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I have a problem I am trying to solve using the R programming language and software environment. This isn't a programming question but more how I can use the results however I might describe the problem is more programming speak rather than mathematical.

I have a set of observed data where I have variables V1..V11. V11 is an individuals weight and V1..V10 are all factors which impact the weight. I have performed regression on this data like so.

lm(formula = V11 ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10, data = fDF)

This gives me the results

(Intercept)           V1           V2           V3           V4           V5  
    58.8082       2.4857       0.5811       0.8833       2.8648       7.7457  
         V6           V7           V8           V9          V10  
    -7.3599       3.2055      -6.6382       1.4559       0.8486  

Is it possible using these coefficients solve the inverse of this problem. So given the weight V11 can you predict the values of v1..v10?

Thanks in advance.

share|improve this question
Sounds like an underdetermined problem. –  J. M. Aug 9 '12 at 13:46
In simple regression with 1 predictor and 1 covariate the inverse regression estimate is well-defined. But here it may be possible for several combinations of the covariates v1=v10 to lead to the same V11. Hence there is no unique solution. –  Michael Chernick Aug 9 '12 at 15:14
@MichaelChernick : Even in the simple regression you speak of, there's not enough information given in the posting. If you knew the number of data points and the correlation you could do it. With the information in the anova table, plus a bit of algebra, you could do it. But if the predicted value of $y$ given $x$ is $y=mx+b$, then inverse of that function, $x = (y-b)/m$, is NOT the function you'd use, and not enough information is given to find the right one. –  Michael Hardy Aug 9 '12 at 18:54
If you type "anova(lm(....))", where the dots represent exactly what you put into "lm()" before, you get the anova table. –  Michael Hardy Aug 9 '12 at 18:56
@MichaelHardy I was adressing when it is possible to do the inverse regression not whether or not the OP was supplying enough information to do it in the simple linear regression case. But why do you say that x=(y-b)/m where m and b are the estimated parameters from the regression fit is not the right function to use to determine x given y? –  Michael Chernick Aug 9 '12 at 19:02

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