BUSINESS STATISTICS - MCQS - Study For Buddies

## Sunday, May 30, 2021

F.Y B.COM
SEMESTER - 2

(BS)
MCQ - UNIT 1

CORRELATION AND REGRESSION

1. A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called:

(a) Correlation
(b) Regression
(c) Residual
(d) Slope

2. The method of least squares dictates that we choose a regression line where the sum of the square of deviations of the points from the lie is:

(a) Maximum
(b) Minimum
(c) Zero
(d) Positive

3. A relationship where the flow of the data points is best represented by a curve is called:

(a) Linear relationship
(b) Nonlinear relationship
(c) Linear positive
(d) Linear negative

4. All data points falling along a straight line is called:

(a) Linear relationship
(b) Non linear relationship
(c) Residual
(d) Scatter diagram

5. The value we would predict for the dependent variable when the independent variables are all equal to zero is called:

(a) Slope
(b) Sum of residual
(c) Intercept
(d) Difficult to tell

6. The predicted rate of response of the dependent variable to changes in the independent variable is called:

(a) Slope
(b) Intercept
(c) Error
(d) Regression equation

7. The slope of the regression line of Y on X is also called the:

(a) Correlation coefficient of X on Y
(b) Correlation coefficient of Y on X
(c) Regression coefficient of X on Y
(d) Regression coefficient of Y on X

8. In simple linear regression, the numbers of unknown constants are:

(a) One
(b) Two
(c) Three
(d) Four

9. In simple regression equation, the numbers of variables involved are:

(a) 0
(b) 1
(c) 2
(d) 3

10. If the value of any regression coefficient is zero, then two variables are:

(a) Qualitative
(b) Correlation
(c) Dependent
(d) Independent

11. The straight line graph of the linear equation Y = a+ bX, slope will be upward if:

(a) b = 0
(b) b < 0
(c) b > 0
(b) b # 0

12. The straight line graph of the linear equation Y = a+ bX, slope will be downward If:

(a) b > 0
(b) b < 0
(c) b = 0
(d) b # 0

13. The straight line graph of the linear equation Y = a + bX, slope is horizontal if:

(a) b = 0
(b) b # 0
(c) b = 1
(d) a = b

14. If regression line of = 5, then value of regression coefficient of Y on X is:

(a) 0
(b) 0.5
(c) 1
(d) 5

15. If Y = 2 - 0.2X, then the value of Y intercept is equal to:

(a) -0.2
(b) 2
(c) 0.2K
(d) All of the above

16. If one regression coefficient is greater than one, then other will he:

(a) More than one
(b) Equal to one
(c) Less than one
(d) Equal to minus one

17. To determine the height of a person when his weight is given is:

(a) Correlation problem
(b) Association problem
(c) Regression problem
(d) Qualitative problem

18. The dependent variable is also called:

(a) Regression
(b) Regressand
(c) Continuous variable
(d) Independent

19. The dependent variable is also called:

(a) Regressand variable
(b) Predictand variable
(c) Explained variable
(d) All of these

20. The independent variable is also called:

(a) Regressor
(b) Regressand
(c) Predictand
(d) Estimated

21. In the regression equation Y = a+bX, the Y is called:

(a) Independent variable
(b) Dependent variable
(c) Continuous variable
(d) None of the above

22. In the regression equation X = a+ bY, the X is called:

(a) Independent variable
(b) Dependent variable
(c) Qualitative variable
(d) None of the above

23. In the regression equation Y = a +bX, ais called:

(a) X-intercept
(b) Y-intercept
(c) Dependent variable
(d) None of the above

24. The regression equation always passes through:

(a) (X,Y)
(b) (a, b)
(d) None

25. The independent variable in a regression line is:

(a) Non-random variable
(b) Random variable
(c) Qualitative variable
(d) None of the above

26. The graph showing the paired points of (Xi, Yi) is called:

(a) Scatter diagram
(b) Histogram
(c) Polygon
(d) Pie diagram

27. The graph /_____ represents the relationship that is:

(a) Linear
(b) Non linear
(c) Curvilinear
(d) No relation

28. The graph |“ represents the relationship that is:

(a) Linear positive
(b) Linear negative
(c) Non-linear
(d) Curvilinear

29. When regression line passes through the origin, then:

(a) Intercept is zero
(b) Regression coefficient is zero
(c) Correlation is zero
(d) Association is zero

