Lecture 1: Multiple Linear regression (ARMS, Utrecht University)

Studies must be critically reviewed:

• Is the sample representative?
• Is it a reliable measure of variables?
• Is the correct analysis applied and are the results interpreted correctly?

Association does not mean causation!

Does the effect remain when additional variables are included? For this question we use a multiple regression.

Simple linear regression: involved 1 outcome, and 1 predictor.

Multiple linear regression: involves 1 outcome, and multiple predictors.

The relevance of a predictor is determined by:

1. The amount of variance explained (R2)
2. The slope of the regression line

A multiple regression model is also called an additive lineair model. 

There are 4 types of variables:

• Nominal
• Ordinal
• Interval
• Ratio

We distinguish these in:

Nominal & ordinal = categorical or qualitative

Interval & Ratio = continuous, quantitive, numerical

For MLR we use continuous outcome and continuous predictors. But categorical predictors can be included as dummy variables. Then you’d have to assign numbers to the categorical variables. Dummy variables only have values 0 and 1. 

If you have categorical predictors with more than 2 levels, you will need always 1 variable less than the amount of predictors to create a dummy variable.

Hierarchical MLR: using two or more models. If the first one is accounted for, it the second model better, etc.? You use multiple hypotheses for hierarchical MLR. 

Multiple correlation coefficient: correlation between y observed and y predicted.

The R² of the sample, is not a good indicator of the R² of the population. The more predictors, the more biased it is. If you correct the R²  for this, you call it the adjusted R². This variable you use when talking about the population.

With the R² chance you can see if the added predictors improve the prediction. Then after the output, you decide whether you want to continue with the first or second model.

B-coëfficient: tells you what the unique contribution of that variable is, given that all the others are also in the model.

Questions? Let me know in the contribution section!

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