Chapter 10.1-10.3 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Outline Simple linear

Chapter 10.1-10.3 - Math3200 Intermediate Probability and...

This preview shows page 1 - 9 out of 29 pages.

Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University
Image of page 1

Subscribe to view the full document.

Outline Simple linear regression Model Ordinary least square Inference Nan Lin, Washington University 2
Image of page 2
Regression analysis Response (outcome/dependent) variable ? Predictor (explanatory/independent) variables 𝒙 = (? 1 , ? 2 , … , ? 𝑘 ) Assume ? 𝑖 = ? 𝜃 (? 𝑖1 , ? 𝑖2 , … , ? 𝑖𝑘 ) + 𝜖 𝑖 Goal: infer the regression function ? 𝜃 (⋅) using the data ? 𝑖 , 𝒙 𝑖 , 𝑖 = 1, … , 𝑛 Simplest form of the regression function: linear ? ? = ? + ?? Nan Lin, Washington University 3
Image of page 3

Subscribe to view the full document.

What model to use? Response variable Explanatory variable discrete continuous categorical Contingency table analysis Logistic regression counts Poisson (log-linear) regression continuous ANOVA (two-sample t-test) Linear regression
Image of page 4
Simple linear regression One response variable One explanatory variable Data: ? 𝑖 , ? 𝑖 , 𝑖 = 1, … , 𝑛 from 𝑛 independent subjects Model: ? 𝑖 = ? 0 + ? 1 ? 𝑖 + 𝜖 𝑖 , 𝑖 = 1, … , 𝑛, 𝜖 𝑖 ∼ ?(0, 𝜎 2 ) True regression line: ? ? 𝑖 = ? 0 + ? 1 ? 𝑖 ? 𝑖 ∼ ?(? 0 + ? 1 ? 𝑖 , 𝜎 2 ) Explanatory variable is regarded as non-random Goal: estimate (? 0 , ? 1 ) Nan Lin, Washington University 5
Image of page 5

Subscribe to view the full document.

Nan Lin, Washington University 6
Image of page 6
Linear regression: Assumptions Assumption 1: linearity Assumption 2: errors have equal variances Assumption 3: errors are normally distributed Assumption 4: errors are independent
Image of page 7

Subscribe to view the full document.

Remarks Linear model refers to ‘linear’ in regression coefficients E.g. ? = ? + ??
Image of page 8
Image of page 9

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes