5 a big effect in an economic sense l interpretation

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1 = 18.5 a big effect in an economic sense? l Interpretation of intercept estimate ( b 0=963.2) l Predicted salary for CEO of firm with roe = 0 is 963.2 ($963,200) l Beware l Sometimes intercepts don’t make sense l Suppose Y = CEO salary & X = age of CEO? l Regression models are approximations l In this case only interested in the approximation for adults
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26 SIA: Weekend effect in Australian births l Recall SIA: Baby Bonus l Have Australian Bureau of Statistics data on daily births in Australia l Consider 152 days in 2004, Jan 1 to May 31 l These days are before the baby bonus impact l Time series plot of data shows clear weekend effects l How big is the weekend effect?
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27 SIA: Weekend effect in Australian births… Daily births in Australia 2004: January 1 to May 31 0 100 200 300 400 500 600 700 800 900 1000 0 20 40 60 80 100 120 140 160 Time Births
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28 SIA: Weekend effect in Australian births… l Let Bt be number of births on t th day, t =1,…,152 l Define dummy variable Dt l Dt = 1 if t th day is a Saturday or Sunday l Dt = 0 otherwise (ie a weekday) l Specify our regression model as l Bt = β 0 + β 1 Dt + ε t l What is the interpretation of β 0 & β 1? l E ( Bt | Dt = 0) = β 0 & E ( Bt | Dt = 1) = β 0 + β 1 l β 1 is the difference between means of weekend & weekday births
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29 SIA: Weekend effect in Australian births… l Regression model fits the data well l R 2 = 0.8109  model explains 81% of the variation in daily births l Mean births on weekdays estimated to be 739 l Results indicate 258 fewer births on weekends l Weekend effect is large in a practical sense l t -statistic indicates very precisely estimated Regression Statistics Multiple R 0.9005 R Square 0.8109 Adjusted R Square 0.8097 Standard Error 56.95 Observations 152 Coefficients Standard Error t Stat P-value Intercept 738.70 5.48 134.80 2E-158 X Variable -258.34 10.19 -25.36 4.05E-56
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30 SIA: Weekend effect in Australian births… l Regression framework with dummy variable provides convenient way to test differences between means l Equivalent to case of independent samples with same variance l Have X 1 ~ N ( μ 1, σ 2 ) & X 2 ~ N ( μ 2, σ 2 ) l H 0: μ 1 - μ 2 = 0 l See Keller 13.1 for more detail. l Specific directed reading, Keller pages 449-451 (topic not covered further in lectures)
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31 Practical inference l Large sample inference l In both regression examples sample size was large (209 or 152) l What happens to t-stat as n ∞? Statistical versus economic significance l Weekend effect was large in both economic & statistical sense l What if estimated effect of roe on salary was 18.5 but associated se was 2.1 not 11.1?
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