Chapter 13
Linear Regression and Correlation
True/False
1. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a rather weak correlation.
Answer: False Difficulty: Easy Goal: 1
2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable.
Answer: True Difficulty: Easy Goal: 1 AACSB: AS
3. An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
Answer: True Difficulty: Medium Goal: 1 AACSB: REF
4. There are two variables in correlation analysis referred to as the dependent and determination variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables.
Answer: True Difficulty: Easy Goal: 2 AACSB: AS
6. The purpose of correlation analysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7. Originated by Karl Pearson about 1900, the coefficient of correlation describes the strength of the relationship between two, interval or ratioscaled variables.
Answer: True Difficulty: Easy Goal: 2
8. The coefficient of correlation, r, is often referred to as Spearman's rho.
Answer: False Difficulty: Easy Goal: 2
9. The coefficient of correlation r is often referred to as the Pearson productmoment correlation coefficient.
Answer: True Difficulty: Easy Goal: 2
10. A correlation coefficient equal to –1 or +1 indicates perfect correlation.
Answer: True Difficulty: Easy Goal: 2
11. The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
Answer: False Difficulty: Easy Goal: 2
12. A coefficient of correlation, r, close to 0 (say, 0.08) shows that the relationship between two variables is quite weak.
Answer: True Difficulty: Easy Goal: 2
13. Correlation coefficients of –0.91 and +0.91 represent relationships between two variables that have equal strength but different directions.
Answer: True Difficulty: Easy Goal: 2 AACSB: REF
14. A coefficient of correlation of –0.96 indicates a very weak negative correlation.
Answer: False Difficulty: Easy Goal: 2
15. The coefficient of determination is the proportion of the total variation in the dependent variable Y that is explained or accounted for by its relationship with the independent variable X.
Answer: True Difficulty: Easy Goal: 2
16. The coefficient of determination is found by taking the square root of the coefficient of correlation.
Answer: False Difficulty: Easy Goal: 2
17. If the coefficient of correlation is –0.90, the coefficient of determination is –0.81.
Answer: False Difficulty: Medium Goal: 2
18. If the coefficient of correlation is –0.50, the coefficient of determination is +0.25.
Answer: True Difficulty: Medium Goal: 2
19. If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624.
Answer: True Difficulty: Medium Goal: 2
20. The correlation coefficient is the proportion of total variation in Y that is explained by X.
Answer: False Difficulty: Easy Goal: 2
21. The coefficient of determination is the proportion of total variation in Y that is not explained by X.
Answer: False Difficulty: Easy Goal: 2
22. The coefficient of determination is the proportion of total variation in Y that is explained by X.
Answer: True Difficulty: Easy Goal: 2
23. Pearson's productmoment correlation coefficient, r, requires that the data be interval or ratio scaled, such as incomes and weights.
Answer: True Difficulty: Easy Goal: 2
24. The standard error of estimate measures the accuracy of our prediction.
Answer: True Difficulty: Medium Goal: 2
25. Pearson's coefficient of correlation can be used if the data is nominally scaled.
Answer: False Difficulty: Easy Goal: 2
26. The coefficient of determination can only be positive.
Answer: True Difficulty: Easy Goal: 2
27. If the coefficient of determination is expressed as a percent, its value is between 0% and 100%.
Answer: True Difficulty: Easy Goal: 2
28. A t test is used to test the significance of the coefficient of correlation.
Answer: True Difficulty: Medium Goal: 3
29. To test the significance of Pearson's r, we use the standard normal z distribution.
Answer: False Difficulty: Medium Goal: 3
30. When testing the strength of the relationship between two variables, the null hypothesis is: .
Answer: True Difficulty: Medium Goal: 3
31. When testing the strength of the relationship between two variables, the alternate hypothesis is: .
Answer: True Difficulty: Medium Goal: 3
32. The basic question in testing the significance of ρ (rho) is to make a statistical inference about the true relationship between two variables.
Answer: True Difficulty: Medium Goal: 3 AACSB: AS
33. One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.
Answer: False Difficulty: Easy Goal: 4 AACSB: AS
34. The technique used to measure the strength of the relationship between two variables using the coefficient of correlation and the coefficient of determination is called regression analysis.
