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    BUSINESS MATHEMATICS

    AND

    STATISTICS PROJECT

    Submitted to: Submitted by:Dr. Gulshan Kumar Shubham Goyal

    Class: B.COM/LLB

    (4TH semester)

    Roll No.: 153/11

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    REGRESSION

    The technique of regression is considered to be the most useful

    statistical tool. It is helpful in making quantitative predictions in

    business in the behavior of the related variables. The main uses ofregression analysis are:

    (1) Prediction of Unknown Value: The regression analysistechnique is very useful in predicting the probable value of an

    unknown variable in response to some known related variable.

    (2) Nature of Relationship: The regression device is useful inestablishing the nature of relationship between two variables.(3) Estimation of Relationship: Regression analysis isextensively used for the measurement and estimation of the

    relationship among variables. It is an important statistical device

    which provides basis for analysis and interpretation in research

    studies.

    (4) Calculation of co-efficient of determination: The regressionanalysis provides regression co-efficients which are generally usedin calculation of co- efficients of correlation. The square of co-

    efficient of correlation is called the co- efficient of determination

    which measures the degree of association that exists between two

    variables.

    (5) Helpful in calculation of error: regression analysis is veryhelpful in estimating the error involved in using the regression lines

    as a basis for estimation.

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    Despite all utilities, the regression analysis, too, has various

    limitations. They are:

    1.Assumption of linear relationship: Regression analysis is based onthe assumption that there always exists linear relationship

    between related variables. The linear type of relationship does not

    always exist in the field of social sciences.

    2.Assumption of Static condition: While calculating the regressionequations a static condition of relationship between the variables

    is presumed. It is supposed that the relationship has not changed

    since the regression equation was computed. Such type of

    assumption has made the regression analysis a static one.3.Study of relationship in prescribed limits: The linear relationshipbetween the variables can only be ascertained within limits. When

    prescribed limits are crossed, the results become incorrect and

    inconsistent.

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    METHODOLOGY

    Under the normal equation method, computation of regression

    equations is done by solving two normal equations.

    Regression Equation of Y on X:

    We know, regression equation of Y on X is expressed as follows:

    Y = a + b.X

    Where, Y = dependent variable;

    X = Independent variable;

    a = Y- intercept;

    b = X- intercept.

    Under the normal equation method the values ofa and b is obtained by

    using the following two normal equations:

    Y = Na+bX

    XY=aY + bX2

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    DAILY DATA OF VALUE OF SHARES OF STOCKS IN INDIAN STOCK MARKETAND THREE OTHER COMPANIES.

    DATE sensex(X) T C S(Y1) S B I(Y2) RECAPITAL(Y3)

    31-Jan-13 19894.98 1342.75 2436.6 474.8

    30-Jan-13 20,005.00 1343.85 2435.4 470.95

    29-Jan-13 19,990.90 1342.5 2457.3 468.45

    28-Jan-13 20,103.35 1343.65 2490.15 476.95

    25-Jan-13 20,103.53 1337.8 2513.25 475.7524-Jan-13 19,923.53 1325.75 2458.4 464.1

    23-Jan-13 20,026.61 1311.85 2480.3 479.5

    22-Jan-13 19,981.57 1315.75 2464.35 483.95

    21-Jan-13 20,101.82 1331.6 2497.75 490

    18-Jan-13 20,039.04 1351.15 2491.2 480.55

    17-Jan-13 19,964.03 1362.25 2468.35 478.85

    16-Jan-13 19,817.63 1348.1 2432.9 479.9

    15-Jan-13 19,986.82 1334.3 2488.9 496.1

    14-Jan-13 19,906.41 1334.3 2498.25 494.9

    11-Jan-13 19,663.64 1306.35 2490.95 479.65

    10-Jan-13 19,663.55 1258.55 2539.2 494.2

    09-Jan-13 19,666.59 1275.75 2521.65 497.55

    08-Jan-13 19,742.52 1298.3 2493.45 501.65

    07-Jan-13 19,691.42 1290.55 2467 501.35

    04-Jan-13 19,784.08 1297.5 2484.8 501.7

    total 398,057.02 26452.6 49610.15 9690.85

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    FITTING REGRESSION EQUATION OF Y1 ON X:

