Applies to: StatTools 6.x and Up

Error:

“Must have at least two more data points than independent variables.”

Question:

Why can’t I solve m+1 equations for m+1 unknowns?

Answer:
If you have exactly m+1 points for m independent variables, you could mathematically solve the equations to fit those points perfectly. But that’s not regression — it gives no information about how the model would perform on new data.

StatTools regression is a statistical method to estimate coefficients that best predict the dependent variable across all possible values of the independent variables, not just fit the existing points exactly.

• Let m = number of independent variables

• Let p = number of data points

The absolute minimum required is p = m + 2, because degrees of freedom in ANOVA are df = p − m − 1, and df must be greater than 0.

More data points improve reliability:

• a rule of thumb is p ≥ 10·m
  • Princeton suggests ideally p ≥ 20·m, never less than 5·m.
  • Fewer points → larger standard errors and weaker predictive ability.