30. When bxy is positive, then byx will be:

(a) Negative
(b) Positive
(c) Zero
(d) One

31. The correlation coefficient is _______ of two regression coefficients.

(a) Geometric mean
(b) Arithmetic mean
(c) Harmonic mean
(d) Median

32. When two regression coefficients bear same algebraic signs, then correlation coefficient is:

(a) Positive
(b) Negative
(c) According to two signs
(d) Zero

33. It is possible that two regression coefficients have:

(a) Opposite signs
(b) Same signs
(c) No sign
(d) Difficult to tell

34. Regression coefficient is independent of:

(a) Units of measurement
(b) Scale and origin
(c) Both (a) and (b)
(d) None of them

35. The purpose of simple linear regression analysis is to:

(a) Predict one variable from another variable
(b) Replace points on a scatter diagram by a straight-line
(c) Measure the degree to which two variables are linearly associated
(d) Obtain the expected value of the independent random variable for a given value of the dependent variable

36. The sum of the difference between the actual values of Y and its values obtained from the fitted regression line is always:

(a) Zero
(b) Positive
(c) Negative
(d) Minimum

37. If all the actual and estimated values of Y are same on the regression line, the sum of squares of error will be:

(a) Zero
(b) Minimum
(c) Maximum
(d) Unknown

38. A measure of the strength of the linear relationship that exists between two variables is called:

(a) Slope
(b) Intercept
(c) Correlation coefficient
(d) Regression equation

39. When the ratio of variations in the related variables is constant, it is called:

(a) Linear correlation
(b) Nonlinear correlation
(c) Positive correlation
(d) Negative correlation

40. If both variables X and Y increase or decrease simultaneously, then the coefficient of correlation will be:

(a) Positive
(b) Negative
(c) Zero
(d) One

41. If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be:

(a) Perfect positive
(b) Perfect negative
(c) Negative
(d) Zero

42. If the points on the scatter diagram show no tendency either to increase together or decrease together the value of r will be close to:

(a) -1
(b) +1
(c) 0.5
(d) 0

43. If one item is fixed and unchangeable and the other item varies, the correlation coefficient will be:

(a) Positive
(b) Negative
(c) Zero
(d) Undecided

44. In scatter diagram, if most of the points lie in the first and third quadrants, then coefficient of correlation is:

(a) Negative
(b) Positive
(c) Zero
(d) All of the above

45. If the two series move in reverse directions and the variations in their values are always proportionate, it is said to be:

(a) Negative correlation
(b) Positive correlation
(c) Perfect negative correlation
(d) Perfect positive correlation

46. If both the series move in the same direction and the variations are in a fixed proportion, correlation between them is said to be:

(a) Perfect correlation
(b) Linear correlation
(c) Nonlinear correlation
(d) Perfect positive correlation

47. The value of the coefficient of correlation r lies between:

(a) 0 and 1
(b) -1 and 0
(c) -1 and +1
(d) -0.5 and +0.5

48. If X is measured in yours and Y is measured in minutes, then correlation coefficient has the unit:

(a) Hours
(b) Minutes
(c) Both (a) and (b)
(d) No unit

49. The range of regression coefficient is:

(a) -1 to +1
(b) 0 to 1
(c) - to +
(d) 0 to

50. The signs of regression coefficients and correlation coefficient are always:

(a) Different
(b) Same
(c) Positive
(d) Negative

51. The arithmetic mean of the two regression coefficients is greater than or equal to:

(a) -1
(b) +1
(c) 0
(d) r

52. In simple linear regression model Y = Î± + Î²X + Îµ where Î± and Î² are called

(a) Estimates
(b) Parameters
(c) Random errors
(d) Variables

53. Negative regression coefficient indicates that the movement of the variables are in:

(a) Same direction
(b) Opposite direction
(c) Both (a) and (b)
(d) Difficult to tell

54. Positive regression coefficient indicates that the movement of the variables are in:

(a) Same direction
(b) Opposite direction
(c) Upward direction
(d) Downward direction

55. If the value of regression coefficient is zero, then the two variables are called:

(a) Independent
(b) Dependent
(c) Both (a) and (b)
(d) Difficult to tell

56. The term regression was used by:

(a) Newton
(b) Pearson
(c) Spearman
(d) Galton

57. In the regression equation Y = a + bX, b is called:

(a) Slope
(b) Regression coefficient
(c) Intercept
(d) Both (a) and (b)

