518.sagews

Sage Tool 1

This worksheet is designed to be used with Activity 1 in Section 1.2.

Plot the per capita cigarette consumption in the US (for persons 18 or older) for the period 1975-2000.

data=[(1975,4123),(1980,3851),(1985,3461),(1990,2827),(1995,2515),(2000,2092)]

plot1=point(data,pointsize=20)
show(plot1,axes_labels=['Year','Consumption'])

Determine $m$ and $b$ to define your line in the form $y=mt+b$.  Then plot the line together with the data points.  Adjust $m$ and $b$ until you think you have the best fit.

m=100
b=-196000
var('t')
L(t)=m*t+b
plot2=plot(L,1975,2000,color='red',thickness=1)
plot1+plot2

Use your linear model to estimate cigarette consumption in 1985 and 1990.

L(1985);L(1990)

2500 3000

Answers: 2500 per person in 1985, 3000 in 1990.

Use your linear model to estimate cigarette consumption in 2002.

L(2002)

4200

Answer: 1957 per person.

Note that the answers here are a little different from those in the Comment - here the first and last points were used to get the slope, but the intercept at $x=1975$ was 'eyeballed'.  There are many ways to make the estimations inherent in this model.