PPT-Lecture 5: Linear Regression, Confidence Intervals, Standard Errors

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 . Remember we saw The sample proportion will differ from the population proportion by more than the margin of error less than 5 of the time The Margin of Error for a sample of size n is 1 n Suppose we wanted to estimate a Population Mean rather than a e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Excel. GrowingKnowing.com © 2011. 1. GrowingKnowing.com © 2011. Estimates. We are often asked to predict the future!. When will you complete your team project?. When will you make your first million dollars?. GrowingKnowing.com © 2011. 1. GrowingKnowing.com © 2011. Estimates. We are often asked to predict the future!. When will you complete your team project?. When will you make your first million dollars?. NBA 2013/14 Player Heights and Weights. Data Description / Model. Heights (X) and Weights (Y) for 505 NBA Players in 2013/14 Season. . Other Variables included in the Dataset: Age, Position. Simple Linear Regression Model: Y = . GrowingKnowing.com © 2011. 1. GrowingKnowing.com © 2011. Estimates. We are often asked to predict the future!. When will you complete your team project?. When will you make your first million dollars?. TAU Bootstrap Seminar 2011. Dr. Saharon Rosset. Shachar Kaufman. Based on Efron and Tibshirani’s . “An introduction to the bootstrap”. Chapter 14. Agenda. What’s wrong with the simpler intervals?. John Krickl. Glenbrook North High School. Northbrook, IL. jkrickl@glenbrook225.org. DUALITY STICKS. Motivation. “. Using the same sample, a two-tailed hypothesis test with significance level α will . Chapter 6 Confidence Intervals Sections 6-1 and 6-2 Confidence Intervals for Large and Small Samples   VOCABULARY: Point Estimate – A single value estimate for a population parameter. Linear Regression Formula: . Used for prediction purposes for values beyond the region of the given data.. Equation: . and . are the means of x and y. is the standard deviation of x. is the covariance. Instructor: Prof. Wei Zhu. 11/21/2013. AMS 572 Group Project. Motivation & Introduction – Lizhou Nie. A Probabilistic Model for Simple Linear Regression – Long Wang. Fitting the Simple Linear Regression Model – . : A British biometrician, Sir Francis Galton, defined regression as ‘stepping back towards the average’. He found that the offspring of abnormally tall or short parents tends to regress or step back to average.. explore how to model an outcome variable in terms of input variable(s) using linear regression, principal component analysis and Gaussian processes. At the end of this class you should be able to . …. Regression Trees. Characteristics of classification models. model. linear. parametric. global. stable. decision tree. no. no. no. no. logistic regression. yes. yes. yes. yes. discriminant. analysis.