F.Y B.COM
SEMESTER - 2
BUSINESS STATISTICS
(BS)
MCQS
1. If the plotted points in a scatter diagram lie from upper left to lower right, then the correlation is
(a) Positive
(b) Zero
(c) Negative
(d) None of these
2. Some of the cell frequencies in a bivariate frequency table may be
(a) Negative
(b) Zero
(c) a or b
(d) None of these
3. Bivariate Data are the data collected for
(a) Two variables
(b) More than two variables
(c) Two variables at the same point of time
(d) Two variables at different points of time.
4. Regression analysis is concerned with
(a) Establishing a mathematical relationship between two variables
(b) Measuring the extent of association between two variables
(c) Predicting the value of the dependent variable for a given value of the independent variable.
(d) Both (a) and (c)
5. Scatter diagram is considered for measuring
(a) Linear relationship between two variables.
(b) Curvilinear relationship between two variables
(c) Neither (a) nor (b)
(d) Both (a) and (b)
6. What is spurious correlation ?
(a) It is a bad relation between two variables.
(b) It is very low correlation between two variables.
(c) It is the correlation between two variables having no causal relation.
(d) It is a negative correlation
7. Correlation analysis aims at
(a) Predicting one variable for a given value of the other variable
(b) Establishing relation between two variables.
(c) Measuring the extent of relation between two variables
(d) Both (b) and (c)
8. If u = 2x + 5 and v = –3y – 6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u ?
(a) 3.6
(b) - 3.6
(c) 2.4
(d) - 2.4
9. If the regression line of y on x and of x on y are given by 2x + 3y = -1 and 5x + 6y = -1 then the arithmetic means of x and y are given by
(a) (1, -1)
(b) (-1, 1)
(c) (-1, -1)
(d) (2, 3)
10. Given the regression equations as 3x + y = 13 and 2x + 5y = 20, which one is the regression equation of y on x ?
(a) 1st equation
(b) 2nd equation
(c) both (a) and (b)
(d) none of these
11. Given the following equations : 2x –3y = 10 and 3x + 4y = 15, which one is the regression equation of x on y ?
(a) 1st equation
(b) 2nd equation
(c) both the equations
(d) none of these
12. A Time series consists of data arranged _______ .
(a) Geographically
(b) Chronologically
(c) either (a) or (b)
(d) both (a) and (b)
13. If y = 3x + 4 is the regression line of y on x and the arithmetic mean of x is –1, what is the arithmetic mean of y ?
(a) 1
(b) -1
(c) 7
(d) none of these
14. If 4y – 5x = 15 is the regression line of y on x and the coefficient of correlation between x and y is 0.75, what is the value of the regression coefficient of x on y ?
(a) 0.45
(b) 0.9375
(c) 0.6
(d) none of these
15. If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?
(a) No restriction.
(b) The product of the standard deviations should be more than 15.
(c) The product of the standard deviations should be less than 15.
(d) The sum of the standard deviations should be less than 15.
16. If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation coefficient ?
(a) 0.01
(b) 0.625
(c) 0.4
(d) 0.5
17. If y = a + bx, then what is the coefficient of correlation between x and y ?
(a) 1
(b) -1
(c) 1 or – 1 according as b > 0 or b < 0
(d) none of these
18. If the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is – 0.6, then what is the correlation coefficient between u and y ?
(a) - 0.6
(b) 0.8
(c) 0.6
(d) - 0.8
19. If the covariance between two variables is 40 and the variance of one of the variables is 16, what would be the variance of the other variable ?
(a) More than 100
(b) More than 10
(c) Less than 10
(d) More than 1.25
20. If u + 5x = 6 and 3y – 7v = 20 and the correlation coefficient between x and y is 0.58 then what would be the correlation coefficient between u and v?
