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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