International School of Business & Media; Kolkata

Co-relation between BSE sensex and gold price.

Abhijit Samanta

2

(Q) Take the Sensex and Gold Price for last one month.

Q1. Draw the Scatter Diagram. Q2. Calculate the value of Co-relation coefficient (r). Q3. Estimate the two regression equation.

In the chart below we have taken the data from 01 July 2009 to 21st August 2009 (38 days). There we

take the value of Sensex as "x" and the value of Gold Prices as "y".

Sl. Date Sensex (x)

Gold Price (y) Rs./10 Gram

1 1-Jul-09 14494 14,580.00

2 2-Jul-09 14646 14,440.00

3 3-Jul-09 14658 14,490.00

4 4-Jul-09 14913 14,470.00

5 7-Jul-09 14043 14,590.00

6 8-Jul-09 14170 14,615.00

7 9-Jul-09 13769 14,615.00

8 10-Jul-09 13757 14,510.00

9 11-Jul-09 13504 14,485.00

10 14-Jul-09 13400 14,585.00

11 15-Jul-09 13854 14,655.00

12 16-Jul-09 14253 14,745.00

13 17-Jul-09 14250 14,825.00

14 18-Jul-09 14745 14,795.00

15 21-Jul-09 15191 14,940.00

16 22-Jul-09 15062 14,920.00

17 23-Jul-09 14843 14,935.00

18 24-Jul-09 15231 14,972.00

19 25-Jul-09 15379 14,955.00

20 28-Jul-09 15375 15,020.00

21 29-Jul-09 15332 14,985.00

22 30-Jul-09 15173 14,765.00

SOLUTION: - (Q - 1)

3

23 31-Jul-09 15388 14,725.00

24 1-Aug-09 15670 14,700.00

25 4-Aug-09 15924 14,850.00

26 5-Aug-09 15831 14,810.00

27 6-Aug-09 15904 14,920.00

28 7-Aug-09 15514 14,945.00

29 8-Aug-09 15160 14,970.00

30 11-Aug-09 15010 14,870.00

31 12-Aug-09 15075 14,810.00

32 13-Aug-09 15020 14,885.00

33 14-Aug-09 15518 14,970.00

34 15-Aug-09 15412 15,034.00

35 18-Aug-09 14785 14,905.00

36 19-Aug-09 15035 14,890.00

37 20-Aug-09 14810 14,905.00

38 21-Aug-09 15012 14,925.00

Source of Data: - www.timesofindia.indiatimes.com (Times of India E-papers.)

y = 0.175x + 12178R² = 0.429

14,400.00

14,500.00

14,600.00

14,700.00

14,800.00

14,900.00

15,000.00

15,100.00

13000 13500 14000 14500 15000 15500 16000 16500

Gold

Pric

e

S e n s e x

Scatter Diagram of Sensex and Gold Price

Gold Price (y) Rs./10 Gram

Linear (Gold Price (y) Rs./10 Gram )

4

In the Scatter Diagram the "X" axis denotes the values of Sensex and the "Y" axis denotes the values of

Gold Prices corresponding to the sensex values on the same day.

Interpretation :-

1. The line passing through the different points of the scatter diagram have an upward movement

or have a positive (+ve) slope.

2. It suggests that Sensex and Gold Price are positively co-related to each other. In other word

when Sensex Increase, Gold price also increases and when Sensex decreases Gold Price also

decreases.

3. Scatter Diagram shows the value of co-relation coefficient (r) = 0.655 which is >0.5 and <1.0. It

shows that Sensex and Gold Prices are highly positively co-related with each other.

Calculation of Co-relation coefficient "r"

By Direct Excel Formula Sensex (X)

Gold Price (Y) Rs./ 10 Gram

Co-relation Coefficient "r".

