Hey there! Let's figure out what's going on with your linear regression model. First, let's recap the output you got (formatted for clarity):

lm(formula = Age ~ L.1.HU + L.1.V + L.2.HU + L.2.V + L.3.HU + L.3.V + L.4.HU + L.4.V + L.5.HU + L.5.V, data = CT)

Residuals: ALL 11 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) 88.106023         NA      NA       NA
L.1.HU     -0.049377         NA      NA       NA
L.1.V       0.169878         NA      NA       NA
L.2.HU     -0.052153         NA      NA       NA
L.2.V      -0.367214         NA      NA       NA
L.3.HU     -0.038905         NA      NA       NA
L.3.V       0.378833         NA      NA       NA
L.4.HU     -0.001531         NA      NA       NA
L.4.V      -0.923230         NA      NA       NA
L.5.HU      0.150823         NA      NA       NA
L.5.V       0.871423         NA      NA       NA

The Core Problem #

The key red flag here is the message: Residuals: ALL 11 residuals are 0: no residual degrees of freedom!

This happens because:

• You have 11 total observations (that's why there are 11 residuals)
• Your model is trying to estimate 11 parameters: 1 intercept + 10 predictor variables (the L..HU and L..V terms)

When the number of parameters equals the number of data points, the model can perfectly fit every single observation—there's no leftover data to calculate things like standard errors, t-values, or p-values (hence all the NAs). This is called an over-specified model or a model with "no degrees of freedom for error".

How to Fix This #

Here are practical steps to resolve this:

1. Add more observations: The simplest fix is to collect more CT data. You need way more samples than the number of predictors (a general rule of thumb is at least 10-20 observations per predictor, though this varies by field).
2. Reduce the number of predictors:
   • Use feature selection methods like stepwise regression, LASSO, or random forest feature importance to pick the variables that actually correlate with Age.
   • Check for collinearity between your predictors (e.g., do L.1.HU and L.2.HU move together?). If two variables are highly correlated, you can drop one without losing much information.
3. Start simple: Try building a model with just a few predictors first (e.g., only the HU terms, or only the V terms), see how it performs, and gradually add variables as you get more data.

内容的提问来源于stack exchange，提问作者Maria Kischenko