Lecture 24: Partial correlation, multiple regression, and ...
[Pages:56]Lecture 24: Partial correlation, multiple regression, and correlation
Ernesto F. L. Amaral
November 21, 2017 Advanced Methods of Social Research (SOCI 420)
Source: Healey, Joseph F. 2015. "Statistics: A Tool for Social Research." Stamford: Cengage Learning. 10th edition. Chapter 15 (pp. 405?441).
Chapter learning objectives
? Compute and interpret partial correlation coefficients
? Find and interpret the least-squares multiple regression equation with partial slopes
? Find and interpret standardized partial slopes or beta-weights (b*)
? Calculate and interpret the coefficient of multiple determination (R2)
? Explain the limitations of partial and regression analysis
2
Multiple regression
? Discuss ordinary least squares (OLS) multiple regressions
? OLS: linear regression ? Multiple: at least two independent variables
? Disentangle and examine the separate effects of the independent variables
? Use all of the independent variables to predict Y ? Assess the combined effects of the independent
variables on Y
3
Partial correlation
? Partial correlation measures the correlation between X and Y, controlling for Z
? Comparing the bivariate (zero-order) correlation to the partial (first-order) correlation
? Allows us to determine if the relationship between X and Y is direct, spurious, or intervening
? Interaction cannot be determined with partial correlations
4
Formula for partial correlation
? Formula for partial correlation coefficient for X and Y, controlling for Z "#.% = "# - "% #% 1 - ")% 1 - #)%
? We must first calculate the zero-order coefficients between all possible pairs of variables (Y and X, Y and Z, X and Z) before solving this formula
5
Example
? Husbands' hours of housework per week (Y) ? Number of children (X) ? Husbands' years of education (Z)
Source: Healey 2015, p.409.
6
Correlation matrix
? The bivariate (zero-order) correlation between husbands' housework and number of children is +0.50
? This indicates a positive relationship
Source: Healey 2015, p.410.
7
First-order correlation
? Calculate the partial (first-order) correlation between husbands' housework (Y) and number of children (X), controlling for husbands' years of education (Z)
"#.% = "# - "% #% 1 - ")% 1 - #)% 0.50 - ? 0.30 ? 0.47
"#.% = 1 - ? 0.30 ) 1 - ? 0.47 ) "#.% = 0.43
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