PPT-1 Lecture 15: Least Square Regression

Metric Embeddings COMS E69989 F15 Administrivia Plan PS2 Pick up after class 120gt144 auto extension Plan Least Squares Regression finish Metric Embeddings reductions for distances. . 12. Correlation. and . linear. . regression. y = . ax. + b. The. . least. . squares. . method. of Carl Friedrich . Gauß. .. D. y. 2. OLRy. D. y. Covariance. Variance. C. orrelation. coefficient. Introduction. Course Information. Your instructor: . Hyunseung. (pronounced Hun-Sung). Or HK (not Hong Kong . ). E-mail. : khyuns@wharton.upenn.edu . Lecture:. Time: Mon/Tues/Wed/. Thur. . at 10:45AM-12:15PM. Eric Feigelson. Classical regression model. ``The expectation (mean) of the dependent (response) variable Y for a given value of the independent variable X (or vector of variables . X. ) is equal to a specified mathematical function . Statistical models in . R. --- Recap ---. Stefan Bentink . bentink@jimmy.harvard.edu. Linear Regression Models. residual error. regression coefficient. dependent variable. intercept. independent variable. Classification pt. 3. September 29, 2016. SDS 293. Machine Learning. Q&A: questions about labs. Q. 1: . when are they “due”?. Answer:. Ideally you should submit your post before you leave class on the day we do the lab. While there’s no “penalty” for turning them in later, it’s harder for me to judge where everyone is without feedback. . Some Review and Some New Ideas. Remember the concepts of variance and the standard deviation…. Variance is the square of the standard deviation. Standard deviation (s) - the square root of the sum of the squared deviations from the mean divided by the number of cases. . Regression Wisdom. 1. Percentage of Men Smokers (18 – 24 years of age) from 1965 through 2009. The centre for Disease Control and Prevention track cigarette smoking in the US. How has the percentage of people who smoke changed since the danger became clear during the last half of the 20. Example Data Set. Y. X. 5. 20. 6. 23. 7. 27. 8. 33. 8. 31. 9. 35. 10. 43. 5. 19. 6. 25. 7. 29. 8. 31. Estimate two models. Model with y-intercept. Y = a b * X. Regression Statistics. Multiple R. 0.984. Price. and . Size. (in square feet) of 117 homes. A regression to predict . Price. (in thousands of dollars) from . Size . has r = 0.84. The residuals plot indicated that a linear model is appropriate.. Frank Wood, fwood@stat.columbia.eduLinear Regression Models Lecture 4, Slide 2Today: Normal Error Regression Model Frank Wood fwoodstatcolumbiaeduLinear Regression Models Lecture 3 Slide 2Least Squares MaxminimizationFunction to minimize wrt Minimize this by maximizing QFind partials and set both equal to zero go Lecture Outline. 1. Simple Regression:. . Predictor variables Standard Errors. Evaluating Significance of Predictors . Hypothesis Testing. How well do we know . ?. How well do we know . ?. Multiple Linear Regression: . 1. 2. Office Hours. :. More office hours, schedule will be posted soon.. . On-line office hours are for everyone, please take advantage of them.. . Projects:. Project guidelines and project descriptions will be posted Thursday 9/25.. . intensities. in . the. . claim. . frequency. and. Claim. . frequency. . regression. Overview. . pricing. (1.2.2 in EB). Individual. Insurance . company. Premium. Claim. Due to . the. . law.