    DATE sensex(X) T CS(Y1) X.X X.Y1

    31-Jan-

    13 19894.98 1342.75 395810229.2 26713984.430-Jan-

    13 20,005.00 1343.85 400,200,025.00 26883719.2529-Jan-

    13 19,990.90 1342.5 399,636,082.81 26837783.2528-Jan-

    13 20,103.35 1343.65 404,144,681.22 27011866.2325-Jan-

    13 20,103.53 1337.8 404,151,918.46 26894502.4324-Jan-

    13 19,923.53 1325.75 396,947,047.66 26413619.923-Jan-

    13 20,026.61 1311.85 401,065,108.09 26271908.3322-Jan-

    13 19,981.57 1315.75 399,263,139.66 26290750.73

    21-Jan-13 20,101.82 1331.6 404,083,167.31 26767583.51

    18-Jan-

    13 20,039.04 1351.15 401,563,124.12 27075748.917-Jan-

    13 19,964.03 1362.25 398,562,493.84 27195999.8716-Jan-

    13 19,817.63 1348.1 392,738,458.82 26,716,147.003015-Jan-

    13 19,986.82 1334.3 399,472,973.71 26668413.9314-Jan-

    13 19,906.41 1334.3 396,265,159.09 26561122.8611-Jan-

    13 19,663.64 1306.35 386,658,738.05 25687596.1110-Jan-

    13 19,663.55 1258.55 386,655,198.60 24747560.8509-Jan-

    13 19,666.59 1275.75 386,774,762.23 25089652.1908-Jan-

    13 19,742.52 1298.3 389,767,095.95 25631713.7207-Jan-

    13 19,691.42 1290.55 387,752,021.62 25412762.0804-Jan-

    13 19,784.08 1297.5 391,409,821.45 25669843.8

    Total 398,057.02 26452.6 7,922,921,247.00 526542279.3

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    Regression equation of Y on X is

    Y = a+bx

    The two normal equations are :

    Y2 = N.a + bx

    XY = a.x + bY2

    Substituting the value we get,

    26452.6 = 20(a) + b(398057.02)

    526542279.3 = a.398057.02 + b 7922921247

    Multiply (1) by 19902.851 and subtracting it from (2)

    526482156.3626 = 398057.02(a) + 7922469558.56

    (-)526482156.3626 =(-) a. 398057.02 +(-) b 7922921247

    -47382156.3626 = b 784323548311.56

    -0.6042072985 = b

    Therefore, the value of b = -0.6042072985

    Putting the value of b in equation (1)

    26452.6 = 20a + 240508.95

    -214056.35 = 20a

    a = 10702.81

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    FITTING REGRESSION EQUATION OF Y2 ON X:

    DATE sensex(X) S B I(Y2) X.X X.Y2

    31-Jan-

    13 19894.98 2436.6 395810229.2 96952216.5430-Jan-

    13 20,005.00 2435.4 400,200,025.00 4872017729-Jan-

    13 19,990.90 2457.3 399,636,082.81 49,123,638.5728-Jan-

    13 20,103.35 2490.15 404,144,681.22 5006035725-Jan-

    13 20,103.53 2513.25 404,151,918.46 26894502.4324-Jan-

    13 19,923.53 2458.4 396,947,047.66 48980006.1523-Jan-

    13 20,026.61 2480.3 401,065,108.09 49672000.7822-Jan-

    13 19,981.57 2464.35 399,263,139.66 26290750.73

    21-Jan-13 20,101.82 2497.75 404,083,167.31 50209320.91

    18-Jan-

    13 20,039.04 2491.2 401,563,124.12 49921256.4517-Jan-

    13 19,964.03 2468.35 398,562,493.84 49278213.4516-Jan-

    13 19,817.63 2432.9 392,738,458.82 48214312.0315-Jan-

    13 19,986.82 2488.9 399,472,973.71 26668413.9314-Jan-

    13 19,906.41 2498.25 396,265,159.09 49731188.7811-Jan-

    13 19,663.64 2490.95 386,658,738.05 48981144.0610-Jan-

    13 19,663.55 2539.2 386,655,198.60 49929686.1609-Jan-

    13 19,666.59 2521.65 386,774,762.23 49592256.6708-Jan-

    13 19,742.52 2493.45 389,767,095.95 49226986.4907-Jan-

    13 19,691.42 2467 387,752,021.62 48578733.1404-Jan-

    13 19,784.08 2484.8 391,409,821.45 49159481.98

    Total 398,057.02 49610.15 7,922,921,247.00 966184643.3

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    Regression Equation Y on X

    Y = a+bx

    The two normal equations are :

    Y2 = N.a + bx

    XY = a.x + bY2

    Substituting the value we get,

    49610.15 = 20a + b 398057.02

    9661846643.3 = a. 398057.02 + b 7922921247

    Multiply (1) by 19902.851 and subtracting it from (2)

    987383423.53765 = 398057.02a + b7922469558.56402

    966184643.3 = 398057.02 a+ b7922921247

    21198780.23765 = - 451688.43598b

    b = 46.9323067607

    therefore, the value of b = 46.9323067607

    Putting the value of b in equation (1)

    49610.15 = 20a + 18681734.1708901

    -18632124.0208901 = 20a

    a = -931606.201044505

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    FITTING REGRESSION EQUATION OF Y3 ON X:

