For Egression Calculations, we draw the following table

Considering the regression line as Y = a + bX, we can obtain the values of a and b from the above values.
\(a=\frac { \sum { Y } \sum { X } ^{ 2 } }{ { N\sum { X } }^{ 2 }-{ (\sum { X } ) }^{ 2 } } \)
\(a=\frac { 796.2x385-55x4887.5 }{ 10x385-55x55 } \)
\(b=\frac { N\sum { XY-\sum { X } \sum { Y } } }{ N{ \sum { X } }^{ 2 }-{ (\sum { X } ) }^{ 2 } } \)
\(a=\frac { 10x4887.5-55x796.2 }{ 10x385-55x55 } \)
= 6.16
Hence the regression line can be written as
Y = 45.73 + 6.16x

Let price of the commodity be denoted by X and quantity be denoted by Y
Calculations for Coefficient of Correlation

\({ r }_{ xy }=\frac { N\sum { XY-\sum { X\sum { Y } } } }{ \sqrt { N{ \sum { X } }^{ 2 }-{ (\sum { X } ) }^{ 2 } } \sqrt { N{ \sum { Y } }^{ 2 }-{ \left( \sum { Y } \right) }^{ 2 } } } \)
\({ r }_{ xy }=\frac { 5x226-55x21 }{ \sqrt { (5x609-55x55)(5x95-21x21) } } \)
\({ r }_{ xy }=\frac { 1130-1155 }{ \sqrt { 20x34 } } \)
\({ r }_{ xy }=\frac { 25 }{ \sqrt { 680 } } \)
\({ r }_{ xy }=-0.98\)
The negative sign of r indicate negative correlation and its large magnitude indicate a very
1. high degree of correlation.
2. So there is a high degree of negative correlation between pricesand quantity demanded.

(a) The Scatter Diagram of the given data is shown in Figure

i. Figure shows that the plotted points are close to each other and reveal an upward trend.
ii. So there is a high degree of positive correlation between sales and expenses of the firm.

Formula for Assumed Mean Deviation method.
\(r=\frac { N\sum { dxdy-(\sum { dx } )(\sum { dy } ) } }{ \sqrt { { N\sum { dx } }^{ 2 }-{ (\sum { dx } ) }^{ 2 } } \sqrt { { N\sum { dy } }^{ 2 }-{ (\sum { y } ) }^{ 2 } } } \)

\(\bar { X } =\frac { \sum { } }{ N } =\frac { 113 }{ 7 } =16\frac { 1 }{ 7 } \)
\(\bar { Y } =\frac { \sum { Y } }{ N } =\frac { 193 }{ 7 } =27\frac { 4 }{ 7 } \)
Take the assumed values A = 16 & B =27 therefore dx = X - A → X - 16 and Wdy = → Y - 27
\(r=\frac { N\sum { dxdy-(\sum { dx } )(\sum { dy } ) } }{ \sqrt { { N\sum { dx } }^{ 2 }-{ (\sum { dx } ) }^{ 2 } } \sqrt { { N\sum { dy } }^{ 2 }-{ (\sum { y } ) }^{ 2 } } } \)
\(=\frac { 7X187-1X4 }{ \sqrt { 7X159-{ (1) }^{ 2 } } \sqrt { 7X230-{ (4) }^{ 2 } } } \)
\(=\frac { 1309-4 }{ \sqrt { 1112 } \sqrt { 1610-16 } } \)
\(=\frac { 1305 }{ \sqrt { 1112 } \sqrt { 1594 } } =\frac { 1305 }{ \sqrt { 33.34 } \sqrt { 39.92 } } \)
\(=\frac { 1305 }{ 1330.9 } =0.9865\quad =0.986\)

Let us take price as X and supply as Y

\(r=\frac { N\sum { XY-(\sum { X } )(\sum { Y } ) } }{ \sqrt { N\sum { { X }^{ 2 }-{ (\sum { X } ) }^{ 2 } } \sqrt { N\sum { { Y }^{ 2 }-{ (\sum { y } ) }^{ 2 } } } } } \)
\(r=\frac { (5x3414)-70x239) }{ \sqrt { (5x1026)-{ (70 })^{ 2 } } \sqrt { 5x11685-{ (239) }^{ 2 } } } \)
\(r=\frac { 17,070-16,730 }{ \sqrt { 230x } \sqrt { 1304 } } \)
\(r=\frac { 340 }{ 547.65 } =+0.621\)
Pirce of the product and supply for the product is positively correlated. When price of the product increases then the supply for the product also incresases.