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This multiple linear regression (MLR) learning project explains the concepts and principles of MLR and provides practical data analysis exercises.
[edit] Assumed knowledge
[edit] What is MLR?
[edit] MLR visualised
[edit] Assumptions
[edit] Statistics
MLR analyses produce several statistics, which are important to understand. It is also important to learn how to find and interpret these statistics from statistical software output.
[edit] Correlations
Big R is the multiple correlation coefficient and its interpretation is similar to that for little r which represents the linear correlation between two variables, ranging between -1 (perfect negative relationship) to 1 (perfect positive relationship), with 0 indicating no relationship. However R can only range from 0 to 1, with 0 indicating that linear relationships between the independent variables (IV) and the dependent variable (DV) don't explain any of the variance in the DV. Large values of R indicate more variance explained in the DV. R can be squared and interpreted as for r2, with a rough rule of thumb being .1 (small), .3 (medium), and .5 (large). These R2 values would indicate 10%, 30%, and 50% of the variance in the DV explained respectively. However, when generalising findings to the population, the R2 for a sample tends to overestimate the R2 of the population. Thus, adjusted R2 is recommended when generalising from a sample, and this value will be adjusted downward based on the sample size; the smaller the sample size, the greater the reduction. Finally, the statistical significance of R can be examined using an F test.
[edit] Regression coefficients
- B (unstandardised)
- β (standardised)
- Partial correlations
- Part correlations
- t, p
- Confidence intervals
[edit] Equation
- direct / standard
- hierarchical
- forward, backward
- stepwise
[edit] Advanced
- Partial correlations
- Use of hierarchical regression to partial out or remove the effect of 'control' variables
- Interactions between IVs
- Moderation and mediation
[edit] Writing up
- Assumptions
- Correlations
- Regression coefficients - e.g., see example table
- Causality
[edit] Data analysis exercises
[edit] See also
[edit] External links