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.

S.No	X	X - X	(X - X)2	Y	Y - Y	(Y - Y)2	XY
1	45	-19.5	380.25	25	-18.5	342.25	360.75
2	48	-16.5	272.25	30	-13.5	182.25	222.75
3	50	-14.5	210.25	35	-8.5	72.25	123.25
4	55	-9.5	90..25	30	-13.5	182.25	128.25
5	65	0.5	0.25	40	-3.5	12.25	-1.75
6	70	5.5	30.25	50	6.5	42.25	35.75
7	75	10.5	110.25	45	1.5	2.25	15.75
8	72	7.5	56.25	55	11.5	132.25	86.25
9	80	15.5	240.25	60	16.5	272.25	255.75
10	85	20.5	420.25	65	21.5	462.25	440.75
10	645		1810.50	435		1702.5	1667.5

\(\bar{X}=\frac{645}{10}=64.5 \)
\(\sigma x=\sqrt{\frac{\sum(x-\bar{x})^{2}}{n}}  \)
\(=\sqrt{\frac{1810.50}{10}} \)
\(=\sqrt{181.05}=13.4 \)
\(\bar{\gamma}=\frac{435}{10}=43.5 \)
\(\sigma y=\sqrt{\frac{\sum(y-\bar{y})^{2}}{n}} \)
\(=\sqrt{\frac{1702.5}{10}}=\sqrt{170.25}=13.05 \)
\(r=\frac{\sum x y^{\prime}}{\sqrt{\sum x^{2}} \sqrt{\sum y^{2}}} \)
\(=\frac{1667.5}{\sqrt{1810.50} \sqrt{1702.5}} \)
\(=\frac{1667.5}{42.55 \times 41.25}=\frac{1667}{1755}=0.95 \)
\(\bar{x} =64.5  \)
\(\bar{y} =43.5  \)
\(\sigma y =13.05  \)
\(\sigma x =13.4\)
r =0.95
The regression X on Y is
\(x-\bar{x} =r \times \frac{\sigma x}{\sigma y} \times(y-\bar{y})  \)
\(x-64.5 =0.95 \times\left(\frac{13.4}{13.05}\right) \times y-43.5 \)
x-64.5 =(0.95 x 1.03) x y-43.5 
x =0.9785 x (y-43.5)+64.5 
x =0.9785 y-42.56+64.5 
x =0.9785 y+21.94
The regression Y on X is
\(y-\bar{y}=r \times \frac{v y}{\sigma x} \times(x-\bar{x}) \)
\(y-43.5=0.95 \times \frac{13.05}{13.4} \times x-64.5\)
y=0.95(0.97) x (x-64.5)+43.5
y=0.9215 x (x-64.5)+43.5
y=0.9215 x-59.44 + 43.5
Ans: y=0.9215 x-15.94

S.NO.XYXYX²Y² 1 23 18 414 529 324 2 27 22 594 729 484 3 28 23 644 784 529 4 29 24 696 841 576 5 30 25 750 900 625 6 31 26 806 961 676 7 33 28 924 1089 784 8 35 29 1015 1225 841 9 36 30 1080 1296 900 10 39 32 1248 1521 1024 N=10 311 257 8171 9875 6763 \(r =\frac{N \sum X Y-\left(\sum X\right)\left(\sum Y\right)}{\sqrt{N \sum X^{2}-\left(\sum X\right)^{2}} \sqrt{N \sum Y^{2}-\left(\sum Y\right)^{2}}} \)
\(=\frac{(10 \times 8171)-311 \times 257}{\sqrt{(10 \times 9875)-(311)^{2}} \sqrt{10 \times 6763-(257)^{2}}} \)
\(=\frac{81710-79927}{\sqrt{98750-96721} \sqrt{67630-66049}} \)
\(=\frac{1783}{\sqrt{2029} \sqrt{1581}}=0.9955\)
Ans: + 0.9955 high correleated 

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
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Statistics and Commerce
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Statistics and Education
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Statistics and Planning
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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.
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