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# Math stat 3

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### Math stat 3

1. 1. Statistical Inferenceand RegressionAnalysis: GB.3302.30Professor William GreeneStern School of BusinessIOMS DepartmentDepartment of Economics
2. 2. Statistics and Data Analysis Part 3 – Estimation Theory
3. 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 FrequencyPepper 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. 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 FrequencyPepper 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. 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 FrequencyPepper 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. 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 FrequencyPepper 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. 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 FrequencyPepper 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