(a) 0.58
(b) - 0.58
(c) - 0.84
(d) 0.84
21. If there are two variables x and y, then the number of regression equations could be
(a) 1
(b) 2
(c) Any number
(d) 3
22. Since Blood Pressure of a person depends on age, we need consider
(a) The regression equation of Blood Pressure on age
(b) The regression equation of age on Blood Pressure
(c) Both (a) and (b)
(d) Either (a) or (b)
23. If the coefficient of correlation between two variables is – 0.9, then the coefficient of determination is
(a) 0.9
(b) 0.81
(c) 0.1
(d) 0.19
24. What are the limits of the two regression coefficients?
(a) No limit
(b) Must be positive
(c) One positive and the other negative
(d) Product of the regression coefficient must be numerically less than unity
25. The regression coefficients remain unchanged due to a
(a) Shift of origin
(b) Shift of scale
(c) Both (a) and (b)
(d) (a) or (b)
26. The two lines of regression become identical when
(a) r = 1
(b) r = -1 (c) r = 0
(d) (a) or
(b) (a) or (b)
27. The method applied for deriving the regression equations is known as
(a) Least squares
(b) Concurrent deviation
(c) Product moment
(d) Normal equation
28. The correlation between the speed of an automobile and the distance travelled by it after applying the brakes is
(a) Negative
(b) Zero
(c) Positive
(d) None of these
29. If all the plotted points in a scatter diagram lie on a single line, then the correlation is
(a) Perfect positive
(b) Perfect negative
(c) Both (a) and (b)
(d) Either (a) or (b)
30. If the value of correlation coefficient is positive, then the points in a scatter diagram tend to cluster
(a) From lower left corner to upper right corner
(b) From lower left corner to lower right corner
(c) From lower right corner to upper left corner
(d) From lower right corner to upper right corner.
31. If the plotted points in a scatter diagram are evenly distributed, then the correlation is
(a) Zero
(b) Negative
(c) Positive
(d) (a) or (b)
32. When r = 1, all the points in a scatter diagram would lie
(a) On a straight line directed from lower left to upper right
(b) On a straight line directed from upper
left to lower right
(c) On a straight line
(d) Both (a) and (b)
33. Pearson’s correlation coefficient is used for finding
(a) Correlation for any type of relation
(b) Correlation for linear relation only
(c) Correlation for curvilinear relation only
(d) Both (b) and (c)
34. The correlation between shoe - size and intelligence is
(a) Lack of correlation
(b) Positive
(c) Negative
(d) None of these
35. Product moment correlation coefficient may be defined as the ratio of
(a) The product of standard deviations of the two variables to the covariance between them
(b) The covariance between the variables to the product of the variances of them
(c) The covariance between the variables to the product of their standard deviations
(d) Either (b) or (c)
36. The coefficient of correlation between two variables
(a) Can have any unit.
(b) Is a unit free measure
(c) Is expressed as the product of units
(d) None of these of the two variables
37. In case the correlation coefficient between two variables is 1, the relationship between the two variables would be
(a) y = a + bx
(b) y = a + bx, b > 0
(c) y = a + bx, b < 0
(d) y = a + bx, both a and b being positive.
38. The covariance between two variables is
(a) Strictly positive
(b) Strictly negative
(c) Always 0
(d) Either positive or negative or zero.
39. If the relationship between two variables x and y is given by 2x + 3y + 4 = 0, then the value of the correlation coefficient between x and y is
(a) 0
(b) 1
(c) - 1
(d) negative
40. What are the limits of the correlation coefficient ?
(a) No limit
(b) -1 and 1
(c) 0 and 1, including the limits
(d) -1 and 1, including the limits
41. If byx = - 0.5 then the following is true.
(a) With increase in one unit of X expected increase in Y is 0.5
(b) With increase in one unit of X expected decrease in Y is 0.5
(c) Either (a) or (b)
(d) None
42. The unit of correlation coefficient is
(a) Unit in which data are measure
(b) Percentages
(c) Not exist
(d) None
43.The correlation coefficient between two variables keeping the effect of other variables constant is called
(a) Simple correlation
(b) Partial correlation
(c) Multiple correlation
(d) Either (b) or (c)
44. The multiple correlation coefficient is
(a) Joint effect of independent variables on one dependent variable
(b) Correlation coefficient between dependent variable and its estimated value
(c) both (a) and (b)
(d) none
45. The correlation coefficient between two variables having two pairs of observation is
(a) - 1
(b) + 1
(c) Either (a) or (b)
(d) 0.5
46. As the value of X decreases, if value of Y also decreases, then coefficient of correlation will be
(a) negative
(b) positive
(c) perfect linear
(d) zero
47. In a regression line of Y on X, where X is
(a) the explained variable
(b) a constant
(c) explanatory variable
(d) regressed variable
48. Suppose you are told that there is positive relationship between incentives and productivity. Which of the following is correct ?