14,494 14,580 0.6556

14,646 14,440

14,658 14,490

14,913 14,470

14,043 14,590

14,170 14,615

13,769 14,615

13,757 14,510

13,504 14,485

13,400 14,585

13,854 14,655

14,253 14,745

14,250 14,825

14,745 14,795

15,191 14,940

15,062 14,920

14,843 14,935

15,231 14,972

15,379 14,955

SOLUTION: - (Q - 2)

5

15,375 15,020

15,332 14,985

15,173 14,765

15,388 14,725

15,670 14,700

15,924 14,850

15,831 14,810

15,904 14,920

15,514 14,945

15,160 14,970

15,010 14,870

15,075 14,810

15,020 14,885

15,518 14,970

15,412 15,034

14,785 14,905

15,035 14,890

14,810 14,905

15,012 14,925

By manual calculation :- Sensex (X)

Gold Price (Y) Rs./ 10 Gram

X2 Y2 X.Y covariance of x and y {cov (x,y)}

SD of x (ℓx)

SD of y (ℓy)

co-relation coefficient ( r )

14,494 14,580 210076036 212576400 211322520 74690.09 652.12362 174.68806 0.6556

14,646 14,440 214505316 208513600 211488240

14,658 14,490 214856964 209960100 212394420

14,913 14,470 222397569 209380900 215791110

14,043 14,590 197205849 212868100 204887370

14,170 14,615 200788900 213598225 207094550

13,769 14,615 189585361 213598225 201233935

13,757 14,510 189255049 210540100 199614070

13,504 14,485 182358016 209815225 195605440

13,400 14,585 179560000 212722225 195439000

13,854 14,655 191933316 214769025 203030370

14,253 14,745 203148009 217415025 210160485

14,250 14,825 203062500 219780625 211256250

6

14,745 14,795 217415025 218892025 218152275

15,191 14,940 230766481 223203600 226953540

15,062 14,920 226863844 222606400 224725040

14,843 14,935 220314649 223054225 221680205

15,231 14,972 231983361 224160784 228038532

15,379 14,955 236513641 223652025 229992945

15,375 15,020 236390625 225600400 230932500

15,332 14,985 235070224 224550225 229750020

15,173 14,765 230219929 218005225 224029345

15,388 14,725 236790544 216825625 226588300

15,670 14,700 245548900 216090000 230349000

15,924 14,850 253573776 220522500 236471400

15,831 14,810 250620561 219336100 234457110

15,904 14,920 252937216 222606400 237287680

15,514 14,945 240684196 223353025 231856730

15,160 14,970 229825600 224100900 226945200

15,010 14,870 225300100 221116900 223198700

15,075 14,810 227255625 219336100 223260750

15,020 14,885 225600400 221563225 223572700

15,518 14,970 240808324 224100900 232304460

15,412 15,034 237529744 226021156 231704008

14,785 14,905 218596225 222159025 220370425

15,035 14,890 226051225 221712100 223871150

14,810 14,905 219336100 222159025 220743050

15,012 14,925 225360144 222755625 224054100

565,110

562,006 8420089344 8313021290 8360606925

←Total (∑)

Frequency = Total No. of Observation = 38

Interpretation of the value of r :-

1. Here the value of r is positive (+ve), which suggests that both the variable i.e.:- Sensex & Gold Price

are positively correlated with each other.

2. In other words when Sensex increases the Gold Price also increases and when Sensex decreases the

Gold Price also decreases.

3. r = 0.6556 which states that 0.5 < r < 1.0. In other words the both the variables are highly positively

correlated with each other. It means change in one variable causes a change in the other variable with a

higher proportion.

7

Estimation of Regression Equations:-

X Y

Regression Coefficient

Mean 14871.3158 14789.6316 x on y (bxy) 2.4476

SD 652.1236 174.6881 y on x (byx) 0.1756

r 0.6556

cov(x,y) 74690.0900

1. Regression equation of x on y:- x = 2.448 *y - 21327.463

Mean of x - (bxy*mean of y)

-21327.46263

2. Regression equation of y on x:- y = .1756 * x + 12177.756

Mean of y - (byx * mean of x)

12177.75581

SOLUTION: - (Q - 3)