1 / 28

Statistics 101

Statistics 101. Chapter 3 Section 3. Least – Squares Regression. Method for finding a line that summarizes the relationship between two variables. Regression Line . A straight line that describes how a response variable y changes as an explanatory variable x changes. Mathematical model.

lluongo
Download Presentation

Statistics 101

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. Statistics 101 Chapter 3 Section 3

  2. Least – Squares Regression • Method for finding a line that summarizes the relationship between two variables

  3. Regression Line • A straight line that describes how a response variable y changes as an explanatory variable x changes. • Mathematical model

  4. Example 3.8

  5. Calculating error • Error = observed – predicted • = 5.1 – 4.9 • = 0.2

  6. Least – squares regression line (LSRL) • Line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

  7. http://hadm.sph.sc.edu/courses/J716/demos/leastsquares/leastsquaresdemo.htmlhttp://hadm.sph.sc.edu/courses/J716/demos/leastsquares/leastsquaresdemo.html

  8. What we need • y = a + bx • b = r (sy/ sx) • a = y - bx

  9. Try Example 3.9

  10. Technology toolbox pg. 154

  11. Statistics 101 Chapter 3 Section 3 Part 2

  12. Facts about least-squares regression • Fact 1: the distinction between explanatory and response variables is essential • Fact 2: There is a close connection between correlation and the slope • A change of one standard deviation in x corresponds to a change of r standard deviations in y

  13. More facts • Fact 3: The least-squares regression line always passes through the point (x,y) • Fact 4: the square of the correlation, r2, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.

  14. Residuals • Is the difference between an observed value of the response variable and the value predicted by the regression line. • Residual = observed y – predicted y = y - y

  15. Residuals • If the residual is positive it lies above the line • If the residual is negative it lies below the line • The mean of the least-squares residuals is always zero • If not then it is a roundoff error • Technology Toolbox on page 174 shows how to do a residual plot.

  16. Residual plots • A scatterplot of the regression residuals against the explanatory variable. • To help us assess the fit of a regression line. • If the regression line captures the overall relationship between x and y, the residuals should have no systemic pattern.

  17. Curved pattern • A curved pattern shows that the relationship is not linear.

  18. Increasing or decreasing spread • Indicates that prediction of y will be less accurate for larger x.

  19. Influential Observations • An observation is an influential observation for a statistical calculation if removing it would markedly change the result of the calculation.

More Related