Answer: False Goal: 4
35. A regression equation may be determined using a mathematical method called the least squares principle.
Answer: True Difficulty: Easy Goal: 4
36. A regression equation found using the least squares principle is the bestfitting line because the sum of the squares of the vertical deviations between the actual and estimated values is minimized.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
37. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
38. The values of a and b in the regression equation are called the regression coefficients.
Answer: True Difficulty: Easy Goal: 4 AACSB: REF
39. One assumption underlying linear regression is that for each value of X there is a group of Y values that is normally distributed.
Answer: True Difficulty: Medium Goal: 4
40. In order to visualize the regression equation line, we can draw a scatter diagram.
Answer: True Difficulty: Easy Goal: 4
41. A regression equation is a mathematical equation that defines the relationship between two variables.
Answer: True Difficulty: Easy Goal: 4
42. The equation for a straight line going through the plots on a scatter diagram is called a regression equation. It is alternately called an estimating equation and a predicting equation.
Answer: True Difficulty: Easy Goal: 4
43. The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.
Answer: True Difficulty: Medium Goal: 4
44. In regression analysis, the predicted value of rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.
Answer: True Difficulty: Medium Goal: 4
45. Trying to predict weekly sales with a standard error of estimate of $1,955, we would conclude that 68 percent of the predictions would not be off more than $1,955, 95 percent would not be off by more $3,910, and 99.7 percent would not be off by more than $5,865.
Answer: True Difficulty: Medium Goal: 5 AACSB: AS
46. The standard error of estimate is used to construct confidence intervals when the sample size is large and the scatter about the regression line is somewhat normally distributed.
Answer: True Difficulty: Medium Goal: 5
47. A confidence interval can be determined for the mean value of Y for a given value of X.
Answer: True Difficulty: Medium Goal: 5
48. A confidence interval can be determined for the mean value of X for a given value of Y.
Answer: False Difficulty: Medium Goal: 5
49. The smaller the samples, the smaller the standard error of estimate.
Answer: False Difficulty: Medium Goal: 5
50. Explained variation equals total variation minus unexplained variation.
Answer: True Difficulty: Easy Goal: 5
51. In regression analysis, there is no difference in the width of a confidence interval and the width of a predictor interval.
Answer: False Difficulty: Medium Goal: 5
52. A confidence interval is narrower than a prediction interval because a confidence interval estimates a mean Y for a given X.
Answer: True Difficulty: Medium Goal: 5
53. The least squares method assumes the relationship between the dependent and independent variables is linear.
Answer: True Difficulty: Medium Goal: 4
54. When analyzing data with regression, a transformation is necessary when the relationship between the dependent and independent variables is linear.
Answer: False Difficulty: Medium Goal: 4
55. When analyzing a curvilinear relationship between dependent and independent variables, a transformation of the data is necessary.
Answer: True Difficulty: Medium Goal: 4
56. A mathematical transformation can be used to change a curvilinear relationship between two variables to a linear relationship.
Answer: True Difficulty: Medium Goal: 4
Multiple Choice
57. What is the chart called when the paired data (the dependent and independent variables) are plotted?
A) Scatter diagram
B) Bar chart
C) Pie chart
D) Histogram
Answer: A Difficulty: Medium Goal: 1 AACSB: AS
58. What is the variable used to predict the value of another called?
A) Independent
B) Dependent
C) Correlation
D) Determination
Answer: A Difficulty: Medium Goal: 1
59. Which of the following statements regarding the coefficient of correlation is true?
A) It ranges from –1.0 to +1.0 inclusive
B) It measures the strength of the relationship between two variables
C) A value of 0.00 indicates two variables are not related
D) All of the above
Answer: D Difficulty: Medium Goal: 2
60. What does a coefficient of correlation of 0.70 infer?
A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30
Answer: C Difficulty: Medium Goal: 2 AACSB: AS
61. What is the range of values for a coefficient of correlation?
A) 0 to +1.0
B) –3 to +3 inclusive
C) –1.0 to +1.0 inclusive
D) Unlimited range
Answer: C Difficulty: Easy Goal: 2
62. The Pearson productmoment correlation coefficient, r, requires that variables are measured with:
A) An interval scale
B) A ratio scale
C) An ordinal scale
D) A nominal
E) Either A or B.
