ISyE 6414 MSA Homework 6 Due November 18, 2015 1. Solve Exercise 2 from Ch.14 of the textbook. 2. It is assumed that the mean of y has the following relationship with x: E(y) = x . k0 + k1 x Suppose we have data (x1 , y1 ), , (xn , yn ). Explain how linear regression can be used to obtain approximate estimates of k0 and k1 . 3. The reaction rate of the catalytic isomerisation from n-pentane to isopentane depends on various factors, such as partial pressures of the products involved in the reaction. The data frame Isom in the R library nlrwr contains the partial pressures of hydrogen (x1 ), iso-pentane (x2 ), and n-pentane (x3 ), as well as the corresponding reaction rates. Consider the model: y = f (x; ) + , where N (0, 2 ) and f (x; ) = 1 3 (x3 x2 /1.632) . 1 + 2 x1 + 3 x3 + 4 x2 Fit the model using the initial estimates 1 = 20, 2 = 3 = 4 = .1. Also, compute R2 and provide an estimate of . 1