1 / 14

Monday, November 9

Monday, November 9. Correlation and Linear Regression. 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. You will not leave the room until….

claudia-vince
Download Presentation

Monday, November 9

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. zy = zx When X and Y are perfectly correlated

  5. We can say that zx perfectly predicts zy zy’ = zx Or zy = zx ^

  6. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx

  7. Example from hands…

  8. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _

  9. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _

  10. Assumptions • Linearity • Homoscedasticity

  11. SStotal = SSexplained+SSunexplained N N N Explained and unexplained variance SStotal = SSexplained + SSunexplained

  12. σ2Y’ [ =unexplained] σ2Y [ =total] Explained and unexplained variance r2XY = 1 - σ2Y - σ2Y’ = σ2Y r2 is the proportion explained variance to the total variance.

  13. Point-biserial correlation rpb • 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.

More Related