Introduction to Statistical Methods and Econometrics: One Mark Questions, Book Back Answers and Notes

About Introduction to Statistical Methods and Econometrics

Medium ~90 min study

An economic theory says, for example, that demand falls when price rises. To check whether that holds, and by how much, we need data and a method for handling it. This chapter gives you both: statistics to collect and summarise the numbers, and econometrics to test economic relationships against them.

The statistics part starts with data: what counts as primary and secondary data, and how quantitative data differs from qualitative data. You then learn two summary measures, the arithmetic mean for the central value and the standard deviation for spread. Correlation tells you whether two variables such as price and quantity demanded move together, and regression gives you an equation for estimating one from the other.

Econometrics combines economic theory, mathematics and statistics. Ragnar Frisch is credited with coining the term. The feature to remember is the random error term \(U_i\). A mathematical model says consumption depends exactly on income; an econometric model adds \(U_i\) to cover everything the equation leaves out. The chapter ends with India's official statistical system and P.C. Mahalanobis.

What you'll learn

• Distinguish descriptive statistics from inferential statistics.
• Classify data as primary or secondary and as quantitative or qualitative.
• Calculate the arithmetic mean and standard deviation of a simple data set.
• Interpret the sign and size of a correlation coefficient.
• Write a simple linear regression equation and use it to estimate the dependent variable.
• Explain the steps of econometric methodology and why the error term is included.

Before you start

• Simple algebraic equations and plotting points on a graph.
• Basic economic terms such as demand, price, income and investment.
• The idea of an average and a basic sense of probability.

Introduction to Statistical Methods and Econometrics explained

Statistical and Econometric Tools: The Main Ideas

Nature and Scope of Statistics

Statistics is the science of collecting, organising, presenting, analysing and interpreting numerical data. Economists use it to frame policy, follow price and output changes, and test theories. It has limits. It studies groups (aggregates), not single individuals. It deals with quantitative facts, so qualities like honesty must be ranked before they can be studied. Its laws are true only on average, and in careless hands it can mislead.

Data and Central Tendency

Data is the raw material of statistics. By nature it is quantitative (measured in numbers, such as income or height) or qualitative (attributes, such as gender or skill). By source it is primary (collected first-hand through surveys or questionnaires) or secondary (already collected and published by someone else). To represent a whole data set by one value we use a measure of central tendency, mainly the arithmetic mean, \(\bar{X} = \frac{\sum X}{N}\).

Measures of Dispersion

Two data sets can have the same mean and still look very different. Marks of 49, 50 and 51 and marks of 0, 50 and 100 both average 50. Dispersion measures this spread. Standard deviation is the square root of the mean of the squared deviations from the arithmetic mean. A large standard deviation means the values are widely scattered and the mean represents them less well; in finance it is used as a measure of risk.

Correlation Analysis

Correlation measures the direction and degree of the linear relationship between two variables. Karl Pearson's coefficient \(r\) lies between \(-1\) and \(+1\). A positive value means the variables move in the same direction, a negative value means opposite directions, and zero means no linear relationship. A high \(r\) does not prove that one variable causes the other.

Regression Analysis

Regression gives a functional relationship between a dependent variable and one or more independent variables, so you can estimate the value of one from the other. The word comes from Francis Galton's finding that children's heights tend to go back, or regress, towards the average. Economic theory tells us which variable should be the dependent one; for example, consumer spending is regressed on income or on tax rates.

Introduction to Econometrics

Econometrics gives numerical content to economic relationships using theory, mathematics and statistical inference. What separates an econometric model from an exact mathematical model is the stochastic error term \(U_i\), which stands for omitted variables, random human behaviour and errors of measurement. The method runs in steps: state the theory, specify the mathematical and econometric model, collect data, estimate the parameters, test hypotheses, then use the model for forecasting and policy.

Official Statistical System of India

The Ministry of Statistics and Programme Implementation (MOSPI) has two wings: Statistics and Programme Implementation. The statistics wing is the National Statistical Office (NSO). Within it are the Central Statistical Office (CSO), which compiles national accounts, conducts the Annual Survey of Industries and prepares price and production indices, and the National Sample Survey Office (NSSO), which runs large socio-economic surveys.

Common mistakes to avoid

• Treating correlation as proof of cause. A high value of \(r\) only shows that two variables move together in a linear way.
• Leaving out \(U_i\) when writing an econometric equation. Without it the equation is an exact mathematical model, not an econometric one.
• Putting qualitative data straight into a formula. Attributes such as honesty or skill must first be classified or given ranks.
• Calling standard deviation a measure of central tendency. It measures spread around the mean, not the centre itself.
• Fitting a straight-line regression to data that is clearly curved. Look at the scatter diagram before assuming a linear relationship.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What is the difference between correlation and regression?

Correlation measures the direction and strength of the linear relationship between two variables and treats both alike. Regression treats one variable as dependent and the other as independent, and gives an equation for estimating the dependent variable from the independent one.

Why is an error term included in econometric equations?

The error term \(U_i\) covers variables left out of the model, the random element in human behaviour and errors in measuring the data. Real data never fits an exact equation, so the error term makes the model realistic. It is the main thing that separates an econometric model from a mathematical one.

How do primary and secondary data differ?

Primary data is collected for the first time by the investigator, through surveys, interviews, experiments or questionnaires. Secondary data has already been collected by someone else, such as the Reserve Bank or a statistical office, and is taken from published or unpublished records.

What is standard deviation and why is it used?

Standard deviation is an absolute measure of dispersion that shows how far values lie, on average, from the arithmetic mean. A small value means the data is consistent and the mean represents it well. Economists and investors use it to measure variability and risk.

Who is regarded as the father of Indian statistics?

Professor P.C. Mahalanobis. He founded the Indian Statistical Institute and started the National Sample Survey. His birthday, 29 June, is observed every year as National Statistics Day in India.

What does the Central Statistical Office do?

The CSO coordinates statistical work across the country and sets statistical standards. It compiles the national accounts, conducts the Annual Survey of Industries and prepares indices such as the Index of Industrial Production and consumer price indices.

What are the limitations of statistics in economics?

Statistics cannot directly study qualitative things like honesty, leadership or culture unless they are ranked. It deals with groups, not individuals. Its laws are true only on average, not exactly. Data handled by people without proper knowledge can easily lead to wrong conclusions.