# Statistics MCQs-Numerical Descriptive Statistics and Sampling Part 7

121. 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 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: B

122. 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 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: C

123. 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 intercept of the regression line between x and y?

a. -1.115

b. 1.212

c. -2.936

*d. -0.821

e. 1.444

124. Which of the following statements is correct?

a. If X and Y have a correlation coefficient of 0.99, then X and Y are unrelated

b. If the covariance between X and Y is a large negative number, then X and Y have no linear relationship

c. The least squares regression line can be used to forecast values of Y for any given value of X

d. The smaller the sum of squared residuals, the more confidence we will have in our forecasted values of Y

e. None of the above are correct

Answer: D

125. If the sample correlation coefficient between x and y is -1 (i.e. r = -1) then we can be sure that:

a. None of the points in the sample will lie on the least squares regression line.

b. The relationship between x and y is a perfect positive linear relationship.

c. The true value of the population correlation coefficient is also equal to -1.

d. All the points in the sample will lie on the least squares regression line.

e. None of the above

Answer: D

126. If X and Y have a large positive covariance and a coefficient of correlation near 1 then we can say that:

a. X and Y have a strong positive non-linear relationship

b. X and Y have a strong negative linear relationship

c. X and Y have a weak positive linear relationship

d. X and Y have a strong positive linear relationship

e. None of the above

Answer: D

127. The correlation coefficient is used to determine:

*a. The strength of the linear relationship between *x* and *y*

b. The least squares estimates of the regression parameters

c. The predicted value of *y* for a given value of *x*

d. The coefficient of variation

e. None of the above

128. In regression analysis, the residuals represent the:

a. Difference between the actual *y* values and their predicted values

b. Difference between the actual *x* values and their predicted values

c. Square root of the coefficient of correlation

d. Change in *y* per unit change in *x*

e. None of the above

Answer: A

129. In simple linear regression, which of the following statements indicate no linear relationship between the variables *x* and *y*?

a. Coefficient of correlation is 1

b The correlation coefficient is 0

c. Sum of squares for error is 0

d. Covariance is relatively large

e. None of the above

Answer: B

130. Which of the following statements about the correlation coefficient is correct?

a. it is a number that indicates the direction of the relationship between the dependent variable y and the independent variable x

b. it is a number that indicates the strength of the relationship between the dependent variable y and the independent variable x

c. both a and b are correct

d. neither a nor b is correct

e. None of the above are correct

Answer: C

131. If the correlation coefficient, r, is equal to 0, then:

a. the slope of the least squares regression line is zero

b. there is no linear relationship between the dependent variable y and the independent variable x

c. the covariance will also be 0 or close to 0

d. all of the above are correct

e. None of the above are correct

Answer: D

132. If all data points (pairs of x and y observations) lie on a perfectly straight line sloping upwards, the correlation coefficient is equal to:

a. +1

b. -1

c. 0

d. +2

e. None of the above

Answer: A

133. If all data points (pairs of x and y observations) lie on a perfectly straight line sloping downwards, the correlation coefficient is equal to:

a. +1

b. -1

c. 0

d. +2

e. None of the above

Answer: B

134. Which of the following errors can be reduced by good randomization techniques and increasing the sample size?

a. Data acquisition error

b. Sampling error

c. Non-response error

d. Selection bias

e. None of the above

Answer: B

135. During a particular sampling process great care was taken to eliminate all non-sampling error. However, there will still be a difference between the population mean and the sample mean. This difference is due to

a. non-response error

b. selection bias

c. data acquisition error

d. sampling error

e. None of the above

Answer: D

136. Rob, a data-capturer with STATS SA, incorrectly records an age of 52 as 25. Which kind of error is this an example of?

a. sampling error

b. selection bias

c. data acquisition error

d. non-response error

e. None of the above

Answer: C

137. When the respondents to a questionnaire have different characteristics from those who did not choose to participate in the survey, the survey will likely suffer from which kind of error?

a. sampling error

b. selection bias

c. data acquisition error

d. non-response error

e. None of the above

Answer: D

138. Which of the following statements is/are correct?

a. a non-sampling error may be caused by the wording of a questionnaire

b. selection bias occurs when some respondents choose not to answer a questionnaire

c. data acquisition error occurs when a sample is not representative of the population being studied

d. all of the above statements are correct

e. None of the above

Answer: A

139. Which of the following errors is made when data collected in a survey is entered incorrectly by the data capturer?

a. sampling error

b. selection bias

c. data acquisition error

d. non-response error

e. None of the above

Answer: C

140. Which of the following exhibits the characteristics of sampling error?

a. an estimate of the average wages of 10,000 employees using a sample of 400 employees

b. answers to the question, “Do you abuse your children?”

c. a person receives a questionnaire via email and deletes it without replying

d. a data capturer enters the response to a certain question incorrectly

e. None of the above

Answer: A