I have a question on the Mathematics Stack Exchange site where I ask about generating an exponential regression equation.

One of the answers provides a **mathematical solution** to my problem. The solution is written in **mathematical notation**:

Unfortunately, I’m not a math wiz, and I’m having trouble translating the mathematical notation to Microsoft Excel syntax.

**What would the math look like in Excel?**

```
+--------------+---------------+
| X (AGE) | Y (CONDITION) |
+--------------+---------------+
| 0 | 20 |
| 1 | 20 |
| 2 | 20 |
| 3 | 20 |
| 4 | 20 |
| 5 | 20 |
| 6 | 18 |
| 7 | 18 |
| 8 | 18 |
| 9 | 18 |
| 10 | 16 |
| 11 | 16 |
| 12 | 14 |
| 13 | 14 |
| 14 | 12 |
| 15 | 12 |
| 16 | 10 |
| 17 | 8 |
| 18 | 6 |
| 19 | 4 |
| 20 | 2 |
+--------------+---------------+
```

I can verify that your formula for *a* translates as follows into Excel:

```
=SUMPRODUCT(E2:E22,F2:F22)/SUMSQ(E2:E22)
```

where my E2:E22 is just your x and my F2:F22 is ln(21-y). It gives the same answer, 0.147233112, as doing an exponential fit and forcing the intercept to be zero (which corresponds to setting b=1 in

```
y-21=b*exp(ax)
```

as you can verify by taking logs).

The formula quoted is the same as the one mentioned here under **Simple linear regression without the intercept term (single regressor)**

So this begs the question of whether b should, in fact, be equal to 1 and this is outside the scope of the question.

Tags: excelexcel, math