# How to determine if multiple body measurements could be predicted from height & weight

I have a data set of orders of made-to-measure suits where customers have measured themselves and ordered suits. Each record consist of a bunch of body measurements (such as arm length, stomach circumference, etc). I also have the height and weight of the person.

I have the hypothesis that many, if not all, of these measurements could be calculated from just the length and weight of the person, or those two variables plus perhaps some extra variable.

How could I verify this and find such correlations? My guess would be to group all orders by length and weight, and within each such group I take the mean value of each measurement and then check the standard deviation to see if the numbers seem to stay close enough to the mean. I would just put the numbers into Excel and run it there or write a little Python program that makes the calculations (I am a programmer by profession). I am not sure how I can map these results into some usable formula afterwards. The end-result I am looking for is that all measurements should be possible to calculate with only a few input variables (such as height and weight), but I cannot accept too big variations as that would result in ill-fitting suits for many.

I have the feeling I lack the statistical knowledge here. How can I tackle this problem?

First of all, I am not too sure such a correlation exists. People can have very different and varying body forms and density distributions so there may not be an obvious correlation. Even then, this is still a possibility you might want to investigate.

However, when you are trying to compare variables, I feel that instead of trying to handle so many at once, try to limit your scope to 2 variables at a time (one independent variable and 1 dependent variable). For instance, intuitively you would think that arm length and height should be related by some common ratio, where height is your INDEPENDENT VARIABLE (the "input" of your final program / formula) and arm length is your DEPENDENT VARIABLE (the "output" of your final program /formula. I will assume that you would already have / are going to record an excel sheet of these variables, so you should have one column with all the heights and another column with all the arm lengths.

Next, intuition suggests that there should be a (relatively) linear relationship between the arm length and the height, since people's hands normally are no shorter than their hip and do not dangle lower than their waist. As such, you may want to use a Pearson correlation coefficient formula as described here: http://mathbits.com/MathBits/TISection/Statistics2/correlation.htm A step by step guide is given here: http://www.statisticshowto.com/how-to-compute-pearsons-correlation-coefficients/

You can use this same method for other methods which you think have a linear correlation to verify your hypothesis.

Should the correlation be close to 1, then there is a clear linear relationship between your independent and dependent variable.

Should the correlation be close to 0, then there is likely to be no relationship at all.

Should the correlation be negative, then there is an inverse relationship.

If they do have a close relationship, you can then use Excel's graph plotting tool to find a best fit line and work out the equation of the slope from there to arrive at a formula that links the variables.

Hope it helps.

Nicholas Ang

• Amazing response! Tomorrow I'll read up and try your suggested techniques! Thanks. – mojbro Sep 25 '15 at 2:02