Week 3 Advanced multiple regression Flashcards
What is a coefficient?
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
What is the regression equation?
y = mx1 + mx2+ mx3+ b
or Y1 = B0 + B1X1 + B2X2 + B3X1X2 +e
Multiple regression formula is used in the analysis of relationship between dependent and multiple independent variables and formula is represented by the equation Y is equal to a plus bX1 plus cX2 plus dX3 plus E where Y is dependent variable, X1, X2, X3 are independent variables, a is intercept, b, c, d are slopes, and E is residual value.
When do we use a multiple regression?
Multiple regression analysis is used whenever we wish to model the relationship between one response variable and more than one regressor variable.
What is a regression analysis?
Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.
What is hierarchical regression?
A hierarchical linear regression is a special form of a multiple linear regression analysis in which more variables are added to the model in separate steps called “blocks.” This is often done to statistically “control” for certain variables, to see whether adding variables significantly improves a model’s ability to predict the criterion variable and/or to investigate a moderating effect of a variable
How do you do a hierarchical regression?
Using SPSS to do a linear regression and going through the ‘block process’.
What is a moderation analysis?
A moderator analysis is used to determine whether the relationship between two variables depends on (is moderated by) the value of a third variable
What type of variables are used in moderation analysis?
Quantitative and quasi-continuous variables
What are the key processes that you need to go through for moderation (multiplicative) interactions?
have a conceptual overview of interaction effects
centring the variables
computing the interaction term
entering predictors and interaction terms using hierarchical regression
interpreting SPSS output
plotting the interaction to aid interpretation.
What is an interaction?
An interaction is where the effect of one variable depends on the level of another. That is, the variables are not independent and so it is commonly referred to as the multiplicative interaction (literally multiplying two values together).
What are the four steps in testing interactions?
Step 1. Centre or standardise the variables you will be using. (original variable minus its mean) Descriptive - compute
Step 2. Compute the interaction term (new variable)
Step 3. Run the regression to get the SD’s, R2, sig, unstandardized (B) coefficients, standardized (β) coefficients, t-test and sig.
Step 4. Plot the interaction
What do you select in the dialogues when running an interaction test?
- the coefficients, the Bs and betas, which are what you actually require—remembering, of course, that you can’t really interpret the betas but you have to work with the Bs,
- zero order,
- the part and partial correlations, which help you identify if there’s something unique, and which variable is doing the heavy lifting, *collinearity diagnostics, and
- VIF
What does the output tell us in the interaction regression?
Descriptive stats box – SD’s needed for plotting later.
Model summary box Block 2 (the interaction term). A significant change in R2 means that the interaction is sig. (i.e. explains more variance, .154 would indicate a 15% increase in variance).
The coefficients box The Coefficients table provides us with the necessary information to predict the DV from IV, as well as determine whether the IV contributes statistically significantly to the model (by looking at the “Sig.” column). Furthermore, we can use the values in the “B” column under the “Unstandardized Coefficients” column, as shown below:
B = 0.176 – For every one unit increase in social identity score (IV) there is a ( 0.176 increase in anxiety score (DV).
β – For every one standard deviation unit increase in social identity there is a (eg. .204) standard deviation unit increase in anxiety score. This represents a small to medium effect (Cohen’s rule of thumb = .1 small, .3 medium, .5 large)
What is mediation?
Mediation analysis tests a hypothetical causal chain where one variable X affects a second variable M and, in turn, that variable affects a third variable Y. … Moderation analysis also allows you to test for the influence of a third variable, Z, on the relationship between variables X and Y
What is the difference between moderation and mediation?
Direct effects, as the name implies, deal with the direct impact of one individual on another when not mediated or transmitted through a third individual.
Indirect effects can be defined as the impact of one organism or species on another, mediated or transmitted by a third.
