As we mentioned, the advertising response function in equation (7.4) is only one of several nonlinear functions we could have used to get the same “increasing at a decreasing rate” behavior we want in...

As we mentioned, the advertising response function in equation (7.4) is only one of several nonlinear functions we could have used to get the same “increasing at a decreasing rate” behavior we want in Example 7.5. Another possibility is the function f (n) = an^b
, where a and b are again constants to be determined. Using the same data as in Example 7.5 and RMSE as the fitting criterion, find the best fit to this type of function. In terms of RMSE, which function appears to fit the data better, the one here or the one in the example? Can you spot any qualitative difference between the two types of functions?

Example 7.5