As we shall illustrate in Chapter 12, statistical methods

Chapter 5, Problem 4.100

(choose chapter or problem)

As we shall illustrate in Chapter 12, statistical methods associated with linear and nonlinear models are very important. In fact, exponential functions are often used in a wide variety of scientic and engineering problems. Consider a model that is t to a set of data involving measured values k1 and k2 and a certain response Y to the measurements. The model postulated is Y = eb0+b1k1+b2k2, where Y denotes the estimated value of Y, k1 and k2 are xed values, and b0,b1, and b2 are estimates of constants and hence are random variables. Assume that these random variables are independent and use the approximate formula for the variance of a nonlinear function of more than one variable. Give an expression for Var( Y ). Assume that the means of b0,b1, and b2 are known and are 0, 1, and 2, and assume that the variances of b0,b1, and b2 are known and are 2 0, 2 1, and 2 2.