1. PROBLEM SET 1 SOLUTION

2. QUESTION 1

3. Error Term Omitted variables Measurement error Specification error Random or unpredictable occurrences Some of the omitted variables may be correlated with education such as income. Discuss other examples. (i)

4. ii. A simple regression equation like this includes just one independent variable. Other variables such as those mentioned in part (i) may be correlated with education and included in u, thus uncovering the Ceteris Paribus effect.

5. QUESTION 2

6. StudentGPA (Y)ACT (X)(X-Xbar)(Y-Ybar)(X-Xbar)²(X-Xbar)*(Y-Ybar) 12.8021-4.875-0.412523.76562.0109 23.4024-1.8750.18753.5156-0.3516 33.00260.125-0.21250.0156-0.0266 43.50271.1250.28751.26560.3234 53.60293.1250.38759.76561.2109 63.0025-0.875-0.21250.76560.1859 72.7025-0.875-0.51250.76560.4484 83.70304.1250.487517.01562.0109 Ybar=3.2125Xbar=25.875 ∑=56.875∑=5.8125 GPA hat = 0.5681 + 0.1022ACT N=8

7.  Positive relationship ; higher ACT, higher the estimated GPA.  If ACT is 5 points higher, GPA increases by 0.1022*5=0.511.  No meaningful interpretation of intercept as ACT is no where close to zero.

8. GPA (Y)GPA hat (Y hat)e hate hat²(Y-Ybar)² 2.802.71430.08570.00730.1702 3.403.02090.37910.14370.0352 3.003.2253-0.22530.05080.0452 3.503.32750.17250.02980.0827 3.603.53190.06810.00460.1502 3.003.1231-0.12310.01520.0452 2.703.1231-0.42310.17900.2627 3.703.63410.06590.00430.2377 ∑=(0.0002)∑=0.4347∑=1.0288 (iii) GPA (hat) = 0.5681 + 0.1022 (20) = 2.61 (iv) TSS= 1.0288 ; RSS=0.4347; R²=1-(RSS/TSS)=1(0.4347/1.0288)=0.577

9. QUESTION 3

10. (i)When cigs=0, bwght=119.77 When cigs=20, bwght=119.77-10.28=109.49 10.28 is the ounces by which bwght falls if a woman smokes 20 cigs in comparison to 0. (ii) No. A lot of other variables like health facilities available to the mother may also affect birth weight. A regression equation simply shows the impact of one variable on another, thus does not necessarily indicate causality.

11. QUESTION 4

12. i.The intercept implies that when inc=0, consumption=-124.84. This obviously is not true as consumption can not be negative. ii.Cons(hat)=-124.84+0.853*30000= $25465.16 MPC=slope coefficient APC=-124.84/INC + 0.853 1000200030004000 0.853 INC MPC, APC APC MPC

13. QUESTION 5

14. i. A percentage increase in the distance of the house from a recently built garbage incinerator, increases the price of the house by 0.312%, keeping everything else constant. Yes. A house further away from incinerator is worth more. ii. NO. There might be other variables correlated with ‘dist’ leading to a biased estimate of the elasticity of price with respect to dist. iii. Area, Quality of house, size of the house, number of bedrooms, attractiveness of the neighborhood etc. Some of these variables may be correlated with distance.

15. QUESTION 6 (question 5 from Studenmund)

16. i. The intercept and slope coefficients are being estimated. The squared residuals are being minimized. ii. If R² =0, then RSS=TSS meaning the independent variables included in the model do not help explain variation in the dependent variable. ESS=0. In our usual OLS regression model, R² can not be negative as everything is being squared. iii. Model T has estimated signs that meet our expectations. A higher R² does not automatically mean that an equation is preferred. Model T is preferred as it includes an important variable missing in Model A.

17. QUESTION 7

18. i. ATT  +IVE; PS  +IVE Going to classes and doing problem sets should improve student’s grade. ii. Yes. Refer to part i. iii. 25 hours of lecture & 50 hours to complete PS 1 hour  0.04 lecture; 1 hour  0.02 PS 1.74*0.04=0.0696: gain in grade by spending an extra hour on lectures 0.6*0.02=0.012: gain in grade by spending an extra hour on PS. gain from lectures > gain from PS SO, going to class pays off more.

19. iv. 50 Hours of lecture & 10 hours of problem set. 1 hour  0.02 lecture; 1 hour  0.1 PS 0.02*1.74 > 0.1*0.6 0.0348 > 0.06 this time doing problem sets pays off more. Since the units of variables can differ dramatically, coefficient size does not measure importance. v. 33% of variation in the grade received by a student is explained by the regression equation. vi. No. other factors such as students ability may be included.

20. QUESTION 8

21. i. Yes ii. Yes. iii. 1 book  $230; Two excellent articles  2*(102+18)=$240 Three dissertations  3*489=1467 writing dissertation leads to a higher increment in salary. Thus preferred. iv. The coefficient D seems to be too high. May be absorbing the impact of omitted variables e.g. students may choose a dissertation advisor on the basis of reputation or qualification.