F.Y B.COM
SEMESTER - 2
BUSINESS STATISTICS
(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 = α + βX + ε where α and β 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
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