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I am trying to rescales x to lie between lower and upper

rescale <- function(x, lower = 0, upper = 1){
slope <- ??
intercept <- ??
y <- intercept + slope * x
return(list(new = y, coef = c(intercept = intercept, slope = slope)))
}

And this is the hint from my professor: The linear transformation should map the minimum of x to lower and the maximum of x to upper. (Hint: what is the equation for a line passing through two points?) Note in calculating the minimum and maximum that x may contain NA values; make sure your function can handle this. And the return would look like:

    **> rescale(c(1:10, NA), -1, 1)
    $new
    [1] -1.0000000 -0.7777778 -0.5555556 -0.3333333 -0.1111111 0.1111111
    [7] 0.3333333 0.5555556 0.7777778 1.0000000 NA

    $coef
    [1] -1.2222222 0.2222222**

So does anyone has ideas on what the "slope" and "intercept" here should be?

whuber
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user40993
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  • Please add the `self-study` tag and read its [tag wiki info](http://stats.stackexchange.com/tags/self-study/info). What have you tried? – Glen_b Feb 27 '14 at 09:30
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    I've added the tag myself, based on the clear statement in the question that this is study, and its routine textbook-like nature. Please still read the tag-wiki info and modify your question accordingly. – Glen_b Feb 27 '14 at 09:36
  • @Glen_b How is this not off-topic as being about the correct R code? – Nick Cox Feb 27 '14 at 09:58
  • @NickCox I'd have chosen to answer the question as a general question about how to do such rescaling (i.e. the on-topic aspect of the question). Mentioning code doesn't make the statistical aspects of a question disappear! It's really only in the absence of a statistical component that it's off topic. Now that it's been answered with code, you should feel free to close it. (Come to think of it, it's may well be a duplicate as well.) – Glen_b Feb 27 '14 at 10:16
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    @Glen_b Clearly even experienced people can draw the line between on- and off-topic in slightly different places. I didn't see there being a statistical issue here, as if there is uncertainty it's about a point in elementary mathematics. – Nick Cox Feb 27 '14 at 10:35

1 Answers1

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slope is a factor describing the target-range / source-range. If you need a range of 0..2, than you would write:

slope = (2 - 0) / (max(data) - min(data))

The intercept is the offset from zero. So if your target range is 1..3 (instead of 0..2) then your intercept would be 1 (all values +1).

Finally, you the formula only works if your data starts with 0. Elsewise, you'd have to subtract the original intercept.

rescale = function(x, lower=0, upper=1) {
  xMin = min(x)
  xMax = max(x)
  factor = (upper - lower) / (xMax - xMin)
  return((x-xMin) * factor + xMin)
}

Best, BurninLeo

BurninLeo
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  • This is (as plainly stated in the question) coursework. The [`self-study` tag wiki info](http://stats.stackexchange.com/tags/self-study/info) suggests we should not supply code or complete solutions, but help *guide* the asker to the solution with hints, or perhaps pseudocode if necessary. Please read the guidelines at the link and provide hints, rather than just doing the OP's assignment. – Glen_b Feb 27 '14 at 09:32
  • Arg - I am sorry! Actually I missed the `self-study` tag. Gladly, my function is only practical and does not solve all the partial questions... – BurninLeo Feb 27 '14 at 09:40
  • The tag wasn't there when you answered, but the fact that it was coursework was clear from the question. – Glen_b Feb 27 '14 at 10:12