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Multiple Linear Regression: Bivariate & Multivariate Data, Interaction & Model Selection, Study notes of Statistics

International University Institute of Luxembourg (IUIL)Statistics

Multiple linear regression, a statistical method used to analyze the relationship between a response variable and multiple explanatory variables. the importance of having a common sign between the regression coefficient b and correlation coefficient r when dealing with multiple predictors. It also explains the concept of interaction terms and the goal of explaining as much variation in the response variable as possible using a linear model and multiple explanatory variables. an example of blood pressure being predicted by age and BMI, and includes instructions for further reading and assignments.

Typology: Study notes

2021/2022

Uploaded on 08/05/2022

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Lecture 27: Multiple Linear
Regression
Chapter 3: Bivariate, Multivariate
Data and Distributions
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Lecture 27: Multiple Linear

Regression

Chapter 3: Bivariate, Multivariate Data and Distributions

An Important Fact

  • Because of their connection (review from Mon’s notes), b and r have the common sign.

Multiple Linear Regression: the model For a sample of size n , fit a hyper-plane: There are k -1 explanatory variables, k parameters. Goal: There is a total amount of variation in y (SSTO). We want to explain as much of this variation as possible using a linear model and our multiple explanatory variables.

First order Model with two predictors

Continued

Interaction Terms in MLR

Model Selection

After Class…

  • Review Ch.
  • Finish Hw#10 (by this Wed) and Lab #
  • Self-reading: Section 3.6 (not covered in exams)
  • Read Ch. 11