Steffen grønneberg bi lecture 5 gra6036 4th february

  • No School
  • AA 1
  • 61

This preview shows page 13 - 26 out of 61 pages.

Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 13 / 61
Image of page 13

Subscribe to view the full document.

Contents 1 Linear regression Review of statistical inference Analysis of variance Simple linear regression Some conceptual comments Multiple linear regression Interaction, part I Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 14 / 61
Image of page 14
Simple linear regression Boys Girls Age Birth weight Age Birth weight 40 2968 40 3317 38 2795 36 2729 40 3163 40 2935 35 2925 38 2754 36 2625 42 3210 37 2847 39 2817 41 3292 40 3126 40 3473 37 2539 37 2628 36 2412 38 3176 38 2991 40 3421 39 2875 38 2975 40 3231 Means 38.33 3024.00 38.75 2911.33 How does gestational age influence birth weight? Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 15 / 61
Image of page 15

Subscribe to view the full document.

Simple linear regression Let us for the moment ignore gender, and plot gestational age versus birth weight. There is a clear linear trend. How should we best describe this observation? Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 16 / 61
Image of page 16
Simple linear regression A basic observation is that gestational age and birth weight are positively correlated . High X -values correspond to high Y -values: Birth weight increases with gestational age. Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 17 / 61
Image of page 17

Subscribe to view the full document.

Simple linear regression Gestational age and birth weight are correlated by 74 . 4 % , which is a fairly strong linear relationship. While r measures strength of linear relationship, let us try to estimate the actual linear relationship. Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 18 / 61
Image of page 18
Simple linear regression Recall that the equation for a straight line is y = β 0 + β 1 x where β 0 is the intersect with the y -axis, β 1 is the slope of the line. Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 19 / 61
Image of page 19

Subscribe to view the full document.

Simple linear regression Suppose we observe ( Y 1 , X 1 ) , ( Y 2 , X 2 ) , . . . , ( Y n , X n ) and plot the observations Often, scatter plots looks like a line distorted by some noise. That is, Y i = β 0 + β 1 X i | {z } straight line + ε i |{z} noise where ε 1 , . . . , ε n are “small disturbance terms”. Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 20 / 61
Image of page 20
Simple linear regression Suppose Y i = β 0 + β 1 X i + ε i with ε i “small disturbance terms”. What is the best fitting line to the data? Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 21 / 61
Image of page 21

Subscribe to view the full document.

Simple linear regression Suppose Y i = β 0 + β 1 X i + ε i with ε i “small disturbance terms”. What is the best fitting line to the data? Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 22 / 61
Image of page 22
Simple linear regression Suppose Y i = β 0 + β 1 X i + ε i with ε i “small disturbance terms”. What is the best fitting line to the data? We need to define what we mean by “best”! Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 23 / 61
Image of page 23

Subscribe to view the full document.

Simple linear regression theory Steffen Grønneberg (BI) Lecture 5, GRA6036 4th February 2016 24 / 61
Image of page 24
Simple linear regression The ordinary least squares (OLS) estimate ˆ Y = ˆ β 0 + ˆ β 1 X is intuitive, but we can show that if Y i = β 0 + β 1 X i + ε i for ε i N ( 0 , σ 2 ) , the OLS estimates are the optimal approximations of β 0 , β 1 (under several definitions of “best”).
Image of page 25

Subscribe to view the full document.

Image of page 26
  • Fall '19

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 You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes