1.) A researcher is examining the relationship between income inequality and homicide rates across nation-states. They hypothesize that as income inequality increases, a county's homicide rate will increase. Below are two regression models that test this hypothesis. The first model is a bivariate regression where a nation-state's homicide rate (measured as confirmed homicides per 100,000 people) as the dependent variable and their 2010 gini coefficient as the independent variable. (The gini coefficient is a standard measure of income inequality. A larger value indicates a more unequal distribution of income levels across a country's population and a smaller value indicate a more equal distribution. The values range from 0 to 100 and can be expressed as percentages: e.g, a gini coefficient of 0 means that the country's income distribution is 0% clustered, meaning that everyone receives the same income, while a gini coefficient of 100 means that the county's income distributions is 100% clustered-meaning that one person receives all of the country's income while everyone else gets $0.) The second model is a multiple regression. The model keeps the same variables from the bivariate regression, but now adds a series of control variables: the county's government spending on social services (“SocSpnd," measured in $1,000 per person-where, e.g., a value of 2 indicates the country spends an average of $2,000 per person), alcohol consumption per capita (“alcohol," measured as the average liters consumed per person), and guns per capita ("guns," measured as the number of guns in a county per person). Use the output below to answer the following questions. a. Interpret the coefficient for the gini variable in model 1. b. Interpet the coefficient for the gini variable in model 2. How is the interpretation different from the interpretation in model 1? c. The coefficient and statistical significance for the gini effect changed from the bivariate regression to the multiple regression. Does the change suggest that the control variables had a suppressor effect or a spurious effect on the relationship between income inequality and homicide rates in the bivariate regression? Explain. d. What would the change in the gini effect between models 1 and 2 have looked like if the impact of the control variables was the opposite of what you described in (c) above? Explain. e. Interpret the y-intercept for model 1, then interpret the y-intercept for model 2. How are they different/similar?
1.) A researcher is examining the relationship between income inequality and homicide rates across nation-states. They hypothesize that as income inequality increases, a county's homicide rate will increase. Below are two regression models that test this hypothesis. The first model is a bivariate regression where a nation-state's homicide rate (measured as confirmed homicides per 100,000 people) as the dependent variable and their 2010 gini coefficient as the independent variable. (The gini coefficient is a standard measure of income inequality. A larger value indicates a more unequal distribution of income levels across a country's population and a smaller value indicate a more equal distribution. The values range from 0 to 100 and can be expressed as percentages: e.g, a gini coefficient of 0 means that the country's income distribution is 0% clustered, meaning that everyone receives the same income, while a gini coefficient of 100 means that the county's income distributions is 100% clustered-meaning that one person receives all of the country's income while everyone else gets $0.) The second model is a multiple regression. The model keeps the same variables from the bivariate regression, but now adds a series of control variables: the county's government spending on social services (“SocSpnd," measured in $1,000 per person-where, e.g., a value of 2 indicates the country spends an average of $2,000 per person), alcohol consumption per capita (“alcohol," measured as the average liters consumed per person), and guns per capita ("guns," measured as the number of guns in a county per person). Use the output below to answer the following questions. a. Interpret the coefficient for the gini variable in model 1. b. Interpet the coefficient for the gini variable in model 2. How is the interpretation different from the interpretation in model 1? c. The coefficient and statistical significance for the gini effect changed from the bivariate regression to the multiple regression. Does the change suggest that the control variables had a suppressor effect or a spurious effect on the relationship between income inequality and homicide rates in the bivariate regression? Explain. d. What would the change in the gini effect between models 1 and 2 have looked like if the impact of the control variables was the opposite of what you described in (c) above? Explain. e. Interpret the y-intercept for model 1, then interpret the y-intercept for model 2. How are they different/similar?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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