Fig.1 : Perfect Positive Correlation
Fig.2 : Perfect Negative Correlation
Fig.3 : High Degree of Positive Correlation
Fig.4 : High Degree of Negative Correlation
Fig.5 : No Correlation
Fig.6 : No Correlation

\(SD=\sqrt { \frac { \sum { { (x)-\bar { X } ) }^{ 2 } } }{ n } } =7.89\)

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

There are three types based upon the number of variables studied as
a) Simple Correlation
b) Multiple Correlation
c) Partial Correlation
Simple Correlation:
If only two variables are taken for study then it is said to be simple correlation. Ex. Y= a + bx
Multiple Correlations:
If three or more than three variables are studied simultaneously, then it is termed as multiple correlation.
Ex: Determinants of Quantity demanded
Qd = f (P, Pc, Ps, t, y)
Where Qd stands for Quantity demanded, f stands for function.
P is the price of the goods,
Pc is the price of competitive goods
Ps is the price of substituting goods
t is the taste and preference
y is the income.
Partial Correlation:
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

Correlation is classified into two types as Positive correlation and Negative Correlation based on the direction of change of the variables.
Positive Correlation:
The correlation is said to be positive if the values of two variables move in the same direction.
Ex: If income and Expenditure of a Household may be increasing or decreasing simultaneously. If so, there is positive correlation. Ex. Y = a + bx
Negative Correlation:
The Correlation is said to be negative when the values of variables move in the opposite
directions. Ex. Y = a – bx
Ex: Price and demand for a commodity move in the opposite direction.

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.

The Programme Implementation Wing has three Divisions, namely,
(i) Twenty Point Programme
(ii) Infrastructure Monitoring and Project Monitoring
(iii) Member of Parliament Local Area Development Scheme.

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)

National Sample Survey Organisation (NSSO)
i. The National Sample Survey Organisation, now known as National Sample Survey Office, is an organization under the Ministry of Statistic of the Government of India.
ii. It is the largest organisation in India, conducting regular socio-economic surveys.

Central Statistical Office (CSO)
1. The Central Statistical Office is one of the two wings of the National Statistical Organisation (NSO).
2. It is responsible for co-ordination of statistical activities in the country and for evolving and maintaining statistical standards.
3. Its activities include compilation of National Accounts; conduct of Annual Survey of Industries and Economic Censuses, compilation of Index of Industrial Production as well as Consumer Price Indices.
4. It also deals with various social statistics, training, international cooperation, Industrial Classification, etc.

1. The Ministry of Statistics and Programme Implementation (MOSPI) came into existence as an Independent Ministry in 1999 after the merging of the Department of Statistics and the Department of Programme Implementation.
2. The Ministry has two wings, Statistics and Programme Implementation. The Statistics Wing called the National Statistical Office (NSO) consists of the Central Statistical Office (CSO), the Computer Centre and the National Sample Survey Office (NSSO).

The Linear regression model is based on certain assumptions
1. Some of them refer to the distribution of the random variable.
2. Some of them refer to the relationship between Ui and the explanatory variables (x1, x2, x3 given in the above example).
3. Some of them refer to the relationship between Ui the explanatory variables themselves.

\(\bar { X } =A+\frac { \sum { d } }{ n } \)
\(=68+\frac { 31 }{ 5 } \)
= 68 + 6.2 = 74.2
Ans: 74.2