LinModRevF10 - 2 If so is this relationship causal Look at...

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1 Does Sprawl Cause Global Warming The State of California thinks it does –last Spring Gov. Schwarzenegger signed a bill designed to encourage denser evelopment as a way of reducing California’sCO2emissions development as a way of reducing California s CO2 emissions. 1. Do households that live in denser neighborhoods drive less? 2. If so, is this relationship causal? Look at 2001 National Household Travel Survey (NHTS) California Subsample. 1 300 100 200 hhmilesk 2 0 0 2 4 6 residential units (1000's) per sq mile - census block 150 .025000000372529 .1500000059604645 .699999988079071 5 2 4 6 3 50 Graphs by residential units (1000's) per sq mile - census block Tabulation of Annual Household Miles by Density (Table 1) Density Mean Std. Dev. Freq. 0.025 22.31732 19.96523 123 0.15 31.52017 22.66298 144 0.7 23.56423 17.40864 329 2 23.71209 22.65994 934 4 4 20.4344 17.87652 413 6 17.0395 21.48485 384 Total 22.4178 21.10111 2327
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2 T-test for significant differences Recall that  12 YY SE Y Y is a valid test statistic for testing whether the means of 2 subsamples are equal. To test that the mean of miles driven for those living in the 2000 residences per sq. mile group is different than the mean for those living in the greater than 6000 sq. miles group is 22 23.7 17 6.7 5.06 .55 1.2 22.7 21.5  5 934 384 Is the difference in means significant? A. Yes B. No C. Cannot tell without more information. 6 Models of Conditional Expectation Y i = 0 + 1 X i + u i , i = 1,…, n . If |0 ii Eu X Then:   01 ˆ | i YE YX X  (conditional expectation is linear in X ) Is this more or less restrictive than the (implicit) model in Table ? 7 1? A. More restrictive B. Less restrictive C. They are the same model Linear Regression: Some Notation and Terminology (SW Section 4.1) The population regression line : nnual Miles = + ensity Annual Miles 0 1 Density 1 = slope of population regression line = Annual Miles Density change in es or a unit change in ensity 8 = change in miles for a unit change in density Why are 0 and 1 “population” parameters ? We would like to know the population value of 1 . We don’t know 1 , so must estimate it using data.
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3 The Population Linear Regression Model – general notation Y i = 0 + 1 X i + u i , i = 1,…, n X is the independent variable or regressor Y is the dependent variable 0 = intercept 1 = slope e regression rror 9 u i = the regression error The regression error consists of omitted factors, or possibly measurement error in the measurement of Y . In general, these omitted factors are other factors that influence Y , other than the variable X This terminology in a picture : Observations on Y and X ; the population regression line; and the regression error (the “error term”): 10 The Ordinary Least Squares Estimator (SW Section 4.2) How can we estimate 0 and 1 from data? ecall that as the least squares estimator of olves Recall that Y was the least squares estimator of Y : Y solves, 2 1 min ( ) n mi i Ym By analogy, we will focus on the least squares (“ ordinary least 11 squares ” or “ OLS ”) estimator of the unknown parameters 0 and 1 , which solves, 01 2 ,0 1 1 min [ ( )] n bb i i i Yb b X  The OLS estimator solves: 2 1 1 min [ ( )] n i i i b X
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This note was uploaded on 11/28/2010 for the course ECON Economics taught by Professor Davidbrownstone during the Spring '10 term at UC Irvine.

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LinModRevF10 - 2 If so is this relationship causal Look at...

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