3. Estimation
Nonparametric population features
Mean - income
Correlation – disease incidence and smoking
Ratio – income per household member
Proportion – proportion of ASCAP music played that is
produced by Dave Matthews
Parameters
Fitting distributions – mean and variance of lognormal
distribution of income
Parametric models of populations – relationship of loan
rates to attributes of minorities and others in Bank of
America settlement on mortgage bias
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
C ategory
Meatball 900000 900000 900000 14
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
2.3% Plain StDev 156865
Mushroom and Onion
Pepperoni
Mushroom 800000 800000 StDev 156865 800000
9.2%
21.8% 95 N 51 12 N 51
Sausage
AD 0.994 80
Pepper and Onion 700000 90 700000
3
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50
40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
4. Measurements as Observations
Population Measurement
Theory
The theory argues that there are Characteristics
meaningful quantities to be statistically Behavior Patterns
analyzed. Choices
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
C ategory
Meatball 900000 900000 900000 14
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
2.3% Plain StDev 156865
Mushroom and Onion
Pepperoni
Mushroom 800000 800000 StDev 156865 800000
9.2%
21.8% 95 N 51 12 N 51
Sausage
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50
40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
5. Application – Health and Income
German Health Care Usage Data, 7,293 Households, Observed 1984-1995
Data downloaded from Journal of Applied Econometrics Archive.
Some variables in the file are
DOCVIS = number of visits to the doctor in the observation period
HOSPVIS = number of visits to a hospital in the observation period
HHNINC = household nominal monthly net income in German marks / 10000.
(4 observations with income=0 were dropped)
HHKIDS = children under age 16 in the household = 1; otherwise = 0
EDUC = years of schooling
AGE = age in years
PUBLIC = decision to buy public health insurance
HSAT = self assessed health status (0,1,…,10)
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
C ategory
Meatball 900000 900000 900000 14
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
2.3% Plain StDev 156865
Mushroom and Onion
Pepperoni
Mushroom 800000 800000 StDev 156865 800000
9.2%
21.8% 95 N 51 12 N 51
Sausage
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50
40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
6. Observed Data
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
C ategory
Meatball 900000 900000 900000 14
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
2.3% Plain StDev 156865
Mushroom and Onion
Pepperoni
Mushroom 800000 800000 StDev 156865 800000
9.2%
21.8% 95 N 51 12 N 51
Sausage
AD 0.994 80
Pepper and Onion 700000 90 700000
6
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50
40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
7. Inference about Population
Population Measurement
Characteristics
Behavior Patterns
Choices
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
C ategory
Meatball 900000 900000 900000 14
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
2.3% Plain StDev 156865
Mushroom and Onion
Pepperoni
Mushroom 800000 800000 StDev 156865 800000
9.2%
21.8% 95 N 51 12 N 51
Sausage
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50
40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000