58. When the two regression lines are parallel to each other, then their slopes are:

(a) Zero
(b) Different
(c) Same
(d) Positive

59. The measure of change in dependent variable corresponding to a unit change in independent variable is called:

(a) Slope
(b) Regression coefficient
(c) Both (a) and (b)
(d) Neither (a) and (b)

60. In correlation problem both variables are:

(a) Equal
(b) Unknown
(c) Fixed
(d) Random

61. In the regression equation Y = a + bX, where a and b are called:

(a) Constants
(b) Estimates
(c) Parameters
(d) Both (a) and (b)

62. If byx = bxy = 1 and Sx = Sy, then r will be:

(a) 0
(b) -1
(c) 1
(d) Difficult to calculate

63. The correlation coefficient between X and -X is:

(a) 0
(b) 0.5
(c) 1
(d) -1

64. If byx = bxy = rxy, then:

(a) Sx ≠ Sy
(b) Sx = Sy
(c) Sx > Sy
(d) Sx < Sy

65. If rxy =0.4, then R² is equal to:

(a) 0.86
(b) 0.8
(c) 0
(d) 1

66. Regression coefficient is dependent of change of _________

(a) scale
(b) origin
(c) both a and b
(d) none

67. If rxy = 0.75, then correlation coefficient between u = 1.5X and v = 2Y is:

(a) 0
(b) 0.75
(c) -0.75
(d) 1.5

68. If byx = -2 and rxy= -1, then bxy, is equal to:

(a) -1
(b) -2
(c) 0.5
(d) -0.5

69. If byx = 1.6 and bxy = 0.4, then rxy will be:

(a) 0.4
(b) 0.64
(c) 0.8
(d) -0.8

70. If byx = -0.8 and bay = -0.2, then rx is equal to:

(a) -0.2
(b) -0.4
(c) 0.4
(d) -0.8

71. The correlation coefficient between X and Y is 0.9 then

(A) there is high degree of positive correlation
(B) 19% variation is not explained by independent variable in dependent variable
(C) 81% variation is explained by independent variable in dependent variable
(D) All of the above

72. If Y = -10X and X = -0.1Y, then r is equal to:

(a) 0.1
(b) 1
(c) -1
(d) 10

73. A perfect positive correlation is signified by:

(a) 0
(b) -1
(c) +1
(d) -1 to +1

74. If rxy = 1, then:

(a) byx = bxy
(b) byx > bxy
(c) byx < bxy
(d) byx • bxy =1

75. If the sum of the product of the deviation of X and Y from their means is zero, the correlation coefficient between X and Y is:

(a) Zero
(b) Maximum
(c) Minimum
(d) Undecided

76. If rxy = 0.75, then ryx will be:

(a) 0.25
(b) 0.50
(c) 0.75
(d) -0.75

77. When rxy < 0, then byx and bxy, will be:

(a) Zero
(b) Not equal to zero
(c) Less than zero
(d) Greater than zero

78. When rxy > 0, then byx and bxy are both:

(a) 0
(b) <0
(c) > 0
(d) <1

79. If rxy = 0, then:

(a) byx = 0
(b) bxy = 0
(c) Both (a) and (b)
(d) byx ≠ bxy

80. If bxy = 0.20 and rxy = 0.50, then byx is equal to:

(a) 0.20
(b) 0.25
(c) 0.50
(d) 1.25

81. A regression model may be:

(a) Linear
(b) Non-linear
(c) Both (a) and (b)
(d) Neither (a) and (b)

82. If rxy = 0.65, then correlation coefficient between u = 1.5X + 8 and v = -2Y+9 is __________.

(a) 0
(b) 0.65
(c) -0.65
(d) 1.5

83. The units of measurement of correlation coefficient between height and weight will be ________

(a) Inches
(b) Kilogram
(c) inches/kgs
(d) None

84. If the two lines of regression are X+2Y-5=0 and 2X+3Y-8=0, the means of X and Y are

(a) -3,4
(b) 2,4
(c) 1,2
(d) 0,2

85. From the following data regarding the rainfall and the crop yield, estimated the yield when the rainfall is 22 cms.

 Y Yield X Rainfall (In kgs.) (In cms.) Average 508.4 26.7 S.D. 36.4 4.6
Correlation co-efficient = 0.52

(a) 32.65
(b) 488.85
(c) 466.6
(d) 848.8