Answer: E Difficulty: Medium Goal: 2
63. If the correlation between two variables is close to one, the association is
A) strong.
B) moderate.
C) weak.
D) none.
Answer: A Difficulty: Easy Goal: 2
64. If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?
A) Not related
B) Dependent on each other
C) Highly related
D) All of the above are correct
Answer: A Difficulty: Easy Goal: 2
Scrambling: Locked
65. What can we conclude if the coefficient of determination is 0.94?
A) Strength of relationship is 0.94
B) Direction of relationship is positive
C) 94% of total variation of one variable is explained by variation in the other variable.
D) All of the above are correct
Answer: C Difficulty: Easy Goal: 2
Scrambling: Locked
66. If r = –1.00, what inferences can be made?
A) The dependent variable can be perfectly predicted by the independent variable
B) All of the variation in the dependent variable can be accounted for by the independent variable
C) High values of one variable are associated with low values of the other variable
D) Coefficient of determination is 100%.
E) All of the above are correct
Answer: E Difficulty: Medium Goal: 2 AACSB: CA
67. If r = 0.65, what does the coefficient of determination equal?
A) 0.194
B) 0.423
C) 0.577
D) 0.806
Answer: B Difficulty: Easy Goal: 2
68. What does the coefficient of determination equal if r = 0.89?
A) 0.94
B) 0.89
C) 0.79
D) 0.06
Answer: C Difficulty: Medium Goal: 2
69. Which value of r indicates a stronger correlation than 0.40?
A) –0.30
B) –0.50
C) +0.38
D) 0
Answer: B Goal: 2
70. What is the range of values for the coefficient of determination?
A) –1 to +1 inclusive
B) –100% to +100% inclusive
C) –100% to 0% inclusive
D) 0% to 100% inclusive
Answer: D Difficulty: Easy Goal: 2
71. If the decision in the hypothesis test of the population correlation coefficient is to reject the null hypothesis, what can we conclude about the correlation in the population?
A) It is zero
B) It could be zero
C) It is not zero
D) It equals the computed sample correlation
Answer: C Difficulty: Easy Goal: 3 AACSB: AS
72. A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
A) 1.96
B) 2.07
C) 2.94
D) 3.60
Answer: D Difficulty: Hard Goal: 3
73. In the regression equation, what does the letter "a" represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) None of the above
Answer: A Difficulty: Medium Goal: 4
74. In the regression equation, what does the letter "b" represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X=0
Answer: B Difficulty: Medium Goal: 4
75. Suppose the least squares regression equation is = 1202 + 1,133X. When X = 3, what does equal?
A) 5,734
B) 8,000
C) 4,601
D) 4,050
Answer: C Difficulty: Medium Goal: 4 AACSB: AS
76. What is the general form of the regression equation?
A) = ab
B) = a + bX
C) = a – bX
D) = abX
Answer: B Difficulty: Medium Goal: 4
77. What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be?
A) Regression equation
B) Slope of the line
C) Standard error of estimate
D) Least squares principle
Answer: C Goal: 2
78. Which of the following are true assumptions underlying linear regression: 1) for each value of X, there is a group of Y values which is normally distributed; 2) the means of these normal distributions of Y values all lie on the straight line of regression; and/or 3) the standard deviations of these normal distributions are equal?
A) Only (1) and (2)
B) Only (1) and (3)
C) Only (2) and (3)
D) All of them
Answer: D Difficulty: Hard Goal: 4
79. Based on the regression equation, we can
A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
D) all of the above.
Answer: A Difficulty: Medium Goal: 4
80. Which of the following is true about the standard error of estimate?
A) It is a measure of the accuracy of the prediction
B) It is based on squared vertical deviations between Y and
C) It cannot be negative
D) All of the above
Answer: D Difficulty: Medium Goal: 2
81. If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
A) –1
B) +1
C) 0
D) Infinity
Answer: C Difficulty: Medium Goal: 2
82. In the least squares equation, = 10 + 20X the value of 20 indicates
A) the Y intercept.
