Updates exam 2 for advnace research methods

What are the 5 assumptions in a Regression

1. True Model

2. Variables

3. Specification

4. Measurement

5. Error Term

True Model

This is an assumption that is solved by theory and focuses on including all relevant variables while excluding all irrelevant variables

Who do you solve True Model

Theory

What are the dependent variables in a regression assumption

Interval Ratio

What are the Independent Variables in a regression Assumptions

Interval, Ratio, Dummy, Dichotomous, Binary, this allows for nominal and ordinal variables to be added as long as they are coded 0 and 1

What are the problems with variables in Regression

Perfect Multicollinearity and Truncation

Perfect Multicollinearity

occurs when independent variables are perfectly correlated, meaning one variable is a linear combinations of others - fixed by theory

Truncation

When observations are dropped from your dataset because they fall above or below a certain threshold, meaning that portion of the population is entirely invisible to your analysis - fixed by theory

Specification

The relationship between X and Y in a regression is assumed to be linear. However, a line is not always the best representation of a relationship; we need to trick the regression to make a non-straight line. Omitting relevant variables leads to changes in the beta and t-value, which leads to a change in the line. Including irrelevant variables creates noise and error. You fix this error by squaring a term to fix the line and you know to do this by your theory

How do you fix Specfication

Square a term

How do you know you have Specification

Theory

Measurement

Make sure that the way variables are being interpreted and understood is representative of the theory

How do you know your measurement is correct

Theory

What violates the Expected Value of Error Term

When relevant, independent variables are omitted

How does a violation of the expected value of error term impact the regression

Screws up the intercept, which then leads to the interpretation of the hypothesis as wrong. If the expected value is greater than zero, it will have a positive bias to the intercept; if it is less than zero, it has a negative bias to the intercept

What is the solution to the violation of the expected value of error term

Including all necessary independent variables will fix the graph which relay on theory

What violates the Covariance Between Independent Variables and the Error Term

This error term appears when independent variables are correlated with the error term

How does a violation of the Covariance between Independent Variables and the Error terms impact the regression

The consequences include biased coefficients and unreliable hypothesis this is because omitting a correlated variable creates an effect on the beta, while omitting a slightly correlated variable affects the alpha and beta

How do you fix the covariance between the independent variables and the error term

You must relay on theory to include all relevant variables

What violated the variance of the error term (Homodcedasticity)

when the variance of the error term is not constant across observations

What impact does Variance of the Error Term (Homoscedasticity) have on the regression assumption

Residuals are not randomly scattered, which can bias the estimation of the standard error

How can you fix Variance of the Error Term (Homoscedasticity)

You first need to run a het test to see if Homoscedasticity is present, if it is present, then you need to run a robust test to fix the distributions of the standard errors

When does a violation in Covariance of Error Terms (Autocorrelation) happen

occurs when error terms are correlated with themselves. This specifically happens with time series models.

How does covariance among error terms impact a regression model

Impacts the hypothesis test, t-statistics, and standard error, making it unreliable

How do you test for Covariance of error terms

Use the Durbin-Watson Test, which ranges from 0 to 4. A value near 2 indicates no autocorrelation, values near 0 indicate positive autocorrelation, and values near 4 indicate negative autocorrelation.

How do you fix a Covariance of Error Terms

Include a dependent lagged variable to adjust the model so that error term becomes uncorrelated

Multiple Regression

How the dependent variable changes based on multiple independent variables along with a random error term.

How to fix multiple regression

reduce error term by using theory to ensure that all relevant variables are included and irrelevant ones are excluded

What Variables for Chi-Square

Nominal Ordinal

What do you report as signficant in the Chi Square

Chi Square

How do you interpret a relationship in Chi-Square

Significant- Dependent

Not Significant - Independent

What Variables are used in ANOVA

Dependent: Interval Ratio

Independent: Nominal Ordinal

What do you report as significant in ANOVA

F vlaue

What do your report in and ANOVA (before interpreting)

If the variables are different from each other

What variables can be used in a T-Test

Dependent: Interval Ratio

Independent: Nominal Ordinal

What do you report before analyzing the t-value

You chose which test you will be analyzing: less than, different, or more than

What are the two main aspects of a t-test interpretation

t- value and different

What variables can be used in a regression

Dependent: Interval Ratio

Independent: Interval ratio, dummy, dichotomous, binary

What do you have to do before analyzing a f-value in a regression

Perform a Het test to test for homoscedasticity, and if present, then use a robust test to correct the distribution of the standard errors

What are the three main parts of a regression interpretation

R2 or Adjusted R2, F value, constant comparison