(a) High or low incentives hardly make any impact on productivity
(b) Productivity tends to be more when incentives are more
(c) Productivity and incentives move in different direction
(d) Productivity tends to be low when more incentives are given
49. If regression lines intersect at angle 90° then two variables are uncorrelated.
(a) True
(b) False
50. Given that the equation for a regression line is Y = 26 - 24X, we may say that the relationship of Y to X is positive and linear.
(a) True
(b) False
51. Regression coefficients are independent of change of _______
(a) neither origin nor scale
(b) scale but not of origin
(c) origin and scale both
(d) origin but not of scale
52. From the following correlation coefficients _______ shows the lowest degree of association.
(a) - 0.91
(b) 0.28
(c) 0.75
(d) 0.1
53. If two lines of regression are perpendicular to each other then rxy = _______.
(a) 0
(b) + 1
(c) - 1
(d) none of these
54. The regression lines for variables X and Y are 2X + 4Y = 8 and X + 2Y = 5 then correlation coefficient between X and Y is
(a) - 1
(b) - 1/2
(c) - 2
(d) 1
55. The variable which are used to predict the values of dependent variables are called _______
(a) independent variables
(b) explanatory variables
(c) both (a) and (b)
(d) none of these
56. If bxy = - 0.2, byx = - 0.2 then correlation coefficient rxy is
(a) - 0.2
(b) 0.2
(c) 0.4
(d) 0.04
57. For the bivariate data : {(x, y) = (10, 4), (11, 3), (12, 2), (14, 0), (8, 6)} the coefficient of correlation between X and Y is
(a) - 1
(b) + 1
(c) 0
(d) 0.5
58. Regression coefficients are independent of the change of
(a) scale
(b) origin
(c) both origin and scale
(d) neither origin nor scale
59. If the 2X + 3Y = 10 is the regression of X on Y, then bYX is
(a) 2
(b) 10
(c) - 3/2
(d) - 2/3
60. Regression equation is also known as
(a) Prediction equation
(b) Line of average relationship
(c) Estimating equation
(d) All of the above
61. If correlation coefficient r = +1; then correlation between both variables X and Y is said to be _______ .
(a) Positive
(b) Perfectly Positive
(c) negative
(d) perfectly negative
62. The function Y = a + bX + cX2 represents
(a) Simple linear regression
(b) Simple nonlinear regression
(c) Multiple linear regression
(d) Multiple nonlinear regression
63.Correlation coefficient will be negative when
(a) X increases, Y decreases
(b) X decreases, Y increases
(c) X decreases, Y decreases
(d) Both (a) and (b)
64. For two regression lines 3X - 4Y = - 8 and 4X - 3Y = 1, mean values of X and Y are
(a) (4, 5)
(b) (3, 4)
(c) (4, 3)
(d) (5, 4)
65. If the correlation coefficient between X and Y is 0.7, then percentage of variation unaccounted for (unexplained), is
(a) 70
(b) 51
(c) 30
(d) 49
66. The _______ is the graphical method of measuring the relationship between two variables.
(a) Scatter diagram
(b) dot diagram
(c) both (a) and (b)
(d) none
67. The two lines of regression will be _______, if the variables are perfectly related.
(a) Perpendicular
(b) Coincided
(c) Parallel
(d) None of these
68. If one regression coefficient is greater than unity, then other must be
(a) Less than unity
(b) Greater than unity
(c) Equal to one
(d) Equal to infinity
69. The quantity “b” in the regression equation Y = a + bX is called the _______.
(a) regression coefficient
(b) slope coefficient
(c) correlation coefficient
(d) both (a) and (b)
70. Y =
(a) T x S + C + I
(b) T x S x C x I
(c) T + S - C - I
(d) T x S x C - I
71. The most important factors causing seasonal variations are :
(a) growth in population
(b) technological improvement
(c) weather and social customs
(d) change in fashion
72. The most widely used method of measuring seasonal variations is :
(a) Simple average
(b) Ratio to trend
(c) Ratio to moving
(d) Link relative
73. In the least squares linear trend equation Y = a + bx, if b is positive, it indicates :
(a) declining trend
(b) rising trend
(c) no trend
(d) all of these
74. In a regression line Y on X, the variable Y is known as _______
(a) regressor
(b) explanatory variable
(c) predictor
(d) regressed variable
75. The coefficient of correlation between demand and price of a commodity is - 0.7, then the coefficient of determination is _______
(a) 0.7
(b) 0.14
(c) - 0.49
(d) 0.49
76. If bxy > 1, then byx is _______
(a) less than 1
(b) greater than 1
(c) equal to 1
(d) equal to 0
77. Seasonal variations are short term variations with period
(a) one year
(b) less than one year
(c) more than one year
(d) all of these
78.Regression coefficient is independent of change of _______
(a) origin
(b) scale
(c) both origin and scale
(d) neither origin nor scale
79. A Positive a significant correlation between the number of shoes produced and the steel produced per year is :
(a) a nonsense correlation
(b) a spurious correlation
(c) a meaningless correlation
(d) all the above
80. If the correlation coefficient between two variables X and Y is 1, then the two lines of regression :
(a) coincide
(b) are at right angles
(c) are at 45° angle
(d) none of the above
81. If the slopes of the two regression lines are negative, then correlation coefficient is :
(a) positive
(b) negative
(c) either (a) or (b)
