3 11m The Percent Of Households That Own At Least One Computer In Selected Years From 1981 To 2010 According To The 1 (76.65 KiB) Viewed 28 times
3. (11m) The percent of households that own at least one computer in selected years from 1981 to 2010, according to the U.S. census bureau, is listed in the following table: Year 1981 1984 1989 1993 1997 2000 2001 2003 2004 2010 Hc (%) 0.5 8.2 15 22.9 36.6 51 56.3 61.8 65 76.7 The data can be modelled with a function in the form Hc = C/(1 + Ae-Bx) (logistic equation), where Hc is percent of households that own at least one computer, C is a maximum value for Hc in this case C = 90, A and B are constants, and x is the year. 1 (a) (2m) Linearize the problem, (b) (3m) Use equation 6.14 in the text to solve for ao and a₁, and then determine the constants A and B. (c) (2m) Use the function to estimate the percent of ownership in 1982 and in 2009. (d) (2m) Calculate R². (e) (2m) Make a plot of year (independent variable) versus Hc (dependent variable) for both the data and the best-fit linear model. It should be a nonlinear plot. Include x and y labels, a title and a legend.
With these definitions, the equations for the coefficients a, and a are: nSxy-S,Sy ху = a₁ ao SxxSy-SySx nSxx-(S₂)² (6.14) nSxx-(S₂)²
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