W5: RQ for Predictions 2 Flashcards
What is a full regression equation involving 2 IVs
Yi = a + b1X1i + b2X2i + ei
What is a model regression equation involving 2 IVs
Y^i = a + b1X1i + b2X2i
What is an intercept in a regression equation. What is it signified by
a. Expected score on DV when all IVs = 0
What is a partial regression coefficient in a regression equation. What is it signified by
b1, b2. Expected change in IV variable for each unit change in an IV, holding constant scores on all other IV
What is the Sum of Squares in a regression equation. What is SS Total Indicated by
SStotal = SSreg + SSres
What is the aim of OLS. Use sum of squares to explain
Maximize SSreg; Minimize SSres
What is R^2.
Effect size measuring strength of prediction.
Formula of R^2. And what does it mean? What is another name for R^2
R^2 = SSreg/SStotal.
R&2 is the proportion of SStotal account for by SSreg.
Another name: Coefficient of Determination
What is the range of R^2
0 to 1. Closer to 1 = Stronger
To calculate a confidence on R^2, what are the 4 things we require
- ) Estimated R^2 value
- ) Numerator df (no. of IVs)
- ) Denominator df (n-IVs-1)
- ) Desired confidence level
Typically what is the biasness/consistency of R^2
IT is often biased, but consistent
How is an adjusted R^2 better than R^2
It is usually less biased, but we should always report both values
How do we make meaningful comparison between IVs in a multiple regression
- ) Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)
- ) Semi-Partial Correlations as effect size esimate
Making meaningful comparison between IVs in a multiple regression: Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)… When interpreting coefficients, what is the difference. When is this method useful?
Coefficients are interpreted in SD units
Example: One SD increase in variable X will increase in 0.5 SD decrease in variable Y.
Only useful when IV has an arbitrary scaling
Making meaningful comparison between IVs in a multiple regression: Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)… What is the intercept
Always 0
Making meaningful comparison between IVs in a multiple regression: Semi-Partial Correlations. Overview.
Correlation between DV and EACH focal IV, when effects of other IVs have been removed from focal IV.
Making meaningful comparison between IVs in a multiple regression: Semi-Partial Correlations. What is the SQUARED semipartial correlation
Indicates proportion of variation in DV uniquely explained by each IV.
What are the 4 statistical assumptions underlying the linear regression model
- ) Independence of Observations
- ) Linearity
- ) Constant variance of residuals/ homoscedastiscity
- ) Normality of Residual Scores
ILHN I love Honey Nougats
Statistical Assumption Linear Regression: Independence of Observations. How do we meet this
Met usually as long as
- ) Scores are not duplicated for bigger sample
- ) Responses on one variable does not determine person’s response to another variable
Statistical Assumption Linear Regression: Linearity. How do we meet this. There are 4 ways
- ) Scatterplot Matrix
- ) Scatterplot of Residual Scores
- ) Marginal Model Plots
- ) Marginal Conditional Plots
Statistical Assumption Linear Regression: Linearity. Scatterplot Matrix
Defined by variables being assigned to rows (Y-Axis) or Column (X-axis)
Examine scatter plots where DV is on the Y-Axis.
Non-Linearity would be a U shape.
Statistical Assumption Linear Regression: Linearity. Scatterplot of Residual Scores
Scatterplot of Residual Scores against
(1) Observed IV scores
(2) Predicted scores on DV
Statistical Assumption Linear Regression: Linearity. Marignal Model Plot
Marginal model plots of scores on the DV (Y) against scores on each IV and on predict scores (on X)
Statistical Assumption Linear Regression: Linearity. Marignal Conditional Plot. Why is it especiallyg good
It shows partial regression line after other IVs are partialled out.
Statistical Assumption Linear Regression: Homoscedasticity, What are the 2 ways
1,) Residual Plots (Similar to linearity)
2.) Breusch-Pagan Test
Statistical Assumption Linear Regression: Homoscedasticity, Residual Plots
Even distribution of residuals
Statistical Assumption Linear Regression: Homoscedasticity, Breusch-Pagan Test Overview
Null-Hypothesis Test that assumes the variance of residuals are constant/homoscedastic
Statistical Assumption Linear Regression: Homoscedasticity, Breusch-Pagan Test. What happens when the P value is small
We have reason to reject the assumption of constant variance for the residuals
Statistical Assumption Linear Regression: Normality of Residuals. What are the 3 ways
- ) qqplot
- ) Histogram
- ) boxplot
Statistical Assumption Linear Regression: Normality of Residuals. qqplot. What does it contain
Middle line: Strict normality
Side Lines: confidence
See residuals inside confidence
Statistical Assumption Linear Regression: Normality of Residuals. qqplot. What must we look out for
- ) Outliers: Vary large studentized residual value in absolute terms (High standard deviation)
- ) influential Case: If removed from analysis, results in regression coefficient changing notably in value
Statistical Assumption Linear Regression: Normality of Residuals. qqplot. How do we find influential cases
Cook’s D as a measure of overly influential values.
> 1: problem.
