for loops for regression over multiple variables &

I have tried to apply this QA: "efficient looping logistic regression in R" to my own problem but I cannot quite make it work. I haven't tried to use apply, but I was told by a few people that a for loop is the best here (if someone believes otherwise please feel free to explain!) I think this problem is pretty generalizeable and not too esoteric for the forum.

This is what I want to achieve: I have a dataset with 3 predictor variables (gender, age, race) and a dependent variable (a proportion) for 86 genetic positions for several people. I want to run bivariate linear regressions for each position (so 86 linear regressions for 3 predictor variables). Then I want to output the results in some easily legible format; my idea is a matrix with rows=gender, age, and race, and columns=the 86 positions. There would be a p value for each row*column combination. Then I could call the p values<0.1 (or whatever threshold I want) to easily see which predictors are significantly associated with proportion at each position.

This is the code I have so far.

BB <- seq.csv[,6:91]   #the data frame containing the 86 positions
AA <- seq.csv[,2:4]    #the data frame containing the 3 predictor variables

linreg <- matrix(NA,3,86)  #make a results vector and fill it with NA
    for (i in 1:86)     #loop over each position variable
    {
              for (j in 1:3)  #for each position variable, loop over each predictor
    {
              linreg[i,j] <- lm(BB[,i]~AA[,j])  #bivariate linear regression
}}

No matter how I change this (for example, simplifying it to loop over the positions for only one predictor), I still get an error that my matrices are not the same length (number of items to replace is not a multiple of replacement length). In fact, length(linreg)=286 (3*86) and length(BB)=86 and length(AA)=3. I know the latter two are dataframes, not matrices...but if I convert them to matrices I get an invalid type error (invalid type (list) for variable 'BB[, i]'). I do not know how to resolve this error because I just don't understand R well enough...I've consulted the books Applied Statistical Genetics with R and Art of R Programming to no avail, and I'm been Google searching all day. And I haven't even gotten to the coding for outputting the results...

I'd appreciate any debugging tips or some suggestions on a better way to code this! Thank you all in advance.

Really hard to give a definitive answer without knowing the structure of your data beforehand, but this might work. I'm assuming that your two data frames have the same number of rows (observations):

df <- cbind( AA[ , 2:4 ] , BB[ , 6:91 ] )
mods <- apply( as.data.frame( df[ , 4:89 ] ) , 2 , FUN = function(x){ lm( x ~ df[,1] + df[,2] + df[,3] } )

# The rows of this matrix will correspond to the intercept, gender, age, race, and the columns are the results for each of your 86 genetic postions
pvals <- sapply( mods , function(x){ summary(x)$coefficients[,4] )

As to whether or not that is the right thing to do I will trust to your judgement as a genetic epidemiologist!