# L5h - Bivariate data Looking for a linear relationship The...

This preview shows pages 1–6. Sign up to view the full content.

Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals MATH1005 Statistics Lecture 5 M. Stewart School of Mathematics and Statistics University of Sydney

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals Outline Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals
Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals Bivariate data Until now we have only considered univariate data , where each observation is a single number. We also come across situations where for each “individual”, two or more numbers are recorded: multivariate: more than one number; bivariate: exactly two numbers. For bivariate data we usually have an independent variable ( x ) and a dependent variable ( y ). Interest centres on how y behaves in relation to x . Rarely do the y -values behave as a simple function of x . Usually the best we can do is to say that the y -values behave approximately like a simple function of x . What does this mean?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals Decompose data Non-random part + random part We can perhaps decompose each y -value into a non-random part and a random part. More precisely, for each i = 1 , 2 , . . . , n we can write y i = f ( x i ) + e i where f ( · ) is some (simple) function and the resultant residuals or errors e 1 , e 2 , . . . , e n are randomly distributed about zero. The value f ( x i ) represents the “systematic” component of y i , dependent on x i while the residual e i (= y i - f ( x i )) represents the “noise”, should have no dependence on x i .
Bivariate data Looking for a linear relationship The least-squares line Using R Checking residuals What sort of function f ( · )? Is the relationship (i.e. the function f ( · )) monotone: do larger values of y tend to be associated with larger (smaller?) values of x ? Is the relationship approximately linear?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/28/2011 for the course SCIENCE 1002 taught by Professor Pu during the Three '11 term at University of New South Wales.

### Page1 / 18

L5h - Bivariate data Looking for a linear relationship The...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online