Question

You are the account manager in charge of Internet advertising at Impact Sales. Spending on Internet advertising has increased steadily over the last few years and you predict the growth will continue.

) Do you think a linear model is appropriate for this data? Explain clearly.

f) Find a quadratic model for this data since 2000.

g) Which model better fits your data? Support your answer with a scatter plot of the data and both models on the same set of axis.

h) Using the quadratic model what is the average rate of change between 2002 and 2004?

i) As the account manager what would you budget for Internet advertising in 2008?

TABLE:

Year Internet Advertising Spending (Billions)

2001 0

2002 0.3

2003 0.8

2004 1.9

2005 3

2006 4.3

2007 5.8

Answer 1

The linear model is not an appropriate fit as is quite visible from the plot. As can be seen for example, in the year 2001 the linear model predicts spendings in negative amount which is unrealistic.

The quadratic model fits the data much bettter as shown below.

The average rate of change between the year 2002 and 2004 is calculate as follows using the code.

Budget for Internet advertising in 2008, 7.6714 billions using the quadratic model.

The calculations and plots are done using the followin Octave/Matlab script.

clear;
clc;

data = [2001 0;
2002 0.3;
2003 0.8;
2004 1.9;
2005 3;
2006 4.3;
2007 5.8;];

y = data(:,1);
s = data(:,2);

p1 = polyfit(y,s,1);

p2 = polyfit(y,s,2);

rateAvg = (polyval(p2,2004)-polyval(p2,2002))/(2004-2002)

budget2008 = polyval(p2,2008)

figure(1)
hold on
xlabel('Year')
ylabel('Spendings [Billions]')
plot(y,polyval(p1,y),'linewidth',2)
plot(y,s,'o','MarkerFacecolor','black','MarkerEdgeColor','black')
grid on
legend('Linear Model','Data','Location','NorthWest')

figure(2)
hold on
xlabel('Year')
ylabel('Spendings [Billions]')
plot(y,polyval(p1,y),'linewidth',2)
plot(y,polyval(p2,y),'linewidth',2)
plot(y,s,'o','MarkerFacecolor','black','MarkerEdgeColor','black')
grid on
legend('Linear Model','Quadratic Model','Data','Location','NorthWest')