Final answer:
To forecast sales using the dummy variable approach, dummy variables are created for each month and included in a regression model, which captures seasonal trends in sales. Each dummy variable indicates a month and allows for a separate adjusted forecast for that month in the prediction model.
Step-by-step explanation:
To forecast sales for January through December of the fourth year using the dummy variable approach, one would typically create dummy variables for each month to account for seasonal effects on sales and incorporate these into a regression model. Karen needs to understand that each dummy variable represents a different month and allows us to capture seasonal trends in the sales data that a simple linear trend might miss.
The model would include a constant term, as well as a coefficient for each dummy variable, which reflects the expected change in sales relative to the omitted month (usually the first month in the series or the one with the least variation). The forecast for each month is then calculated by plugging the value 1 for the respective dummy month and 0 for all others into the model equation.
For example, if Karen has sales data for the past three years, she could estimate a model such as:
Sales = β0 + β1DJanuary + ... + β12DDecember + ε
where DJanuary to DDecember are the dummy variables for each month, and β coefficients measure the effect of each month on sales. Once the coefficients are estimated using historical sales data, these can be used to predict future sales for each month in the fourth year.