B) for each unit increase in X, Y increases by 20.
C) for each unit increase in Y, X increases by 20.
D) none of the above.
Answer: B Difficulty: Medium Goal: 4
83. In the equation = a + bX, what is ?
A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X=0
Answer: C Difficulty: Medium Goal: 4
84. Assume the least squares equation is = 10 + 20X. What does the value of 10 in the equation indicate?
A) Y intercept
B) For each unit increased in Y, X increases by 10
C) For each unit increased in X, Y increases by 10
D) None of the above
Answer: A Difficulty: Medium Goal: 4 AACSB: AS
85. What is the variable used to predict another variable called?
A) Independent variable
B) Dependent variable
C) Important variable
D) Causal variable
Answer: A Difficulty: Medium Goal: 4
86. In regression, the difference between the confidence interval and prediction interval formulas is
A) the prediction interval is the square root of the confidence interval.
B) the addition of "1" to the quantity under the radical sign.
C) the prediction interval uses and the confidence interval uses r.
D) no difference.
Answer: B Difficulty: Medium Goal: 5 AACSB: AS
87. Which of the following is NOT a difference between a confidence interval and a prediction interval?
A) Addition of "1" under the radical for the prediction interval.
B) Confidence interval uses the standard error of estimate and the prediction interval does not.
C) Prediction interval refers to a specific case.
D) Confidence interval is narrower than the prediction interval.
Answer: B Difficulty: Medium Goal: 5
88. When comparing the 95% confidence and prediction intervals for a given regression analysis,
A) the confidence interval is wider than a prediction interval
B) the confidence interval is narrower than a prediction interval
C) there is no difference between confidence and prediction intervals
D) None of the above
Answer: B Difficulty: Easy Goal: 5
89. In regression analysis, a transformation is used when
A) the confidence interval is wider than a prediction interval
B) two variables are not independent
C) the relationship between dependent and independent variables is not linear
D) the correlation is near zero
Answer: C Difficulty: Hard Goal: 4
90. The covariance is
A) the same sign as the correlation
B) always greater than zero
C) used to detect curvilinear relationships
D) computed by multiplying two variances.
Answer: A Difficulty: Easy Goal: Covariance AACSB: AS
FillintheBlank
91. In plotting paired data in a scatter diagram, on which axis is the dependent variable scaled? ___________________
Answer: Y or vertical axis Difficulty: Easy Goal: 1
92. If we are studying the relationship between high school performance and college performance, and want to predict college performance, what kind of variable is high school performance? ________________
Answer: independent variable Difficulty: Easy Goal: 1
93. How do we designate the sample coefficient of correlation? _____
Answer: r Difficulty: Easy Goal: 2
94. How do we designate the population coefficient of correlation? _____
Answer: ρ Difficulty: Easy Goal: 2
95. If there is absolutely no relationship between two variables, what will Pearson's r equal? _____
Answer: zero (0) Difficulty: Easy Goal: 2
96. If the coefficient of correlation is 0.80, what is the coefficient of determination? ______
Answer: 0.64 Difficulty: Easy Goal: 2
97. If the coefficient of determination is 0.81, what is the coefficient of correlation? ______
Answer: 0.9 or 0.9 Difficulty: Medium Goal: 2
98. If the coefficient of correlation is –0.81, what is the coefficient of determination? _______
Answer: 0.6561 Difficulty: Medium Goal: 2
99. How is the coefficient of determination related to the correlation coefficient? ________
Answer: coefficient of determination = Difficulty: Hard Goal: 2
100. What is the range of values that the coefficient of determination can assume? _____ and ______
Answer: 0%, 100% Difficulty: Easy Goal: 2
101. What is the range of values that the covariance can assume?
Answer: between infinity or any value Difficulty: Hard Goal: Covariance
102. A financial advisor is interested in predicting bond yield based on bond term, i.e., one year, two years, etc. What is the dependent variable? ___________________
Answer: bond yield Difficulty: Medium Goal: 1
103. Suppose a sample of 15 homes recently sold in your area is obtained. The correlation between the area of the home, in square feet, and the selling price is 0.40. We want to test the null hypothesis that the correlation in the population is less than or equal to zero versus the alternate that it is greater than zero. The rejection region will fall in the ________ tail of a t distribution.
