How to find an exponential regression model for weekly sales data

Key takeaway: This is a classic regression question: the numbers are growing fast, and the key is to test whether an exponential model matches that growth. The residual plot is the real clue, not just the equation itself.

Step 1: Look at the pattern in the sales data

The sales values rise by a much larger amount each week, which suggests exponential growth rather than a linear trend.

Let weeks be $x$ and sales be $y$. A suitable model has the form

$y = ab^x$

Because the problem asks for a rounded model, you would normally use exponential regression to get values for $a$ and $b$.

Step 2: Interpret the fit

To decide whether the model is good, check the residual plot:

• If the residual plot shows a clear pattern, the model is not a good fit.
• If the residual plot does not show a clear pattern, the model is a good fit.

So the correct statement is:

The model is not a good fit because the residual plot shows a clear pattern.

Step 3: What equation should look like

Using technology, your regression equation should come out in the form

$y = a(b)^x$

with $a$ and $b$ rounded to 3 decimals.

If your calculator gives a specific model, that is the one to place after $Y=$.

---

Pitfalls the pros know 👇 A common mistake is to look only at how fast the sales grow and assume that automatically means the model is good. It doesn’t. Exponential growth can still be the wrong model if the residuals curve or trend instead of scattering randomly.

Another slip is mixing units: the prompt says sales are in thousands of dollars, so keep the interpretation consistent when writing the model.

What if the problem changes? If the data had a residual plot with points scattered randomly around 0, then the exponential model would be considered a good fit. If the teacher asked for a different model, like linear or quadratic regression, you would compare the residual patterns and choose the one with the least structure.

Tags: exponential regression, residual plot, model fit