    DATE sensex(X) RECAPITAL(Y3) X.X X.Y3

    31-Jan-

    13 19894.98 474.8 395810229.2 9446136.50430-Jan-

    13 20,005.00 470.95 400,200,025.00 9421354.7529-Jan-

    13 19,990.90 468.45 399,636,082.81 9364737.10528-Jan-

    13 20,103.35 476.95 404,144,681.22 9588292.78325-Jan-

    13 20,103.53 475.75 404,151,918.46 9564254.39824-Jan-

    13 19,923.53 464.1 396,947,047.66 9246510.27323-Jan-

    13 20,026.61 479.5 401,065,108.09 9602759.495

    22-Jan-13 19,981.57 483.95 399,263,139.66 9670080.802

    21-Jan-

    13 20,101.82 490 404,083,167.31 9849891.818-Jan-

    13 20,039.04 480.55 401,563,124.12 9629760.67217-Jan-

    13 19,964.03 478.85 398,562,493.84 9559775.76616-Jan-

    13 19,817.63 479.9 392,738,458.82 9510480.63715-Jan-

    1319,986.82

    496.1399,472,973.71

    9915461.402

    14-Jan-

    13 19,906.41 494.9 396,265,159.09 9851682.30911-Jan-

    13 19,663.64 479.65 386,658,738.05 9431664.92610-Jan-

    13 19,663.55 494.2 386,655,198.60 9717726.4109-Jan-

    13 19,666.59 497.55 386,774,762.23 9785111.85508-Jan-

    13 19,742.52 501.65 389,767,095.95 9903835.15807-Jan-

    13 19,691.42 501.35 387,752,021.62 9872293.41704-Jan-

    13 19,784.08 501.7 391,409,821.45 9925672.936

    Total 398,057.02 9690.85 7,922,921,247.00 1928574283

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    Regression Equation Y on X

    Y = a+bx

    The two normal equations are :

    Y2 = N.a + bx

    XY = a.x + bY2

    Substituting the value we get,

    9690.85 = a. 20 + b 398057.2

    1928574283 = a. 398057.02 + b 7922921247

    Multiply (1) by 19902.851 and subtracting it from (2)

    192875543.61335 = 398057.02a + b 7922473141.0772

    (-)1928574283 = (-)398057.02a +(-) b 7922921247

    -1735698739.38665 = -b 448105.92228

    b = 3873.4117338622

    Putting the value of b in equation (1)

    9690.85 = 20a + 1541839429.22833

    a = -77091486.9189165

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    Date Adj Close*

    7 Feb, 2013 19,540.08

    6 Feb, 2013 19,611.27

    5 Feb, 2013 19,631.97

    4 Feb, 2013 19,728.21

    1 Feb, 2013 19,736.45

    (I) REGRESSION EQUATION OF Y1 ON X IS:

    Y= 10702.81 0.6042072985 X

    Putting the values of X in the above equation, the next five value of Y are :-

    (i) Y = 10702.81 0.6042072985 ( 19736.45)Y = 1222.0971364803

    (ii) Y = 10702.81- 0.6042072985 ( 19728.21)= 1217.1184683407

    (iii) Y=10702.81 0.6042072985(19631.97)=1158.969557933

    (iv) Y= 10702.81 0.6042072985(19,611.27)=1146.4624668541

    (v) Y = 10702.81 0.6042072985(19540.08)Y = 1103.4489492739

    (II) REGRESSION EQUATION OF Y2 ON X IS:

    Y = -931606.201044505 + 46.9323067607X

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    Putting the values of X in the above equation, the next five value of Y are :-

    (i) Y = -931606.201044505 + 46.9323067607 (19,736.45)=1857883.32681172

    (ii) Y = -931606.201044505 + 46.9323067607 (19,728.21)=1857496.60460401

    (iii) Y = -931606.201044505 + 46.9323067607 (19631.97)=1852979.83940136

    (iv) Y = -931606.201044505 + 46.9323067607 (19,611.27)=1851830.34710382

    (v) Y = -931606.201044505 + 46.9323067607 (19540.08)=1707870.30945102

    (III) REGRESSION EQUATION OF Y3 ON X IS:

    Y = -77091486.9189165 +3873.4117338622X

    Putting the values of X in the above equation, the next five value of Y are :-

    (i) Y = -77091486.9189165 +3873.4117338622(19736.45)= 153538883.933701

    (ii) Y=-77091486.9189165 +3873.4117338622(19728.21)=153506967.021014

    (iii) Y=-77091486.9189165 +3873.4117338622(19631.97)=153134189.875747

    (iv) Y=-77091486.9189165 +3873.4117338622(19611.21)=153053777.848152

    (v) Y=-77091486.9189165 +3873.4117338622(19540.08)=152778262.071522

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    CONCLUSION

    From the above calculations done and projections made, we can conclude that-

    (i) When there will be fall in sensex, the share price of TCS will also fall, but the fall inshare prices is less than the fall in sensex.

    (ii) When there will be fall in sensex, the share price of SBI will also fall, but the fall inshare prices is more than the fall in sensex.

    (iii) When there will be fall in sensex, the share price of Reliance capital will also fall, butthe fall in share prices is more than the fall in sensex.