M120 Project 3

Due Date:                                                                     25 points [5 point penalty for each class day late]

Objective:  Model and Interpret Real Data with Regression on the TI-83

I.  Life Cycle Hypothesis

An individual's income varies with his/her age. Below is the median income I of individuals of different age groups within the US for 1995. For each class let the class midpoint represent the independent variable, x. For the class "65 year and older," we will assume the class midpoint is 69.5.

Age

Class Midpoint, x

Median Income

15-24 years

19.5

20,979

25-34 years

29.5

34,701

35-44 years

39.5

43,645

45-54 years

49.5

48,058

55-64 years

59.5

38,077

65 years and older

69.5

19,096
  1. Draw a scatter diagram
  2. Find the quadratic function of best fit.
  3. Draw the function over the scatter diagram
  4. At what age can an individual expect to earn the most income & what is the income?

II.  Aids Cases in the US

The data below represents the cumulative number of reported AIDS cases in the U.S. from 1983-1994.

Year, t

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

# of AIDS Cases, A

4,589

10,750

22,399

41,256

69,592

104,644

146,574

193,878

251,538

326,648

388,613

457,280
  1. Let 1980 be t = 0.  Enter data into STAT and draw a scatter diagram
  2. Find the cubic function of best fit
  3. Draw the cubic function over the scatter diagram
  4. Use the function to predict the cumulative number of Aids cases report in the U.S. in 1995.
  5. Discuss using this info to predict the cumulative number of AIDS cases in 1999?

III.  Economics/Marketing

A store manager collected the following data regarding price and quantity demanded of shoes:

Price ($/unit)

79

67

54

46

38

31

Quantity Demanded

10

20

30

40

50

60
  1. Draw a scatter diagram with Demand as x, and Price as y.
  2. Find an exponential curve to the data.
  3. Graph the exponential function over the scatter diagram

IV.  Economics/Marketing

The following data represents the price and quantity supplied in 1997 for IBM personal computers.

Price ($/Computer)

2300

2000

1700

1500

1300

1200

1000

Quantity Supplied

180

173

160

150

137

130

113
  1. Draw a scatter diagram with Price as x and Quantity demanded as y.
  2. Fit a logarithmic model to the data
  3. Draw the logarithmic function over the scatter plot.
  4. Use the function to predict the number of IBM personal computers that would be supplied if the price were $1650

V.  Population Model

The following data obtained from the U.S. Census Bureau represents the population of Illinois. An urban economist is interested in finding a model that describes the population of Illinois.

Year

Population

 

Year

Population

1900

4,821,550

 

1950

8,712,176

1910

5,638,591

 

1960

10,081,158

1920

6,485,280

 

1970

11,110,285

1930

7,630,654

 

1980

11,427,409

1940

7,897,241

 

1990

11,430,602
  1. Let t=0, 10, 20, etc. for the years.  Enter data and draw a scatter diagram
  2. Fit a logistic model to the data.  (** this model is VERY slow to compute**)
  3. Draw the function over the scatter diagram.
  4. Predict the population of Illinois in 2000.
  5. What appears to be the "carrying capacity" of Illinois

 VI.  Economics

The data that follows are the levels of the Consumer Price index for food items.

Year

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

CPI for food items

103.2

105.6

109.0

113.5

118.2

125.1

132.4

136.3

137.9

140.9

 

  1. Let t=0 be 1980, so 1984 is t=4.  Draw a scatter diagram of the data.
  2. Find a function of each of the following type to fit the relationship between time and the CPI data.  Record the function and its r-value.

 

i.  Exponential model

 

 

 

 

ii.  Power model

 

 

 

 

iii.  Logarithmic model

 

 

 

 

iv.  Linear model

 

 

 

 

v.   Cubic model

 

 

 

     c.   Identify your choice of  "best" model and use it to predict the CPI for food items for 1994.