Multivariate OLS and Logistic Regression

Multivariate OLS Regression Model

Multivariate OLS and Logistic Regression

Answer the following:

You are interested in explaining the violent crime rate of states in 2015, and you wish to build a model that includes several variables at once.  

Estimate a multivariate OLS regression model in which Violent_Crime is the dependent variable and the following variables are independent:  state income per capita in thousands of dollars (Income_PC), percentage of the population with a bachelor’s degree (Bach_Degree), state unemployment rate (UNEMP), and Republican governor (REPGOV).  

Violent_Crime is a continuous variable measured as the number of violent crimes committed per 100,000 population.

Income_PC is a continuous variable measured in thousands of dollars.

Bach_Degree is a continuous variable measured as a percentage.

UNEMP is a continuous variable measured as a percentage.  

REPGOV is a dichotomous (nominal) variable with Republican governors coded as a “1” and other governors (Democrats and Independents) coded as a “0.”

Steps:

• Select analyzefrom the top menu bar.  
• From the drop-down box, select regression, then click on linear.  
• A dialog box should appear.  Select the variable named VIOLENT_CRIME and select the arrow that points to the right for the dependent variable box.  Select the name of first independent variable and select the arrow that points to the right for the independent variable box.
• Repeat Step 3 until you have added all of the independent variables you want included in the model
• Click ok. 

Based on the output, answer the following questions:

a.)  What is the equation of the regression line?  Identify a and the bs in the equation Violent_Crime = a + b(INcome_PC) + b(Bach_Degree) + b(UNEMP) + b(REPGOV).

b.)  Interpret each regression coefficient.

c.)  Interpret the constant term (the intercept).

d.)  Are any of the relationships mentioned above statistically significant?  Which ones?  (Use a 95 percent confidence level.)

e.)  What is the Adjusted R²Â value?  What does this value tell us?

You are interested in explaining why individuals oppose the death penalty for situations involving murder.  To attempt to answer this question, you analyze data taken from the 2014 General Social Survey, which includes responses to several items that measure individuals’ policy attitudes.

Using the SPSS file named “2014 GSS Dataset,” please provide the descriptive statistics for the variable CAPPUM.       

Steps:

• Select analyze from the top menu bar.  
• From the drop-down box, select descriptive statistics, then click on frequencies.  
• A dialog box should appear.  Select the variable named CAPPUM and select the arrow that points to the right.
• Click ok. 

Based on the output:

• Report the number of valid responses and the number of missing responses.

• Of the valid responses, what percentage of respondents “favor” using the death penalty as a penalty for murder?

Based on your review of the literature, you suspect that people’s level of education may influence their opinions concerning capital punishment.

Relying on data from the 2014 General Social Survey (use the SPSS file named “2014 GSS Dataset”), estimate a binary logistic regression model in which CAPPUN is the dependent variable and DEGREE is the independent variable.  

CAPPUN is a dichotomous variable with those individuals who favor the death penalty coded as a “1” and those who oppose the death penalty coded as a “2.”  

DEGREE is an ordinal variable measured as the level of education of the respondent (less than high school, high school, junior college, bachelor, graduate).  Higher values indicate more education.  

Steps:

• Select analyzefrom the top menu bar.  
• From the drop-down box, select regression, then click on binary logistic.  
• A dialog box should appear.  Select the variable named CAPPUN and select the arrow that points to the right for the dependent variable box.  Select the variable named DEGREE and select the arrow that points to the right for the independent variable box.
• Click ok.  

Based on the output, answer the following:

a.)  Interpret the regression coefficient by computing the odds ratio.  (Do not worry about the constant term.)

b.)  Is the relationship between the respondent’s degree and their views concerning the death penalty statistically significant?  

c.)  What is the Nagelkerke R²Â value?  What does this value tell us?

You remain interested in explaining individuals’ opposition to the death penalty, and you wish to build a model that includes several variables at once.

Estimate a binary logistic regression model in which CAPPUN is the dependent variable and the following variables are independent:  educational attainment (DEGREE), age (AGE), sex (SEX), and political party affiliation (PARTYID).  

CAPPUN is a dichotomous variable with those individuals who favor the death penalty coded as a “1” and those who oppose the death penalty coded as a “2.”  

DEGREE is an ordinal variable measured as the level of education of the respondent (less than high school, high school, junior college, bachelor, graduate).  Higher values indicate more education.  

AGE is a continuous variable measured in the number of years comprising the respondent’s age.

SEX is a dichotomous variable with males coded as a “1” and females as a “2.”

PARTYID is an ordinal variable measured as a seven-point likert scale ranging from “Strong Democrat” to “Strong Republican.”  (Note that higher values along this scale correspond to being more strongly Republican.)  

Follow the same procedure as above in Question 3, except this time add additional independent variables by selecting and clicking the arrow that points to the right for the independent variable box.  

Based on the output, answer the following:

a.)  Interpret the regression coefficients by computing the odds ratio for each independent variable.  (Do not worry about the constant term.)

b.)  Are any relationships between the independent variables and individuals’ views concerning the death penalty statistically significant?  

c.)  What is the Nagelkerke R²Â value?  What does this value tell us?