Linear Regression Part 1: Fitting Lines INFO-1301, Quantitative - PowerPoint PPT Presentation

Linear Regression Part 1: Fitting Lines INFO-1301, Quantitative Reasoning 1 University of Colorado Boulder April 19, 2017 Prof. Michael Paul

Interpreting Linear Functions Fishermen in the Finger Lakes Region have been recording the dead fish they encounter while fishing in the region. The Department of Environmental Conservation monitors the pollution index for the Finger Lakes Region. The model for the number of fish deaths y for a given pollution index x is y = 9.607x + 111.958. What can we do with this function? • Estimate fish deaths for pollution values that we’ve never measured

Interpolation and Extrapolation y = 9.607x + 111.958 x is the pollution index Suppose we came up with this formula as an approximation after measuring fish deaths when the pollution index was: 1.1, 1.8, 2.5, 3.0, 3.9, 5.2 • What if we wanted to know deaths at x=3.5? Interpolation is when we use our linear function to estimate a value at a point in between points we have already measured

Interpolation and Extrapolation y = 9.607x + 111.958 x is the pollution index Suppose we came up with this formula as an approximation after measuring fish deaths when the pollution index was: 1.1, 1.8, 2.5, 3.0, 3.9, 5.2 • What if we wanted to know deaths at x=7.0? Extrapolation is when we use our linear function to estimate a value at a point outside of points we have already measured • Why might this fail?

Fitting Linear Functions Where does a linear function such as “y = 9.607x + 111.958” come from? Want to pick slope and y-intercept (y= mx + b ) such that the line is as close as possible to the true data points • Want to minimize distance from each point to the line • We’ll be more concrete next time

Fitting Linear Functions The process of picking the parameters of a function (e.g., m and b ) to make it is close as possible to a set of data points is regression If the function is linear (i.e., a line) then this is linear regression Statistical software such as MiniTab Express can perform linear regression automatically

Practice Regression in MiniTab Express.

Revisiting Correlation The Pearson correlation measures how strongly data points are related linearly A perfect correlation of 1 or -1 occurs the best-fit line exactly matches every data point • No error → perfect linear fit • 1 if slope is positive, -1 if slope is negative The size of the correlation tells you how well the points can be approximated with a line The sign of the correlation tells you the slope

Revisiting Correlation

R squared A common metric for measuring the quality of the fit of a line is called R 2 This is the square of the correlation (sometimes called R) between the true Y values and the Y values that you estimate with the y=mx+b line

Linear Regression Part 1: Fitting Lines INFO-1301, Quantitative - PowerPoint PPT Presentation

Linear Regression Part 1: Fitting Lines INFO-1301, Quantitative Reasoning 1 University of Colorado Boulder April 19, 2017 Prof. Michael Paul Interpreting Linear Functions Fishermen in the Finger Lakes Region have been recording the dead fish

Regression Methods 1. Linear Regression and Logistic Regression: definitions, and a common

Notes on the Non-linear Regression The model Non-linear regression models, like ordinary linear

LINEAR REGRESSION LINEAR REGRESSION - FROM A MACHINE LEARNING POINT OF VIEW 25 SIMPLE LINEAR

Logistic regression CS 446 1. Linear classifiers Linear regression Last two lectures, we studied

Which models can be fit with linear regression? Simple linear regression in Matlab X = rand(3,3)

Trendlines Simple Linear Regression Multiple Linear Regression Systematic Model

Outline The Simple Linear Regression Model (12.1) Fitting the Regression Line (12.2)

Unit 7: Multiple linear regression 1. Introduction to multiple linear regression Sta 101 - Fall

Linear Models for Regression Greg Mori - CMPT 419/726 Bishop PRML Ch. 3 Regression Linear Basis

Regression 1: Linear Regression Marco Baroni Practical Statistics in R Outline Classic linear

Overview IAML: Linear Regression The linear model Fitting the linear model to data

Learning From Data Lecture 8 Linear Classification and Regression Linear Classification Linear

Linear regression Linear regression is a simple approach to supervised learning. It assumes

10-601 Machine Learning Regression Outline Regression vs Classification Linear regression

Introduction to Linear Regression Rebecca C. Steorts September 15, 2015 Today

Secure Linear Regression on Secure Linear Regression on Vertically Partitioned Datasets

Revisiting Leakage Abuse Attacks Laura Blackstone Seny Kamara Tarik Moataz AROKI SYSTEMS

GEARNET: Summary and successes of a new approach to conservation engineering Michael Pol

NFWF National Fish and Wildlife Foundation Presentation by Gulf Restoration Network Payout

CSI-FiSh: Efficient Isogeny based Signatures through Class Group Computations Ward Beullens

Its time to go scoop me some mud! Its time to go scoop me some mud! STOP

DIOS A distributed Operating System for your Data Centre Malte Schwarzkopf @ms705 University

Autism Spectrum Disorder in Child ren and Adolescents Aura Lee A. Motus, M.D. UNM

Total Wellness 6 Easy to implement initiatives for a longer, healthier, more productive life Why