Polynomial regression in R with multiple predictors

Question

I wanted to use polynomial regression on my data, but I have more than 10 predictors and my predictors' name change on my samples. I also used linear regression on my data in the below code:

 model_lm = lm(gene_expression ~ ., data = donor_snp_sample)
 summary_lm <- summary(model_lm)

I used "gene_expression ~." in my code, but I don't know how to use the same format in polynomial regression. Can you help me?

thanks a lot

Answer 1

The question is ambiguous as to the specific model desired but here is one possible model where we independently take a quadratic in each independent variable.

fo <- reformulate(sprintf("poly(%s, 2)", names(airquality)[-1]), "Ozone")
fo
## Ozone ~ poly(Solar.R, 2) + poly(Wind, 2) + poly(Temp, 2) + poly(Month, 
##     2) + poly(Day, 2)

lm(fo, na.omit(airquality))

giving:

Call:
lm(formula = fo, data = na.omit(airquality))

Coefficients:
      (Intercept)  poly(Solar.R, 2)1  poly(Solar.R, 2)2     poly(Wind, 2)1  
            42.10              64.80             -24.13            -124.10  
   poly(Wind, 2)2     poly(Temp, 2)1     poly(Temp, 2)2    poly(Month, 2)1  
            89.41             128.16              55.40             -18.45  
  poly(Month, 2)2      poly(Day, 2)1      poly(Day, 2)2  
           -32.10              27.20              11.87 

or write it like this if it is desired to see the formula written out on the Call: line of the output.

do.call("lm", list(fo, quote(na.omit(airquality))))

giving:

Call:
lm(formula = Ozone ~ poly(Solar.R, 2) + poly(Wind, 2) + poly(Temp, 
    2) + poly(Month, 2) + poly(Day, 2), data = na.omit(airquality))

Coefficients:
      (Intercept)  poly(Solar.R, 2)1  poly(Solar.R, 2)2     poly(Wind, 2)1  
            42.10              64.80             -24.13            -124.10  
   poly(Wind, 2)2     poly(Temp, 2)1     poly(Temp, 2)2    poly(Month, 2)1  
            89.41             128.16              55.40             -18.45  
  poly(Month, 2)2      poly(Day, 2)1      poly(Day, 2)2  
           -32.10              27.20              11.87