Lecture 1, What is Multiple Regression Analysis (MRA)?

What will we learn in this course?

All the techniques we will discuss in the upcoming weeks have one thing in common: They explore the relationship among several variables. Up until now, we have always focused on 2 variables; but in this course, we will deal on 3.

We will learn how to choose a method for a specific problem, how to perform data analysis, to understand the output, to understand the theoretical properties, to interpret the parameters of the technique, and to judge if the interpretations are valid (so check for assumptions).

When do we do multiple regression analysis?

When we want to predict Y from X_i variables, in the case of interval variables, then we do multiple regression anaysis.Binary variables are variables with only 2 categories; and they can be included in the analysis both as nominal and interval variables. An example of a multiple regression model; Can depression (Y) be predicted from life events (X₁) and/or coping style (X₂)?

What is the multiple regression equation?

A multiple regression equation has the following formula:

Y = b0 + b1X1 + b2X2 + ... + bkXk + e

We choose the regression line such that the summed difference between Y and the predicted Y is as small as possible. With two predictors, we make a regression plane instead of a regression line; a three-dimensional space.

What are the hypotheses in multiple regression analysis?

H₀: b₁ = b₂ = ... = b_k = 0      

H_a; at least one b_j ≠ 0

So, the null hypothesis is that there

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