STA302: Regression Analysis. Statistics Objective: To draw reasonable conclusions from noisy numerical data Entry point: Study relationships between variables.

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Presentation transcript:

STA302: Regression Analysis

Statistics Objective: To draw reasonable conclusions from noisy numerical data Entry point: Study relationships between variables

Data File Rows are cases Columns are variables

Variables can be Independent: Predictor or cause (contributing factor) Dependent: Predicted or effect

Simple regression and correlation Simple means one IV DV quantitative IV usually quantitative too

Simple regression and correlation High School GPAUniversity GPA ……

Scatterplot

Least squares line

Correlation coefficient r -1 ≤ r ≤ 1 r = +1 indicates a perfect positive linear relationship. All the points are exactly on a line with a positive slope. r = -1 indicates a perfect negative linear relationship. All the points are exactly on a line with a negative slope. r = 0 means no linear relationship (curve possible). Slope of least squares line = 0 r 2 = proportion of variation explained

r = 0.004

r = 0.112

r = 0.368

r = 0.547

r = 0.733

r =

r = 0.025

r =

Why -1 ≤ r ≤ 1 ?

A Statistical Model

One Independent Variable at a Time Can Produce Misleading Results The standard elementary tests all have a single independent variable, so they should be used with caution in practice. Example: Artificial and extreme, to make a point Suppose the correlation between Age and Strength is r = -0.96

Need multiple regression

Multiple regression in scalar form

Multiple regression in matrix form

So we need Matrix algebra Random vectors, especially multivariate normal Software to do the computation

Copyright Information This slide show was prepared by Jerry Brunner, Department of Statistical Sciences, University of Toronto. It is licensed under a Creative Commons Attribution - ShareAlike 3.0 Unported License. Use any part of it as you like and share the result freely. These Powerpoint slides are available from the course website: