Enable Excel Macros

Excel Macros must be enabled when the downloaded NLS program is opened to use the curve fit capability. See Excel Help for instructions.

Visual NLS Curve Fit

Our Visual Nonlinear Curve Fit does not use Excel Solver. Rather, we built our nonlinear least squares (NLS) curve fit program using the Levenberg–Marquardt algorithm. Fit statistics (e.g., standard error) are provided. Graphical visualization of the fit-in-progress provides insight.

How to Enter Your Own Data

Select “Enter Your Own Data” in the Top Dropdown List

Using the left mouse button click the right down-arrow button end of the top dropdown list. Scroll to the second entry (Enter Your Own Data) and release the mouse button. I knew you knew that.

Enter a Product Case Name Below the Dropdown Lists

A product case name is a brief description of the market data being used. It always includes the product name (e.g., VCRs) and may also include additional information such as the region (e.g., USA).  

Select the Type of Observations from the Radio Buttons

Select the type of market data to be used (e.g. adoptions) from the radio buttons. The data are referred to as observations.

The data must be consistent with the Bass Model discrete-tiem equations equations, which express adoptions and cumulative adoptions as a function of time t and the Bass Model parameters M, p and q. Adoptions is sales to first-time buyers at a specific time t while cumulative adoptions is the total of adoptions for all time intervals up to and including the time t.There is an equation form of the Bass Model that expresses adoptions as a function of cumulative adoptions; however, it is not preferred and is not used here.

Market data observation types are typically such measures as: unit sales, new subscriptions, unit production, systems in use, installed base, users, number of subscribers, and penetration. With any observation type care care must be taken to as closely as possible use data consistent with the Bass Model assuplitions (e.g., no repeat purchases).

Enter Your Data Series in the Big Input Box

If your data are in Excel, copy one or two side-by-side columns and paste them into the largest field above. No headings. Paste or type observations one per line as: (a) a number or (b) a time interval label followed by a space followed by a number.

A time Interval label is up to 10 alphanumeric characters with no spaces, e.g., 1998, 1992_Q1). The time intervals must be regular. If a time-interval label is provided for any observation in a series, a label must be provided for each.

With What Time Interval Should the Data Series Start?

The short answer: start with the earliest data available with even earlier intervals handled as missing observations (see below). Most importantly, be consistent when comparing Bass Model parameters between products or using them to create analogies for new products.

Ideally, the market data start with the first full year (or other interval) of sales of a new product. Commonly, however, published data start a few intervals (e.g., years) after the product introduction.

What If There Are No Data For Some Intervals

If the data are equivalent to adoptions (e.g., sales), some observations may be missing. To indicate a missing observation, provide the interval label (e.g., year), but no associated observation. The missing observations can be at the being of the series, in the middle or the end. Observations missing at the beginning of a series are “backcast” by the curve fit; missing observations at the end are forecast.

A cumulative adoptions series (e.g., subscriptions) is differenced by NLS Visual Curve Fit to obtain an equivalent series for adoptions (e.g., New Subscriptions), which is then curve fit to the Bass Model Adoptions equation. This process is the preferred method.

If a cumulative adoption series has missing observations, it is still possible to difference it by losing an additional observation for each missing one. The observation is lost because there is no prior observation (the missing one) to subtract from it. It is also possible to fit the Bass Model cumulative adoptions curve to cumulative adoptions with missing observations. These options are not yet implemented here. Such fits tend to be problematic however, if your data are cumulative with missing observations the parameter estimates carefully scrutinized may still be useful. We expect to implement such options in a future release. In the mean time you can difference the cumulative data manually and submit it here as adoptions (or equivalent).

Forecasting and Backcasting

To forecast adoptions past the time of the last available data, specify the time intervals to be forecasted as missing observations. The NLS Visual Curve Fit will fill in the predicted values by calculating them using the Bass Model equation and the Bass Model parameters M, p and q resulting from the curve fit. Backcasting is like forecasting except that the missing observations are at the beginning of the series.

How Many Observations Do I Need?

The short answer: one or two data points after the peak in adoptions. If you have fewer, then determine M through marketing research or expert guesstimate and fix it during the curve fit of the Bass Model to the data to estimate p and q. A parameter is fixed after the Excel program is downloaded by specifying TRUE under the Fixed column on the line corresponding to the fixed parameters. If a parameter is fixed, after the curve fit,  the Initial value of the parameter will appear in the Estimate column and be used in the Bass Model calculations.

Theoretically, only three observations are sufficient to determine the Bass Model parameters M, p and q. However, more observations are needed because (1) nearly all observation measurements are inaccurate and (2) the first few observations may be due to forces (e.g., production limitations) not consistent with key Bass Model assumptions, for example, that adoptions are due to word of mouth and demand-creation activities (e.g., advertising and PR).

Is the Market Data Compatible with the Bass Model Assumptions?

Virtually all market data are imperfect. Unit sales data measurements may contain replacement sales in addition to sales to first-time buyers. In using the Bass Model, we try to limit the data series to a period where replacement sales are small relative to first-time sales, commonly using only the series to one or two intervals after the adoptions peak. As another example, market penetration data based on periodic surveys are often problematic due to survey inconsistencies and changes in the survey universe. As a last example, subscribers (e.g., cell phones) may be noisy because of churn. In all cases, real world market data must be viewed pragmatically as to whether or not the Bass Model assumptions are sufficiently satisfied by the data.