Common Mistakes

Frequent Errors

1. Calling data exponential from a curved ordinary scatter without a semi-log check. 2. Confusing semi-log (one axis logged) with log-log (both logged). 3. Treating slope of the semi-log line as $b$ instead of $\log_n b$. 4. Treating intercept as $a$ instead of $\log_n a$. 5. Forgetting the advantage: no need to add a constant to $y$ (2.15.A.2). 6. Using inconsistent log bases mid-solution. 7. Saying "linear on semi-log" without specifying log-$y$. 8. Recovering $a,b$ but writing $y=a+bx$ by habit.

Why These Happen

Students blend Unit 1 linear fits with Unit 2 exponential ideas and lose track of which coordinate was transformed.

How to Fix Them

• Label axes: $x$ vs $\log_n y$.
• Write the CED form before computing: $\log_n y=(\log_n b)x+\log_n a$.
• Always convert back to $y=ab^{x}$ for the final model.

Avoidance Scripts

• "Log-$y$ linear $\Rightarrow$ exponential in $y$."
• "Slope is $\log_n b$, not $b$."
• "Semi-log advantage: no added constant needed."

Quick Self-Check

• Did I name which axis is logged?
• Did I convert slope/intercept through base $n$?
• Is the final model exponential in the original $y$?