MLR
What are the three ways to interpret Multiple R squared?
1. The correlation between the observed and the predicted Y scores 2. The degree of association between Y and an optimal linear combination of IVs 3. The proportion of variance in Y that is accounted for by all of the IVs (best definition)
What are four examples of time when X could reasonably cause Y.
1. Y starts after X ends. 2. X is linked to an earlier step in a well-known sequence 3. X (gender/ethnicity) never changes during the lifetime but Y does (perceptions) 4. IF x is relatively stable, hard to change, or has many possible consequences and Y is volatile, easy to change, or has few consequences.
What should you report, R squared or adjusted R squared?
Adjusted R squared.
Why do we call MLR linear?
Because it is based on a linear equation.
What types of variables are our independent variables?
Categorical (multiple categories or dichotomous) Continuous Ordinal (likert, though there is some controversy here)
In MLR, dependent variables must be _________________.
Continuous
How does MLR help us with prediction?
It allows us to find an equation for the regression line that allows you to make predictions about your dependent variables
How does MLR help us with causal analysiS?
It helps us determine whether a predictor variable really affects the dv, and to estimate how strong the effect is while controlling for nuisance variables.
What is the problem with Rsquared?
It is a biased estimate of the true squared multiple correlation (SMC) in the population (squared)
What is multiple linear regression?
It is a linear regression analysis with two or more independent variables.
What does it mean when I put a subscript number next to Rsquared in parentheses?
It means the resulting Rsquared when all predictors except the one in the parentheses are include din the equation.
What are the two purposes of multiple linear regression?
Prediction Causal Analysis
______ tells us about the fit of our overall model.
Rsquared
What is the squared Mulitple Correlation?
Rsquared! The Multiple Rsquared.
What is shrinkage?
The among by which Rsquared is reduced when it is adjusted.
What is the unstandardized regression coefficient (b)?
The average increase or decrease in Y for every one-unit increase in X, holding the influence of all other predictor variables constant. (YEAH!)
What is the standardized regression coefficient (beta!)?
The average increase or decrease in Y in standard deviation units for every one standard deviation increase in X, holding the influence of all other predictor variables constant
The dependent variable is ____________.
The outcome variable or y
The independent variable is ____________.
The predictor variable or X
What is r squared?
The proportion of variance in Y that is accounted for by X.
What is the squared semi partial correlation coefficient (sr squared)?
The unique proportion of the total variance in Y that is explained by a particular X or The increment of Rsquared due to X
What is the squared partial correlation coefficient ( Pr squared)?
The unique proportion of variance in Y that is explained by a particular X.
True or False Even if a true relationship is not entirely linear, a linear equation often provides a good approximation.
True
True or False Linear equations can be modified to include certain types of non-linearity
True
R squared is biased. What can we do about it?
We can adjust R squared to make it an unbiased estimate of the population SMC (adjusted Rsquared will be smaller than regular Rsquared)
In causality you must be careful to choose Xs that could reasonably cause __________.
Y
sr squared is the unique proportion of the total variance in _____ that is explained by a particular ______.
Y X
Can we use other types of equations that are not linear for regression?
Yes, but we start with linear because it is the simplest (science dis driven by parsimony)
_______ is the point where the regression line crosses the y axis.
a
What type of variable is our dependent variables in multiple linear regression?
continuous
A multiple linear regression is a linear regression analysis with two or more ________________ variables.
independent
Small ___ and large ____ lead to more shrinkage.
n k
What is the increment in Rsquared due to X, divided by the variance in Y that isn't explained by other predictors?
pr squared
Shrinker will be greater for ______ (smaller/larger) values of Rsquared than for _____ (smaller/larger) values.
smaller larger
________ is the increment of Rsquared due to X.
sr squared
Causality can only be established by _____________.
study design (not by a statistical analysis)
sr squared is the unique proportion of the__________________ that is explained by a particular X
total variance in Y