l Models with data Transformations Exponential Model General equation for an exponential model y=风0·B1 Corresponding linear regression equation for an exponential model logy=logb+(ogb)·x Multiplicative Model: General equation for a multiplicative model: y=Bo A1,B2 Corresponding linear regression equation for a multiplicative model: log y=log bo+ 6, log x,+b2. log x o 2002 The Wadsworth Group
Models with Data Transformations Exponential Model: • General equation for an exponential model: • Corresponding linear regression equation for an exponential model: Multiplicative Model: • General equation for a multiplicative model: • Corresponding linear regression equation for a multiplicative model: © 2002 The Wadsworth Group x y 0 1 = log y ˆ = log b + (log b ) x 0 1 1 2 0 1 2 y = x x 0 1 1 2 2 log y ˆ = log b + b log x + b log x
Example, problem 17. 8 International Data Corporation has reported the following costs per gigabyte of hard drive storage space for years 1995 through 2000. Using x =1 through 6 to represent years 1995 through 2000, fit a second-order polynomial model to the data and estimate the cost per gigabyte for the year 2008 Y ear x=Yr y=Cost 1995 s26184 1996 137. 94/ The regression equation 1997 69.68 will have the form 1998 29.30 y=b +bx+b,x 1999 123456 13.09 2000 6.46 o 2002 The Wadsworth Group
Example, Problem 17.8 • International Data Corporation has reported the following costs per gigabyte of hard drive storage space for years 1995 through 2000. Using x = 1 through 6 to represent years 1995 through 2000, fit a second-order polynomial model to the data and estimate the cost per gigabyte for the year 2008. The regression equation will have the form: Year x = Yr y = Cost 1995 1 $261.84 1996 2 137.94 1997 3 69.68 1998 4 29.30 1999 5 13.09 2000 6 6.46 © 2002 The Wadsworth Group2 0 1 2 y ˆ = b + b x + b x
l Example, Problem 17.8,cont Microsoft Excel Output SUMMARY OUTPUT Regression Statistics Multiple r 0.99655892 R Square 0.99312968 AdjRSquare.98854948 Standard Error 10.5650522 Observations o 2002 The Wadsworth Group
Example, Problem 17.8, cont. Microsoft Excel Output © 2002 The Wadsworth Group SUMMARY OUTPUT Regression Statistics Multiple R 0.99655892 R Square 0.99312968 Adj R Square 0.98854948 Standard Error 10.5650522 Observations 6