Due Monday August 5, 2002
Bent E. Petersen
Here is some data on cigarette consumption and production in the United States. You can copy and paste the data directly into Maple. If you wish to use Matlab or a spreadsheet instead you will have to do a little bit of work to format the data correctly. The statement of the assignment follows the data.
Source of data: U.S. Department of Treasury Bureau of Alcohol Tobacco and Firearms.
U.S. cigarette consumption per capita over age 18
1945-1994
Year:=[seq(k,k=1945..1994)];
PerCap:=[3449,3446,3416,3505,3480,3522,3744,3886,3778,\
3546,3597,3650,3755,3953,4073,4171,4266,4265,\
4345,4195,4259,4287,4280,4186,3993,3985,4037,\
4043,4148,4141,4123,4092,4051,3967,3861,3849,\
3836,3739,3488,3446,3370,3274,3197,3096,2926,\
2826,2720,2641,2538,2514];
U.S. cigarette production 1956-1994 in billions
YearP:=[seq(k,k=1956..1994)];
Production:=[424.2,442.4,470.1,489.9,506.9,528.3,535.5,550.6,539.9,\
556.8,567.3,576.2,579.5,557.6,583.2,576.4,599.1,644.2,\
635.0,651.2,693.4,665.9,695.9,704.4,714.1,736.5,694.2,\
667.0,668.8,665.3,658.3,689.4,694.4,677.2,710.3,694.5,\
718.5,661.0,725.6];
Do a least squares polynomial fit of degree 1, 2 and 6 for the cigarette consumption data. Plot the results (original data and polynomial fit on each graph). Comment on the apparent (visual) quality of the fit.
What prediciton does each fit make for consumption for the year 2002? Does this sort of extrapolation make any sense? (Reply in a few English sentences.)
Try a very high degree (perhaps 20 or 30 - experiment) fit and comment on what you observe.
Do a least squares polynomial fit of degree 1 and of degree 2 for the cigarette production data. Comment on the apparent (visual) quality of the fit.
Here's an optional non-mathematical question: How do you reconcile U.S. decreasing per capita consumption of cigarettes with increased production? Can you find the data to check your response?
I have provided instructions for how to do least squares fitting in Maple and in Matlab.
Maple instructions in a Maple worksheet
Maple instructions in a PDF file.
Matlab instructions in an HTML file
If you want to do the assignment in some other way then you are on your own.