Econometrics may be defined as the social science in which the tools of economic theory, mathematics and statistical inference are applied to the analysis of economic phenomena.

(i) Correlation is a statistical device that helps to analyse the covariation of two or more variables.
(ii) Correlation is the relationship between two or more variables which vary with the other in the same or the opposite direction.

(i) Based on characteristics there are quantitative and qualitative data.
(ii) Qualitative data is classified as nominal data and rank data.
(iii) Based on the data sources there are primary data and secondary data.

The branch of statistics concerned with using sample data to make an inference about a population of data is called Inferential Statistics.

(i) Statistics as a science of estimates and probabilities.
(ii) Statistics is the collection, organisation, presentation, analysis and interpretation of numerical data.

Linear Correlation: Correlation is said to be linear when the amount of change in one variable tends to bear a constant ratio to the amount of change in the other.
Ex. Y= a + bx
Non Linear: The correlation would be non-linear if the amount of change in one variable
does not bear a constant ratio to the amount of change in the other variables.
Ex. Y= a + bx2

(i) Models in Mathematical Economics are developed based on Economic Theories, while Econometric Models are developed based on Economic Theories to test the validity of Economic Theories in reality through the actual data.
(ii) Regression Analysis in Statistics does not concentrate more on error term while Econometric Models concentrate more on error terms  

(i) Besides verification it is used for the prediction of one value, in relation to the other given value.
(ii) Regression coefficient is an absolute figure. If we know the value of the independent variable, we can find the value of the dependent variable.
(iii) It has wider application, as it studies linear and nonlinear relationship between the variables.
(iv) It is widely used for further mathematical treatment.

Three of the most important ways of classifying correlation are:
(i) Based on the direction of change of variables
Positive Correlation:
(i) The correlation is said to be positive if the values of two variables move in the same direction.
(ii) Ex. Y = a + bx
Negative Correlation:
(i) When the values of variables move in the opposite directions.
(ii)  Ex. Y = a - bx
(ii) Based on the number of variables studied.
Simple Correlation:
(i) If only two variables are taken for study.
Multiple Correlations:
(i) If three or more than three variables are studied simultaneously.
\(\operatorname{Ex}: Q_{d}=f\left(P, P_{v}, P, t, y\right)\)
Partial Correlation:
(i) If there are more than two variables but only two variables are considered keeping the other variables constant, then the correlation is said to be Partial Correlation.
(iii) Based on the constancy of the ratio of change between the variables
Linear Correlation:
(i) When on the amount of change in one variable tends to bear a constant ratio to the amount of change in the other.
(ii) Ex. Y = a + bx²
Non Linear:
(i) The amount of change in one variable does not bear a constant ratio to the amount of change in the other variables.
(ii) Ex. Y = a + bx²

(I) Statistics presents facts in a definite form.
(ii) It simplifies mass of figures.
(iii) It facilitates comparison.
(iv) It helps in formulating and testing.
(v) It helps in prediction.
(vi) It helps in the formulation of suitable policies.

1. Find out the actual mean of given data (x̅)
2. Find out the deviation of each value from the mean (x = X - x̅ )
3. Square the deviations and take the total of squared deviations Σx²
4. Divided the total Σx² by the number of observation \(\left( { \frac { \sum { x } }{ n } }^{ 2 } \right) \)
5. The square root of \(\left( { \frac { \sum { x } }{ n } }^{ 2 } \right) \) is standard deviation.

Econometrics is the statistical and mathematical analysis of economic relationships, often serving as a basis for economic forecasting. It is used by economists to study relationships between economic variables Econometrics is interesting because it provides the tools to enable us to extract useful information about important economic policy issues from the available data. It is used to understand economic issues and test theories. Without evidence economic theories are abstract and has no bearing on reality. Econometrics is a set of tools we can use to confront theory with real world data. A study' could estimate a key parameter such as the price elasticity of demand for it or econometric techniques could be used to generate forecasts. It is used to develop, estimate and evaluate models which relate economic or financial variables.

Nature of Statistics
(i) Different Statisticians and Economists differ in views about the nature of statistics.
(ii) Some call it a science and some say it is an art
(iii) Tippet considers Statistics both as a science as well as an art.
Scope of statistics
(i) Statistics is applied in every sphere of human activity social and physical.
Statistics and Economics
(i) Statistical data and techniques are immensely useful in solving many economic problems.
Statistics and Firms
(i) Statistics is used in many firms to find whether the product is conforming to specifications or not.
Statistics and Commerce
(i) Market survey helps to find the present conditions and to forecast the likely changes in future.
Statistics and Education
- Statistics is necessary for the formulation of policies to start new course.
- Public and private educational institutions do research and development work to test the past knowledge and evolving knowledge.
Statistics and Planning
(i) In the modern world, a "world of planning" almost all the organisations in the government are using planning for efficient working, for the formulation of policy decisions and execution of the same.
(ii) In India, statistics play an important role in planning both at the central and the state government levels, but the quality of data is highly unscientific.
Statistics and Medicine
(i) t-test is used to compare the efficiency of two medicines.
Statistics and Modern applications
(i) Recent developments in computer and information technology have enabled statistics to integrate their models and thus make statistics a part of decision making procedures of many organisations.
(ii) There are many software packages available for solving simulation problems.