ECON 2P91 · Formula sheet

The exam formula sheet, explained

These are the exact formulas provided on the exam. What you are really tested on is knowing when to reach for each one and what the result means.

μx = Σxi / N

Mean. Add everything up, divide by the count. The center of the variable.

cov(x,y) = Σ(xi − μx)(yi − μy) / N

Covariance. Do x and y move together? Positive: above-average x tends to come with above-average y. The units are awkward, which is why correlation exists.

σ²x = Σ(xi − μx)² / N

Variance. Average squared distance from the mean. Spread, in squared units.

σx = √σ²x

Standard deviation. Spread back in the variable's own units.

corr(x,y) = cov(x,y) / (σxσy)

Correlation. Covariance rescaled to live between -1 and +1. Direction and strength of the linear relationship, no units.

β = cov(x,y) / σ²x

Regression slope. The expected change in y for a one-unit change in x. When x is a 0/1 indicator, this is the difference in group means.

CI95 = [β̂ − 2·SE(β̂), β̂ + 2·SE(β̂)]

95% confidence interval. Estimate plus or minus two standard errors. Interpretation the exam loves: across repeated samples, intervals built this way capture the true value 95% of the time. It is a statement about the procedure, never a 95% probability that the truth sits in this one interval.

Pr(A|B) = Pr(A)·Pr(B|A) / Pr(B)

Bayes' rule. Flip a conditional probability around. Use when you know Pr(B|A) and need Pr(A|B).

Pr(B) = Pr(A)·Pr(B|A) + Pr(Ac)·Pr(B|Ac)

Law of total probability. Builds the denominator for Bayes: B can happen with A or without A, add the two paths.

Wald = ITT / Pr(Complier)

Wald estimator. In an experiment with imperfect compliance: the intention-to-treat effect divided by the share who actually complied gives the effect on compliers. ITT stays honest to the randomization; Wald scales it up to the people the treatment actually reached.

Not on the sheet but assumed everywhere