# Statistics MCQs-Numerical Descriptive Statistics and Sampling Part 6

Glide to success with Doorsteptutor material for GATE : fully solved questions with step-by-step explanation- practice your way to success.

101. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 10. The covariance between x and y is given by:

a. 30.3

b. 43.1

c. 34.0

d. 27.4

e. 31.9

Answer: B

102. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 15. The covariance between x and y is given by:

a. 30.3

b. 43.1

*c. 34.0

d. 27.4

e. 31.9

103. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 20. The covariance between x and y is given by:

a. 30.3

b. 43.1

c. 34.0

d. 27.4

e. 31.9

Answer: D

104. A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: ∑x = 276, ∑x^{2} = 6982, ∑y = 193, ∑y^{2} = 3421, ∑xy = 4842 and n = 12. The equation of the least squares regression line is given by:

a. ŷ = 0.64x + 1.46

b. ŷ = 0.51x + 4.75

c. ŷ = 0.75x – 1.08

d. ŷ = 0.93x – 5.88

e. None of the above

Answer: A

105. A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: ∑x = 265, ∑x^{2} = 6982, ∑y = 193, ∑y^{2} = 3421, ∑xy = 4842 and n = 12. The equation of the least squares regression line is given by:

a. ŷ = 0.64x + 1.46

b. ŷ = 0.51x + 4.75

c. ŷ = 0.75x – 1.08

d. ŷ = 0.93x – 5.88

e. None of the above

Answer: B

106. A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: ∑x = 276, ∑x^{2} = 6888, ∑y = 193, ∑y^{2} = 3421, ∑xy = 4842 and n = 12. The equation of the least squares regression line is given by:

a. ŷ = 0.64x + 1.46

b. ŷ = 0.51x + 4.75

c. ŷ = 0.75x – 1.08

d. ŷ = 0.93x – 5.88

e. None of the above

Answer: C

107. A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: ∑x = 276, ∑x^{2} = 6982, ∑y = 185, ∑y^{2} = 3421, ∑xy = 4842 and n = 12. The equation of the least squares regression line is given by:

a. ŷ = 0.64x + 1.46

b. ŷ = 0.51x + 4.75

c. ŷ = 0.75x – 1.08

*d. ŷ = 0.93x – 5.88

e. None of the above

108. You have been given a two-variable data set with the following calculations already completed: ∑x = 496, ∑x^{2} = 37306, ∑y = 508, ∑y^{2} = 39352, ∑xy = 38309 and n = 7. The equation of the least squares regression line is given by:

a. ŷ = 1.07x - 3.29

b. ŷ = 1.04x - 0.95

c. ŷ = 1.03x – 0.56

d. ŷ = 1.03x – 0.39

e. None of the above

Answer: A

109. You have been given a two-variable data set with the following calculations already completed: ∑x = 496, ∑x^{2} = 37306, ∑y = 508, ∑y^{2} = 39352, ∑xy = 38309 and n = 8. The equation of the least squares regression line is given by:

a. ŷ = 1.07x - 3.29

b. ŷ = 1.04x - 0.95

c. ŷ = 1.03x – 0.56

d. ŷ = 1.03x – 0.39

e. None of the above

Answer: B

110. You have been given a two-variable data set with the following calculations already completed: ∑x = 496, ∑x^{2} = 37306, ∑y = 508, ∑y^{2} = 39352, ∑xy = 38309 and n = 9. The equation of the least squares regression line is given by:

a. ŷ = 1.07x - 3.29

b. ŷ = 1.04x - 0.95

c. ŷ = 1.03x – 0.56

d. ŷ = 1.03x – 0.39

e. None of the above

Answer: C

111. You have been given a two-variable data set with the following calculations already completed: ∑x = 496, ∑x^{2} = 37306, ∑y = 508, ∑y^{2} = 39352, ∑xy = 38309 and n = 10. The equation of the least squares regression line is given by:

a. ŷ = 1.07x - 3.29

b. ŷ = 1.04x - 0.95

c. ŷ = 1.03x – 0.56

d. ŷ = 1.03x – 0.39

e. None of the above

Answer: D

112. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 5. The equation of the least squares regression line is given by:

a. ŷ = 0.24x + 3.96

b. ŷ = 0.38x + 0.98

c. ŷ = 0.40x + 0.56

d. ŷ = 0.41x + 0.39

e. None of the above

Answer: A

113. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 10. The equation of the least squares regression line is given by:

a. ŷ = 0.24x + 3.96

b. ŷ = 0.38x + 0.98

c. ŷ = 0.40x + 0.56

d. ŷ = 0.41x + 0.39

e. None of the above

Answer: B

114. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 15. The equation of the least squares regression line is given by:

a. ŷ = 0.24x + 3.96

b. ŷ = 0.38x + 0.98

c. ŷ = 0.40x + 0.56

d. ŷ = 0.41x + 0.39

e. None of the above

Answer: C

115. You have been given a two-variable data set with the following calculations already completed: ∑x = 72, ∑x^{2} = 1544, ∑y = 37, ∑y^{2} = 305, ∑xy = 654 and n = 20. The equation of the least squares regression line is given by:

a. ŷ = 0.24x + 3.96

b. ŷ = 0.38x + 0.98

c. ŷ = 0.40x + 0.56

d. ŷ = 0.45x + 0.40

*e. None of the above

116. You have been given the following calculated values for a set of data containing x and y values: ∑x = 46, ∑y = 76, ∑xy = 473, ∑x^{2} = 284, ∑y^{2} = 794 and n = 8. What is the value of the gradient of the regression line between x and y?

a. 1.846

b. 1.474

c. 2.141

d. 1.795

e. 1.444

Answer: A

117. You have been given the following calculated values for a set of data containing x and y values: ∑x = 45, ∑y = 76, ∑xy = 473, ∑x^{2} = 284, ∑y^{2} = 794 and n = 8. What is the value of the gradient of the regression line between x and y?

a. 1.846

b. 1.474

c. 2.141

d. 1.795

e. 1.444

Answer: B

118. You have been given the following calculated values for a set of data containing x and y values: ∑x = 46, ∑y = 75, ∑xy = 473, ∑x^{2} = 284, ∑y^{2} = 794 and n = 8. What is the value of the gradient of the regression line between x and y?

a. 1.846

b. 1.474

c. 2.141

d. 1.795

e. 1.444

Answer: C

119. You have been given the following calculated values for a set of data containing x and y values: ∑x = 46, ∑y = 76, ∑xy = 472, ∑x^{2} = 284, ∑y^{2} = 794 and n = 8. What is the value of the gradient of the regression line between x and y?

a. 1.846

b. 1.474

c. 2.141

d. 1.795

e. 1.444

Answer: D

120. You have been given the following calculated values for a set of data containing x and y values: ∑x = 46, ∑y = 76, ∑xy = 473, ∑x^{2} = 284, ∑y^{2} = 794 and n = 8. What is the value of the intercept of the regression line between x and y?

a. -1.115

b. 1.212

c. -2.936

d. -0.821

e. 1.444

Answer: A