Week 7 Ch 20 Multiple Regression Hills Flashcards
Use criterion or outcome instead of
DV
Multiple regression is…
An extension of Bivariate correlation and regression beyond two variables to the situation where the researcher wants to establish the relationship between ONE DV (Y) and SEVERAL IVs (X1, X2, X3, X4, etc).
Use PREDICTORS instead of
IVs
What does the multiple regression correlation coefficient measure?
It measures the relationship between one criterion DV and several predictors IVs.
What is the difference between r and R?
The symbol for the Bivariate regression coefficient (Pearson’s) is r.
The symbol for the multiple correlation coefficient is R.
While r has a range of -1 through to 1,
R only has a range of 0-1 (from relationship to perfect relationship).
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R squared…. R2
In multiple regression…
R2 is the squares multiple correlation (RSQ or SMC) and represents the proportion of variance in the DV that is explained by the. Linear combination of the IVs.
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Why a multiple regression equation?
The multiple regression equation is for the line of best fit that allows the best possible prediction of the DV scores on the IVs.
Y (hat) stands for the predicted DV score.
Y (hat) = a + b1X1 + b2X2 + b3X3 etc
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Residuals are…
Residuals are the difference between the actual Y score and the predicted Y (hat) score, that is, Y-Y(hat).
The greater the R the smaller the combined residuals.
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R2..
R squared…
R2 corresponds to variance explained.
Residuals correspond to variance UNEXPLAINED.
What is the story with us correlated IVs?
When IVs are us correlated, their individual correlations With the DV are additive, and to find R2 one simply adds the R2 values for each IV.
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What happens when IVs are correlated?
When IVs are correlated among themselves, their individual correlations with the DV are NOT ADDITIVE.
Correlated IVs are common in the behavioural sciences.
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When IVs are correlated, what is the researcher interested in?
When IVs are correlated, the researcher is interested in their unique relationship with the DV, that is their part of the DV that cannot be attributed to, or is associated with, their relationship to other IVs.
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What is the squared semi-partial correlation?
The portion of R2 that is uniquely attributable to X2.
It reflects the semin-partial correlation of X2 with Y.
See Venn diagram.
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Terminology of semi-partial correlations…
Although strictly speaking, the unique relationships are semi-partial correlations, some texts speak in terms of part correlations, and part regression coefficients.
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What is a semi-partial correlation?
A semi-partial correlation is the relationship between X1 and Y, when shared variance with other X variables has been removed from X1 (and so on for other x variables).
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