Formula sheet

a question asks you to justify why econometrics is not simply 'applied statistics' or 'mathematical economics.'

you are asked to summarise, in one line, what econometric research is ultimately for.

an exam asks you to list, or apply, the standard stages of an empirical econometric study — walk through each with the running example below.

$Y$

consumption

$X$

income (here, GDP)

$\beta_0$

the intercept (constant term)

$\beta_1$

the slope, the marginal propensity to consume (MPC), 0 < \beta_1 < 1

the mathematical (deterministic) stage of the model, step 2, before a disturbance term is added.

$u$

the disturbance (error) term, a random variable capturing everything the deterministic line leaves out

the model is now stochastic rather than exact — the standard starting point for every regression in this course.

$\widehat{MPC}$

the estimated marginal propensity to consume, \hat\beta_1 from the fitted consumption function

a fitted consumption function's slope is used to estimate the impact of a change in government spending on national income — a direct step-8 application.

you are given a dataset's description and need to classify it — a very common short-answer question.

a question asks you to explain why a regression result does not, by itself, prove causation.

$E(Y \mid X_i)$

the conditional mean of Y for a given value X_i

$\beta_0, \beta_1$

the true, unknown population parameters

you need to state the theoretical object regression is trying to uncover — the true relationship in the whole population, not just in one sample.

$u_i$

the disturbance (error) term for observation i, capturing everything that pulls Y_i away from its conditional mean

you write down the full population model, ready to be estimated from a sample — this equation is the starting point of every two-variable regression in this course.

$\hat\beta_0, \hat\beta_1$

estimated parameters (also written b_0, b_1)

$\hat Y_i$

the fitted (predicted) value

$e_i$

the residual, the SAMPLE counterpart of u_i

you are working with actual estimated numbers from a specific dataset, as opposed to the unobservable, purely theoretical PRF.

a model has a squared or otherwise nonlinear term in X, and you need to decide whether ordinary least squares can still be used.

$SSR$

sum of squared residuals

$b_0, b_1$

the candidate intercept and slope being chosen

you need to explain what OLS is actually optimizing, before deriving the formulas for b0 and b1.

$\bar X, \bar Y$

the sample means of X and Y

$S_{xy}$

sum of products of deviations from the means

$S_{xx}$

sum of squared deviations of X from its mean

you need to compute the OLS intercept and slope by hand from raw (X,Y) data — the single most-used formula pair in this course.

you need to check whether a claimed fitted line could actually be the OLS line, or explain a stated algebraic fact about residuals.

$TSS$

total sum of squares

$ESS$

explained sum of squares

$SSR$

residual (unexplained) sum of squares

you need to break down the total variation in Y into the part the regression line explains and the part it leaves unexplained.

$R^2$

the proportion of the total variation in Y explained by the regression, 0 \leq R^2 \leq 1

a question asks how well the fitted line explains the data — the standard, single-number goodness-of-fit measure for a two-variable regression.