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

Statistics and Economics
Statistical data and techniques are immensely useful in solving many economic problems such as fluctuation in wages, prices, production, distribution of income and wealth and so on.
Statistics and Firms
Statistics is widely used in many firms to find whether the product is conforming to specifications or not.
Statistics and Commerce
Statistics are life blood of successful commerce. Market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.

NSSO has four divisions:
1. Survey Design and Research Division (SDRD)
2. Field Operations Division (FOD)
3. Data Processing Division (DPD)
4. Co-ordination and Publication Division (CPD)

Central Statistical Office (CSO)
(i)  It is responsible for co-ordination of statistical activities in the country and for evolving and maintaining statistical standards.
(ii) It compiles National Accounts, conducts Annual Survey of Industries and Economic Census, compiles Index of Industrial Production and Consumer Price Indices.
(iii) It deals with social statistics, training, international co-operation, Industrial Classification, etc.
National Sample Survey
Organisation
NSSO has four divisions:
(i) Survey Design and Research Division
(ii) Field Operations. Division
(iii) Data Processing Division
(iv) Co-ordination and Publication Division
The Programme Implementation Wing has 3 Divisions:
(i) Twenty Point Programme
(ii) Infrastructure Monitoring and Project Monitoring
(iii) Member of Parliament Local Area Development Scheme.
1. There is National Statistical Commission and one autonomous Institute, i.e., Indian Statistical Institute.

(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) The general objective of Econometrics is to give empirical content to economic theory
(ii) The specific objectives are :
(i) It helps to explain the behaviour of a forthcoming period that is forecasting economic phenomena.
(ii)  It helps to prove the old and established relationships among the variables or between the variables.
(iii) It helps to establish new theories and new relationships.
(iv) It helps to test the hypotheses and estimation of the parameter.

(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

S.No xx \(x-\bar{x} \) \((x-\bar{x})^{2}\) 1 14 14 - 15 = -1 1 2 22 22 - 15 = 7 49 3 9 9 - 15 = -6 36 4 15 15 - 15 = 0 0 5 20 20 - 15 = 5 25 6 17 17 - 15 = 2 4 7 12 12 - 15 = 2  9 8 11 11 - 15 = 4 16 N = 8 120   140 \(\bar{x} =\frac{120}{8}=15 \)
\(\sigma =\sqrt{\frac{\sum(x-\bar{x})^{2}}{n}} \)
\(=\sqrt{\frac{140}{8}} \)
\(=\sqrt{17.5} \)
=4.18
Ans: 4.18

(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.