Model 570000019 1 570000019 Prob F 00000 Residual 20743e 14 R

# Model 570000019 1 570000019 prob f 00000 residual

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Model | 5.70000019 1 5.70000019 Prob > F = 0.0000

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Residual | 3.5263e-13 17 2.0743e-14 R-squared = 1.0000 -------------+------------------------------ Adj R-squared = 1.0000 Total | 5.70000019 18 .316666677 Root MSE = 1.4e-07 ------------------------------------------------------------------------------ lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- education | .1 6.03e-09 . 0.000 .1 .1 _cons | 4.60517 6.88e-08 . 0.000 4.60517 4.60517 The coefficient on education, .1, reflects that I created this data set using the assumption that the wage increases by 10% for every additional year of education. I will now introduce a random component that affects the lnwage. I will introduce u = random error, which is defined as u = invnormal(uniform()) The function invnormal(uniform()) returns normally distributed random numbers with a mean of 0 and a standard deviation of 1. gen u = invnormal(uniform()) Note: since I am generating a random variable, what I observe in class will be different than what I record on this handout. Note that u does not appear to be correlated with education or lnwage: lnwageeducation u 4.70517 1 .1952169 4.80517 2 -1.23091 4.90517 3 1.953314 5.00517 4 -.7849584 5.10517 5 -.6400359 5.20517 6 -.9740305 5.30517 7 .7082468 5.40517 8 -.3281993 5.50517 9 -.3066868 5.60517 10 1.85042 5.70517 11 .2078537 5.80517 12 .8249497 5.90517 13 -1.335853 6.00517 14 .9023688 6.10517 15 -.6263756 6.20517 16 -.1184899 6.30517 17 -1.121178 6.40517 18 -.7535513 6.50517 19 -1.787513
FIGURE THREE -2 -1 0 1 2 u 0 5 10 15 20 education Now let’s see what happens when we add this standard normal variable u to Y i . gen lnwageran = lnwage + u twoway (lfitci lnwageran education) (scatter lnwageran education) FIGURE FOUR

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3 4 5 6 7 8 0 5 10 15 20 education 95% CI Fitted values lnwageran Note the correspondence between figure three and figure four.
• Spring '08
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