(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