Part 0 · Start
The exam game plan
Remember this
Six options, two correct, no penalty. Always mark two, and know your pace.
Judge each option on its own. Hunt for the traps: causes, always, the wrong variable, swapped letters, n or n − 1.
Use the standard deviation with n − 1. Keep four decimals, and round only at the very end.
Quiz 5 questions · pick two
Video drillQuestion 1
Real Madrid, 25 players. Corr(age, market value) = −0.21. Which TWO statements are correct?
Video drillQuestion 2
Grades in two groups. Group 1: 50, 60, 70, 80, 90 Group 2: 72, 68, 70, 74, 66 Which TWO are correct?
Video drillQuestion 3
A report says Cov(x, y) = 25.33 and the correlation is −0.37. Which TWO are correct?
Video drillQuestion 4
log(wage) = 0.584 + 0.083 educ (n = 526). Which TWO are correct?
NewQuestion 5
PS2 Q1: Ŷ = 8.33 − 0.84X, where Y = % change in real wages and X = unemployment rate (%). Which TWO are correct?
On paper 5 exercises
Exercise 1 · not on the sheet
X and Y are independent, E(X) = 1, E(Y) = 4, Var(X) = 2, Var(Y) = 5. Find E(3X − 2Y) and Var(3X − 2Y).
E = 3·1 − 2·4 = −5. Var = 3²·2 + (−2)²·5 + 2·3·(−2)·Cov = 18 + 20 + 0 = 38. The constants are squared and the variances add.
Exercise 2 · n or n − 1
A sample: 4, 8, 6, 2 Find the mean, the sample variance and the sample standard deviation. Your calculator shows two standard deviations, 2.24 and 2.58. Which one does the course use?
Mean 5. Squared deviations 1 + 9 + 1 + 9 = 20. s² = 20/3 = 6.67, s = 2.58. The course uses n − 1, so 2.58 (sx). 2.24 = √(20/4) is σx (÷ n).
Exercise 3 · formula sheet
Use the formula sheet. a Simple regression, n = 40, SSR = 78: find σ̂². b n = 40, k = 1, R² = 0.30: find the adjusted R². c Mean 50, s = 12: find the CV.
a σ̂² = SSR/(n − k − 1) = 78/38 = 2.05. b R̄² = 1 − (39/38)(0.70) = 0.282. c CV = 12/50 = 0.24.
Exercise 4 · like PS2 Q3
30 regions. y = employment growth (%), x = GDP growth (%). ȳ = 2.4 x̄ = 3.5 Σ(xi − x̄)(yi − ȳ) = 18.0 Σ(xi − x̄)² = 45.0 SST = 20.0 SSR = 12.8 a Find the OLS estimates of y on x. b Interpret them. c Find and interpret R². d Predict y for x = 5. e Check: does x̄ give back ȳ?
a β̂1 = 18/45 = 0.40; β̂0 = 2.4 − 0.40·3.5 = 1.00; ŷ = 1.00 + 0.40x. b One percentage point more GDP growth goes with about 0.40 points more employment growth, on average. At zero GDP growth the predicted employment growth is 1.00 %. c R² = 1 − 12.8/20 = 0.36: GDP growth explains 36 % of the sample variation in employment growth. d ŷ = 1.00 + 0.40·5 = 3.00. e 1.00 + 0.40·3.5 = 2.40 = ȳ ✓.
Exercise 5 · calculator
Practise your calculator's statistics mode with PS1-7. U: 5.2, 7.2, 6.0, 6.6, 10.8, 8.2 I: 3.4, 9.5, 6.6, 3.3, 3.4, 26.1 Read the means, the sample standard deviation of U, r, and (if your model has it) the regression line of I on U.
Means 7.33 and 8.72; sx(U) = 1.98; r = 0.167; I = 3.24 + 0.746 U (Casio: STAT → A+BX gives A and B).
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