curvelinear relationship. Do your residuals reveal any irregularities?
 
#6
This was more of a "what if" scenario, spawned by mental meanderings during an idle lunch hour, rather than a real-life issue. If I run into an actual data set that illustrates the situation, I'll certainly pass it along. I think you've answered my question, and I appreciate your help. I'm glad I found this forum. I've posted to a few other stat forums with other questions in the past, and gotten no feedback at all. Thanks!