Multiple Linear Regression
NR120.508 Biostatistics for Evidence-based Practice
Multiple Linear Regression
Song Ge
BSN, RN, PhD Candidate Johns Hopkins University School of Nursing
nursing.jhu.edu
Learning Objectives
By the end of this module, you will be able to:
1. Articulate assumptions for multiple linear regression
2. Explain the primary components of multiple linear regression
3. Identify and define the variables included in the regression equation
4. Construct a multiple regression equation 5. Calculate a predicted value of a dependent
variable using a multiple regression equation
Learning Objectives Cont'd
6. Distinguish between unstandardized (B) and standardized (Beta) regression coefficients
7. Distinguish between different methods for entering predictors into a regression model (simultaneous, hierarchical and stepwise)
8. Identify strategies to assess model fit 9. Interpret and report the results of
multiple linear regression analysis
Review of lecture two weeks ago
? Linear regression assumes a linear relationship between independent variable(s) and dependent variable
? Linear regression allows us to predict an outcome based on one or several predictors
? Linear regression allows us to explain the interrelationships among variables
? Linear regression is a parametric test
How to choose X and Y?
? Y can be regressed on X ? X can be regressed on Y ? The regression is not symmetric ? The choice of which regression to
perform depends on the scientific question: Is X to be used to explain or predict Y? ? Is Y to be used to explain or predict X? (e.g. Does poor health status explain high pollution level?)
Linear Regression Assumptions
1. Independent variable can be any scale (ratio, nominal, etc.)
2. Dependent variable need to be ratio/interval scale
3. Dependent variable need to be normally distributed overall and normally distributed for each value of the independent variable
4. If dependent variable is not normally distributed, we can transform it
Review: Normal distribution
Example of transformed data
Positively skewed Normally distributed
Method Log
Math Operation
ln(x) log10(x)
Square root x
Square
x2
Cube root
x1/3
Reciprocal 1/x
Good for: Bad for:
Right
Zero values
skewed data Negative
values
Right
Negative
skewed data values
Left skewed Negative
data
values
Right skewed data Negative values
Not as effective as log transform
Making small Zero values
values
Negative
bigger and values
big values
ll
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