# Adjusted R-squared is too high (=1) in Linear Model

I built a Linear model which has an adjusted r-squared value of 1. I understand that this is a near perfect number. Upon further investigation, I found that one of the 96 independent variables in the dataset is highly correlated with the dependent variable. This is also a variable which I would like to keep (and not drop). Are there any additional steps that I should undertake to handle this?

Sample df reproducing the situation above:

df1 <- data.frame("y" =   c(0.0166 , -0.2380 , -0.3192 , -0.2774 ,  9.3148 , 0.3142) ,
"x1" =  c(0.0103 , -0.2347 ,  -0.3182 , -0.2793 ,  9.4638  , 0.3297) ,
"x2" = c( -0.1838 , -0.2458 , -0.2581 ,-0.2533 , 6.7566 ,-0.0835) ,
"x3" = c(0.3426 ,-0.0543 ,-0.4512 ,-0.0543, 10.4637 , 0.3426) ,
"x4" = c(-0.161 , -0.270 ,-0.318, -0.280 , 8.279 , 0.169))
df1
df1_lm <- lm(y~. , data = df1)
summary(df1_lm)

• Question: is your „good“ x feature a linear combination of y? – Peter Jun 21 '19 at 19:59