Desire to make ceteris paribus interpretations of β

Info icon This preview shows pages 9–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Desire to make ceteris paribus interpretations of β 1  include more explanatory variables in the regression l Leads to extension to multiple regression
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 Engel curve for food l Sample of 40 households with 3 family members l Data on l Y = weekly expenditure on food ($) l X = weekly income ($) l Cross-sectional data l Engel curve (demand function holding prices constant) Y i = β 0 + β 1 X i + ε i i =1, … , n 0 10 20 30 40 50 60 0 20 40 60 80 100 120 140 Income Expenditure
Image of page 10
11 Engel curve for food… l For these data l b 0 = 7.38 & b 1 = 0.23 l How do you interpret b 1? l What is predicted food expenditure for a household with weekly income of $100? l Why restrict to households with 3 people?
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
12 Assumptions of Classical Linear Regression Model l A1: Linear model l Y i = β 0 + β 1 X i + ε i , i = 1, … , n l A2: Random sampling l Have a random sample ( Y i , X i ) governed by model in A1 l A3: Sample variation in X l Values of X 1, X 2, … , X n are not all equal l A4: Zero conditional mean l E( ε i | X i ) = 0 l Key assumption because implies ε i & X i are uncorrelated l A2 & A4 mean we can think of X as fixed rather than random
Image of page 12
13 Assumptions of Classical Linear Regression Model… l A5: Homoskedasticity l Var( ε i ) = σ 2 l A6: Disturbances uncorrelated l Cov( ε i , ε j ) = 0, ( i not equal j ) l A7: Disturbances are normal (used for inference) l ε i ~ N (0, σ 2 ) l In some circumstances these assumptions will not be realistic l Further study of econometrics (beyond BES) l Would cover detection of violations of assumptions l Subsequent remedial methods
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
14 Classical Linear Regression Model (CLRM) l Given A1-A7 l Y i ~ N ( β 0 + β 1 X i , σ 2 ) l The (conditional) mean of Y depends on X l If β 1=0 what is β 0? l Given A1-A4 can show that OLS estimators are unbiased & consistent l Given A1-A6 OLS ‘best’ in a particular sense but beyond scope of BES
Image of page 14
15 Explaining variation in the dependent variable w w w w Y X X Y Y Y ˆ i - i i Y ˆ Y - X b b Y 1 0 ˆ + =
Image of page 15

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
16 Decomposition of variance ( 29 ( 29 ( 29 ( 29 ( 29 SSE SSR SST e Y Y Y Y X e Y Y Y Y Y Y Y Y i i i i i i i i i + = + = + - = - + = + - = - + - = - squares of sum error squares of sum regression squares of sum Total ˆ that show Can d unexplaine part by explained part deviation Total ˆ ˆ ˆ 2 2 2
Image of page 16
17 Standard error of estimate l Population variance σ 2 measures the spread around the population regression line l Standard error of estimate ( SEE ) is an estimator of σ l It measures fit of regression model l Low SEE  good fit estimator unbiased an ensure to estimated) be to need
Image of page 17

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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