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Applied Econometrics Individual Assignment

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1. In the population model: cigsi = βo + β1educi + ui a) Interpret the coefficient β1. β1 represents the slope of the regression line and is the change in cigs associated with a unit change in educ. So for one unit increase of educ there will be β1 units increase/decrease (depending on the sign of β1) in the cigs. b) Can you predict the sign of β1 (without doing any estimation)? Explain.
The sign of β1 would most probably be minus looking at the information from the surveys in the excel spreadsheet. The education value is always a positive number (educi > 0), βo is also a positive number (the intercept with y, as cigsi >=0). In this way in order for the number of cigarettes to be equal to 0, the β1 value should be negative.

2. Use the data in SMOKE.sav (see Blackboard) to estimate the model from question 1. Report the estimated equation in the usual way. Also, plot a handwritten graph of the estimated equation. cigs = 11,412 – 0,219 educ

3. Does educ explain a lot of the variation in the number of cigarettes smoked? Explain.
The regression R2 is the fraction of the sample variance of cigsiexplained by (or predicted by) educi. In this example R2 equals to 0,002 and this amount is closer to 0, which means that the regressor educ is not very good at predicting the value of cigs, thus does not explain a lot of the variation in the number of cigarettes smoked.

4. Find the predicted difference in number of smoked cigarettes for two people whose years of schooling differ by 4. What do you make of your answer?
The predicted difference in number of smoked cigarettes for two people whose years of schooling differ by 4 equals to:
Δcigs = 11,412 – 0,219X – (11,412 – 0,219 (X – 4)) =
= 11,412 – 0,219X – (11,412 – 0,219 X + 0,876) =
= 11,412 – 0,219X – 11,412 + 0,219 X - 0,876 = - 0,876

5. What can you say about the distribution of the estimated slope ( β1)? Explain which theorem is applicable.
The distribution of the estimated slope β1 is normal. The central limit theorem is applicable here.

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