1 / 10

Monday, October 8 Wednesday, October 10

Monday, October 8 Wednesday, October 10. Correlation and Linear Regression. z y = z x When X and Y are perfectly correlated. We can say that z x perfectly predicts z y. z y ’ = z x Or z y = z x. ^. When they are imperfectly correlated, i.e., r xy ≠ 1 or -1. z y ’ = r xy z x.

eron
Download Presentation

Monday, October 8 Wednesday, October 10

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, October 8 Wednesday, October 10 Correlation and Linear Regression

  2. zy = zx When X and Y are perfectly correlated

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

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

  5. Example from hands… • Let’s double-check our understanding of what a correlation coefficient is with respect to z-scores on X and Y variables.

  6. When we want to express the prediction in terms of raw units: zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (σy / σx) aYX = Y - bYXX _ _

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

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

More Related