Download presentation

Presentation is loading. Please wait.

Published byDeirdre Gibbs Modified over 2 years ago

1
Monday, November 9 Correlation and Linear Regression

2
You will not leave the room until… you have understood that a correlation is a systematic quantitative expression of the proportion of explained and unexplained co-variation of two variables.

3
You will not leave the room until… you have understood that a correlation is a systematic quantitative expression of the proportion of explained and unexplained co-variation of two variables … and you love knowing this fact!

4
z y = z x When X and Y are perfectly correlated

5
We can say that z x perfectly predicts z y z y ’ = z x Or z y = z x ^

6
When they are imperfectly correlated, i.e., r xy ≠ 1 or -1 z y ’ = r xy z x

7
Example from hands…

9
When they are imperfectly correlated, i.e., r xy ≠ 1 or -1 z y ’ = r xy z x Y’ = b YX X + a YX b YX = r YX (s y / s x ) a YX = Y - b YX X __

10
When they are imperfectly correlated, i.e., r xy ≠ 1 or -1 z y ’ = r xy z x Y’ = b YX X + a YX b YX = r YX (s y / s x ) a YX = Y - b YX X __

11
Assumptions Linearity Homoscedasticity

12
Explained and unexplained variance SS total = SS explained + SS unexplained N NN

13
Explained and unexplained variance r 2 XY = 1 - σ 2 Y’ [ =unexplained] σ 2 Y [ =total] = σ 2 Y - σ 2 Y’ σ2Yσ2Y r 2 is the proportion explained variance to the total variance.

14
Point-biserial correlation r pb A correlation coefficient r that is calculated when one of the variables being correlated has only two levels, which are assigned arbitrary values (e.g., 0, 1). This coefficient is useful in expressing the effect size of an independent samples t- test, as the proportion of the variance in the dependent variable that is explained by the independent variable.

Similar presentations

OK

Linear Correlation (12.5) In the regression analysis that we have considered so far, we assume that x is a controlled independent variable and Y is an.

Linear Correlation (12.5) In the regression analysis that we have considered so far, we assume that x is a controlled independent variable and Y is an.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on blood stain pattern analysis course Ppt on hard gelatin capsule shells Ppt on charge-coupled device images Animal sounds for kids ppt on batteries Ppt on acid-base titration problems and solutions Ppt on primary and secondary market Ppt on electricity generation from solar energy Ppt on 60 years of indian parliament session Human rights for kids ppt on batteries Ppt on series and parallel circuits pdf