CHAPTER 5: Regression. ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation. Chapter 5 Concepts. Regression Lines Least-Squares Regression Line Facts About Regression Residuals Influential Observations

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Regression Linear Regression Regression Trees. Characteristics of classification models. slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006). slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006). slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006).

Regression Linear Regression. slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006). slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006). slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006). slide thanks to Greg Shakhnarovich (CS195-5, Brown Univ., 2006).

Regression. 10-601 Machine Learning. Outline. Regression vs Classification Linear regression – another discriminative learning method As optimization Gradient descent As matrix inversion ( O rdinary L east S quares) Overfitting and bias-variance

Regression. What is regression to the mean? Suppose the mean temperature in November is 5 degrees What’s your best guess for tomorrow’s temperature? exactly 5? warmer than 5? colder than 5?. Regression. What is regression to the mean?

REGRESSION. What is Regression? What is the Regression Equation? What is the Least-Squares Solution? How is Regression Based on Correlation? What are the Assumptions for Using Regression?. What is Regression?. Predict future scores on Y based on measured scores on X

Regression. Several Explanatory Variables. Example: Scottish hill races data . These data are made available in R as data(hills, package=MASS) They give record times (minutes) in 1984 of 35 Scottish hill races, against distance

Regression. Correlation vs. Causation. Correlation. Causation. Means that one thing will cause the other. A statistical way to measure the relationship between two sets of data. Means that both things are observed at the same time.

Regression . single and multiple. Overview. Defined: A model for predicting one variable from other variable(s). Variables: IV(s) is continuous, DV is continuous Relationship: Relationship amongst variables

REGRESSION. Want to predict one variable (say Y) using the other variable (say X) GOAL: Set up an equation connecting X and Y. Linear regression linear eqn: y= α + β x, α = y-intercept, β = slope. We fit a line, regression line, to the data (scatter plot). y= α + β x.

Quality Kitchens. What problems do they face?How can they overcome these problems?Will correlations help them?. Regression: What is it?. Find the best straight line through the data pointsTry to explain one variable (dependent) using other variables (independent).. Regression. Like correlation,