(d) none of the above
82. Which of the following is most likely to be an inverse relationship ?
(a) Between income and expenditure on education
(b) Between price and sales for a certain product
(c) Between average number of hours studied per day and the performance of the students in the examination
(d) Between advertisement expenditure and sales of a product
83. I. An estimating equation Y = 10 - 15X shows that there is an inverse relationhship between X and Y
II. Correlation coefficient is arithmetic mean of two regression coefficients
(a) I is true, II is false
(b) I is false, II is true
(c) I and II both are true
(d) I and II both are false
84. I. Productivity tends to be low when more incentives are given. It means there is direct relationship between incentives and productivity.
II. If both dependent and independent variables increase in an estimating equation, then coefficient of correlation falls in the range 0 r 1
(a) I is true, II is false
(b) I is false, II is true
(c) I and II both are true
(d) I and II both are false
85. I. Correlation coefficient between X and Y is 0.7. Then correlation coefficient between U = 2X + 3 and V = -5Y - 3 is - 0.7
II. Pair of variables are {(x, y) : (1, 2), (2, 5), (3, 8), (4, 11)} then both variables are perfectly negatively related.
(a) I is true, II is false
(b) I is false, II is true
(c) I and II both are true
(d) I and II both are false
86. Changes that have taken place as a result of booms and depression are classified under “ _______ ” .
(a) Irregular Variation
(b) Cyclical Variation
(c) Secular Variation
(d) Seasonal Variation
87. Trend refers to the long term tendency to
(a) increase only
(b) decrease only
(c) either increasing or decreasing
(d) none of these
88. Seasonal variations repeat during a period of
(a) 20 years
(b) 10 years
(c) 12 months
(d) none of these
89. The four well defined phases of a business cycle in sequence are
(a) prosperity, decline, depression, improvement
(b) prosperity, improvement, depression, decline
(c) decline, improvement, depression, prosperity
(d) depression, improvement, decline, prosperity
90. The most important factors causing seasonal variations are
(a) growth of population
(b) technological improvement
(c) weather and social customs
(d) none of these
91. Cyclical fluctuations are caused by
(a) wars
(b) earthquakes
(c) floods
(d) none of these
92. The most widely used method of measuring seasonal variations is
(a) ratio to moving average method
(b) ratio to trend method
(c) method of simple averages
(d) link relative method
93. The sale of umbrella and rainy season are _______ correlated.
(a) positively
(b) negatively
(c) inversely
(d) none of the above
94. Karl-Pearson’s Coefficient of Correlation is known as _______
(a) Product moment correlation coefficient
(b) Pearsonian correlation coefficient
(c) Both (a) and (b)
(d) none of the above
95. The _______ property in regression analysis that the sign of bxy, byx and rxy are same.
(a) signature
(b) area
(c) special
(d) none
96. The paired values plotted on a graph marked by points lead to _______ diagram.
(a) scatter
(b) dot
(c) both (a) and (b)
(d) none
97. The variable used for prediction is called _______ .
(a) Regressed
(b) Regressor
(c) Explained
(d) dependent variable
98. Multiplicative relationship between four components of the time series given by
(a) Y = T x S x C x I
(b) Y = T + S + C + I
(c) Y = TS x CI
(d) All of the above
99. If the trend is absent in the data then the Seasonal Indices are computed by _______ .
(a) Simple average
(b) Ratio to moving average
(c) Ratio to trend method
(d) none of the above
100. Suppose fitted trend line is Y = 85.4 - 2.4X, then trend line exhibit _______ trend.
(a) increasing
(b) decreasing
(c) normal
(d) parallel
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