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Correlation and Regression Analysis Model Question Paper

11th Standard

    Reg.No. :
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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    4 x 1 = 4
  1. The correlation coefficient is

    (a)

    r(X,Y)=\(\frac { { \sigma }_{ x }{ \sigma }_{ y } }{ cov(x,y) } \)

    (b)

    r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ x }{ \sigma }_{ y } } \)

    (c)

    r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ y } } \)

    (d)

    r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ x } } \)

  2. The variable which influences the values or is used for prediction is called

    (a)

    Dependent variable

    (b)

    Independent variable

    (c)

    Explained variable

    (d)

    Regressed

  3. Scatter diagram of the variate values (X,Y) give the idea about

    (a)

    functional relationship

    (b)

    regression model

    (c)

    distribution of errors

    (d)

    no relation

  4. If regression co-efficient of Y on X is 2, then the regression co-efficient of X on Y is

    (a)

    \(\frac{1}{2}\)

    (b)

    2

    (c)

    >\(\frac{1}{2}\)

    (d)

    1

  5. 3 x 2 = 6
  6. Calculate the correlation coefficient from the following data
    N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597

  7. From the following data calculate the correlation coefficient Σxy=120, Σx2=90, Σy2=640

  8. The following information is given

      X(in Rs.) Y(in Rs.)
    Arithmetic Mean 6 8
    Standard Deviation 5 \(\frac{40}{3}\)

    Coefficient of correlation between X and Y is \(\frac{8}{15}\) . Find (i) The regression Coefficient of Y on X (ii) The most likely value of Y when X =Rs.100.

  9. 5 x 3 = 15
  10. The following table shows the sales and advertisement expenditure of a form

      Sales Advertisement expenditure(Rs.Cross)
    Mean 40 6
    SD 10 1.5

    Coefficient of correlation r= 0.9. Estimate the likely sales for a proposed advertisement expenditure of Rs. 10 crores.

  11. Marks in two subjects X and Y given below: Calculate the rank correlation:

    X 46 54 56 57 58 60 62
    Y 36 40 44 54 42 58 53
  12. prove that the correlation co-efficient is the geometric mean of regression co-efficients.

  13. For the following observations, find the regression co-efficients byx and bxy and hence find the correlation co-efficient between x and y.(4,2) (2, 3)(3, 2)(4, 4)(2, 4)

  14. Compute the co-efficient of correlation batween the variates x and y from the given data:
    No. of pairs of x and y series=8.x-series A.M.=74.5, x-series assumed mean =69, x-series S.D=13.07, y-series S.D=15.85, sum of products of corresponding deviations of x and y series =2176.

  15. 5 x 5 = 25
  16. Find coefficient of correlation for the following:

    Cost(Rs) 14 19 24 21 26 22 15 20 19
    Sales(Rs) 31 36 48 37 50 45 33 41 39
  17. Calculate coefficient of correlation for the ages of husbands and their respective wives:

    Age of husbands 23 27 28 29 30 31 33 35 36 39
    Age of wives 18 22 23 24 25 26 28 29 30 32
  18. Calculate rank correlation coefficient of the following data.

    Subject 1 40 46 54 60 70 80 82 85 87 90 95
    Subject 2 45 46 50 43 40 75 55 72 65 42 70
  19. A computer while calculating the correlation co-efficient between two variables x and y from 25 pairs of observations, obtained the following results. \(\sum\)x=125, \(\sum\)x2=650, \(\sum\)y=100, \(\sum\)y2=460, xy=508. It was later found out that it had copied down two pairs as while the correct values are 

    x y
    6 14
    8 6
    x y
    8 12
    6 8

    Obtain the correlation co-efficient for the correct value.

  20. Out the following two regression lines, find the line of regression of X on Y, 2x+3y=7 and 5x+54=9.

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