Homework 6 results
1.a Y = 150X + 200
Y = 200 + 150X
Six minutes of flight . . .
Y = 150*6 + 200
Y = 1100
1.b. Car rental
Y = .06X + 29
Y = 29 + .06X
Rental for 200 miles . . .
Y = .06 * 200 + 29
Y = $41.00
2.a. Net loss of $20. Loss of $40
for membership plus $20 savings
on $100 spent.
2.b.
Spending
Savings
0
100
200
300
0
20
40
60
400
80
2.c.: Must spend $200 for
membership to be worthwhile.
2.d.: The function is linear because
the change in Y is constant across
all values of X. For every $100
spent, exactly $20 saved.
2.e.
Amount spent = X
Amount saved = Y
Y = .2X - 40
3.a. Tobacco production
2.000
1.800
1.600
1.400
1.200
1.000
0.800
0.600
0.400
y = -0.0606x + 122.28
R² = 0.8244
0.200
0.000
1985
1990
1995
2000
2005
2010
3.b. Predicted 2012 production,
equation method
Y = -.0606 * 2010 + 122.28
Y = 0.353 billion pounds
3.b. Predicted 2012 production,
trendline extension method
2.000
1.800
1.600
1.400
1.200
1.000
0.800
0.600
0.400
0.200
0.000
1985
1990
1995
2000
y = -0.0606x + 122.28
R² = 0.8244
2005
2010
2015
3.c. Confidence in prediction
3.c. Confidence in prediction
Pro:
• Strong R-squared
• Near-term forecast
Con:
• Imperfections in fit to trendline
• Possible shift in trend in last four years
4.a. Percentage smokers
35.0
30.0
25.0
20.0
15.0
y = -0.4397x + 902.33
R² = 0.9494
10.0
5.0
0.0
1980
1985
1990
1995
2000
2005
2010
4.b. Prediction of percentage smoking
in 2010, equation method
Y = -.4397 * 2010 + 902.23
Y = 18.4%
4.b. Prediction of percentage smoking
in 2010, trendline extension method
35.0
30.0
25.0
20.0
15.0
10.0
y = -0.4397x + 902.33
R² = 0.9494
5.0
0.0
1980
1985
1990
1995
2000
2005
2010
2015
4.d. Prediction of percentage smokers
in 1953
Y = -.4397 * 1953 + 902.23
Y = 43.5%
4.d
Confidence in prediction
4.d
Confidence in prediction
Pro:
• Strong fit, R-squared
Con:
• Many years between 1953 and 1983, so many
possible significant economic and social
changes
4.e.
Prediction when 100 percent
smokers
100 = -.4397 * X + 902.23
100-902.23 = -.4397 * X
-802.23/-.4397 = X
1824 = X
5.a Main point of article
Projections of the percentage of the population
who will be obese in 40 years
is quite dubious
if not totally bogus.
5.b
Relevance to linear models
It makes exactly the same point
about projections far into the future
as we considered
with regard to the number of motor vehicles
and consumption of coal