Lecture 15; Regression I Flashcards
What is the purpose of regression analysis?
To describe the relationship between two variables and predict values of one variable from another.
What are the two types of correlation coefficients mentioned?
- Pearson (scale)
- Spearman (ordinal)
What does a positive relationship in regression indicate?
As one variable increases, the other variable also increases.
What does a negative relationship in regression indicate?
As one variable increases, the other variable decreases.
What is a bivariate regression?
A regression analysis involving two variables where change in x causes a corresponding change in y.
Variables are asssymetric
What are the requirements for conducting regression analysis?
- Relationship between the variables must be linear
- Data must be scale data
What is the independent variable in regression?
The variable that influences the dependent variable, plotted on the horizontal (X) axis.
What is the dependent variable in regression?
The variable that is influenced by the independent variable, plotted on the vertical (Y) axis.
What is an endogenous relationship between two variables
Direction of causation goes both ways (mutual causation)
Regression requires exogenous relationship
What is a residual in regression?
The vertical deviation from the regression line.
What is the equation of a line in regression?
Y = mx + b
What does the regression coefficient (slope) represent?
How many units the dependent variable will change for a one-unit change in the independent variable.
Regression slopes are sensitive to the units of measurement, how do you account for that?
Comopute a standardised coefficient
With multivariate regression, what does each independent variable rregression coeffficient represent
Regression effect when all other variablere held constant
What is the importance of the coefficient of determination (R-squared)?
It indicates the proportion of the variation in the dependent variable explained by changes in the independent variables.
What is the difference between R and R^2
R^2 explains how much off the entire regression model explains the Y. Pearson R only poiints to one x.
Pearson R, variables are symmetrical
R^2, variables are assymmetrical
What does a high and low p-value indicate in regression analysis?
High P Value:
High probability thatt the outcome would be observed if the null were true. (Observed outcome is not different than H0, Cannot reject H0)
Low P Value:
There is a low probability that the observed outcome would occur if the null hypothesis were true. (Observed outcome is diffferent than H0, Reject H0)
Interpret the parameters
What is the significance of statistical significance in regression?
It tests the probability that the effect observed is real in the population.
In regression, what does the term ‘multiple regression’ refer to?
A regression analysis that involves more than one independent variable influencing the dependent variable.
What is the purpose of standard errors for coefficients in regression?
To calculate confidence intervals for a regression coefficient.
What does the term ‘exogenous variable’ refer to?
Another name for the independent variable that is assumed to influence the dependent variable.
What is the difference between Pearson R and R-squared?
- Pearson R: Percentage of variation in y explained by variation in x (symmetrical)
- R-squared: Percentage of variation in y explained by the regression model (asymmetrical)
What is the significance of the direction of causation in regression?
It must go one way without reverse causality between the variables.
