ECMT1020 Introduction to Econometrics

How ECMT1020 is assessed

What ECMT1020 covers

ECMT1020 begins with economic questions and data structures, builds probability and sampling foundations, then uses those tools for estimation, hypothesis testing and the regression topics that follow. The Semester 2 2026 assessment structure combines four short quizzes, tutorial group work, an assignment, an in-semester test and a 50% final exam.

It then develops random variables, probability mass and density functions, cumulative distributions, expectations, variance, covariance, correlation and independence. These foundations support the later distinction between a population parameter, a random estimator and the numerical estimate produced by an observed sample. The guide follows that progression rather than presenting regression as a software recipe.

It shows how bias, efficiency, mean squared error and standard errors describe repeated-sample behaviour, why different statistics use normal, t, chi-squared or F reference distributions, and how a hypothesis test connects a population claim to an evidence threshold.

The regression roadmap then places simple and multiple linear models, nonlinear terms, indicator variables, specification questions and heteroskedasticity inside an auditable Stata workflow. Semester 2 2026 assessment totals 100%: four quizzes worth 2% each, tutorial group work worth 7%, an assignment worth 10%, an in-semester test worth 25%, and a final exam worth 50%.

The official outline describes the final as a two-hour, in-person, supervised, closed-book written exam with a provided formula sheet and multiple-choice, fill-in and short-answer questions. The captured materials do not contain a complete released past paper, so the practice bank uses original settings and numbers while rehearsing the question types evidenced by weekly exercises.

Every worked solution keeps formulas, substitutions, arithmetic and interpretation visible, because a correct number without the correct target or conclusion is not a complete econometric answer.

Worked example · free

Calculate a sample mean and corrected variance

Key terms

Random variable

A numerical function of a random outcome, described through a probability distribution.

Probability mass

The probability assigned to each supported value of a discrete random variable.

Probability density

A nonnegative function whose integral over an interval gives a continuous probability.

Cumulative distribution

The probability that a random variable is less than or equal to a specified value.

Expected value

The probability-weighted centre of a random variable across its possible outcomes.

Variance

The expected squared distance from a mean, used to measure dispersion.

Covariance

A signed measure of how two variables move together around their means.

Correlation

Covariance divided by both standard deviations, measuring scaled linear association.

Estimator

A statistic selected as a rule for learning about an unknown population parameter.

Standard error

The standard deviation of an estimator's sampling distribution.

Mean squared error

Estimator variance plus squared bias, measuring expected squared distance from the target.

Null hypothesis

The population claim evaluated as the testing reference.

Type I error

Rejecting a null hypothesis when that null is true.

Heteroskedasticity

Variation in the conditional error variance across observations or regressor values.

ECMT1020 FAQ

Questions students ask in each ECMT1020 chapter

How do I identify panel data?

Look for the same named entities appearing at several dates. Many entities plus many dates is not enough if each date samples different entities; that structure is repeated cross-sectional. Chapter 01 · Econometric Questions and Data Structures

Can a density exceed one?

Yes. A density height is not itself a probability. The integral over the entire support must equal one, and interval areas must remain between zero and one. Chapter 02 · Random Variables, Mass and Density

Why must a cumulative distribution increase?

Raising the threshold can only add possible outcomes to the event X≤x. It cannot remove probability already accumulated, so the cumulative function never decreases. Chapter 03 · Cumulative Probability and Expected Value

Why can covariance be hard to compare?

Its size depends on the units and scales of both variables. Correlation removes those units, making linear association easier to compare across settings with different measurement scales. Chapter 04 · Variance, Covariance and Correlation

Does independence imply zero correlation?

When the relevant moments and nonzero standard deviations exist, independence implies zero covariance and therefore zero correlation. The reverse implication fails in general for nonlinear relationships. Chapter 05 · Independence and Probability Calculations

What is the difference between an estimator and estimate?

An estimator is the rule applied to a random sample. An estimate is the numerical value produced after a particular sample has been observed and substituted into that rule. Chapter 06 · Samples, Statistics and Estimators

Can a biased estimator be preferable?

Yes, under mean squared error. A modest squared bias can be more than offset by a large reduction in variance, producing smaller expected squared distance from the target. Chapter 07 · Bias, Efficiency and Mean Squared Error

Why does t have heavier tails?

Estimating the denominator adds uncertainty. The t distribution assigns more probability to large standardised values, especially when degrees of freedom are low and scale estimation is imprecise. Chapter 08 · Distributions Used for Inference

What does non-rejection mean?

It means the observed statistic did not cross the chosen threshold at the selected significance level. It does not prove the null is exactly true in the population. Chapter 09 · Hypothesis Tests and Standard Errors

Why use a do-file?

It preserves commands in order, makes transformations and model changes visible, and allows the analysis to be rerun from a clean start. Command history alone is fragile and incomplete. Chapter 10 · Regression Roadmap and Reproducible Stata

How to study for the exam

Revise ECMT1020 as a dependency chain. First secure probability language: support, mass or density, cumulative probabilities, expectations and variance. Next connect samples to estimators, then compare bias, variance and mean squared error. Only after that should you drill normal and t standardisation, hypothesis tests and regression interpretation. Use a two-pass routine for every worked problem.

On the first pass, solve without notes and show every substitution. On the second, audit support, signs, denominators, units and the scope of the conclusion. Because the official final is closed book with a provided formula sheet, practise recognising which relationship applies rather than copying formulas from memory.

Alternate short calculations with verbal distinctions such as parameter versus estimate, independence versus zero correlation, statistical significance versus magnitude, and association versus causality. Keep a compact error log organised by the decision that failed: wrong distribution, wrong tail, missing outcome, denominator error, or overclaimed conclusion. Rework each error with new numbers until the method remains stable.

In the final week, time mixed sets containing probability, estimation, testing and regression interpretation so switching between question types becomes routine.

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