Answer: upper Difficulty: Medium Goal: 3 AACSB: AS
104. If the value of r is –0.96, what does this indicate about the dependent variable as the independent variable increases? ___________
Answer: decreases Difficulty: Easy Goal: 2
105. Perfect correlation means that the scatter diagram will appear as a _______________________.
Answer: straight line Difficulty: Easy Goal: 3
106. What is the proportion of explained variation called? ________________
Answer: coefficient of determination Difficulty: Easy Goal: 2
107. What is the value of the correlation coefficient if there is perfect correlation? ___________
Answer: ±1.00 Difficulty: Medium Goal: 2 AACSB: AS
108. If the correlation between sales and advertising is +0.6, what percent of the variation in sales can be attributed to advertising? ______
Answer: 36% Difficulty: Medium Goal: 2
109. What is a chart designed to portray the relationship between a dependent variable and an independent variable called? _______________________
Answer: scatter diagram Difficulty: Easy Goal: 1
110. What is the correlation coefficient developed by Karl Pearson formally known as? ____________________________________
Answer: Pearson product moment correlation Difficulty: Medium Goal: 2
111. What type of correlation designates an inverse relationship between two variables? ___________________
Answer: negative Difficulty: Easy Goal: 2
112. What is the technique used to predict or estimate the value of the dependent variable Y based on a selected value of an independent variable X called? __________________________
Answer: regression analysis Difficulty: Easy Goal: 4
113. What is the equation used to estimate Y based on X? _____________
Answer: regression equation Difficulty: Easy Goal: 4
114. What principle minimizes the sum of the squares of the vertical deviations about the line? _______________
Answer: least squares principle Difficulty: Easy Goal: 4
115. The standard error of the estimate measures the scatter or dispersion of the observed values around a ____________________
Answer: regression line Difficulty: Medium Goal: 2
116. The technique that minimizes the sum of the squared vertical deviations about the _______________________ is called "least squares."
Answer: regression line Difficulty: Medium Goal: 4
117. What do the coefficient of correlation and the slope of the regression line always have in common? __________________
Answer: their sign Difficulty: Medium Goal: 4
118. If the dependent variable is in dollars, the standard error is in what units? ______________
Answer: dollars ($) Difficulty: Medium Goal: 2
119. What is the best model to describe a linear relationship between two variables? ________________________
Answer: regression equation Difficulty: Medium Goal: 4
120. What is another name for the regression or estimating equation? ______________________________
Answer: predicting equation Difficulty: Medium Goal: 4
121. What principle is applied when calculating the regression coefficients? _________________
Answer: principle of least squares Difficulty: Medium Goal: 4
122. What is the general form of the regression equation? _____________
Answer: = a + bX Difficulty: Medium Goal: 4
123. What is a measure of the scatter of observed values around the regression line called? _______________________________
Answer: standard error of estimate Difficulty: Medium Goal: 2
124. An assumption of linear regression states that for each value of X, there is a group of Y values that are statistically __________________ and normally distributed about the regression line.
Answer: independent Difficulty: Medium Goal: 4 AACSB: AS
125. Approximately what percent of the values lie within two standard errors of the regression line? ________
Answer: 95% Difficulty: Medium Goal: 5 AACSB: AS
126. What is the direction of a regression line if its slope equals zero, indicating a lack of a relationship? ____________________
Answer: horizontal Difficulty: Easy Goal: 4
127. What variation does the coefficient of determination measure? _______
Answer: explained variation relative to total variation Difficulty: Medium Goal: 2
128. How does the prediction interval for an individual value of Y compare to the confidence interval for the mean value of Y? _______________
Answer: wider or larger Difficulty: Medium Goal: 5
129. The regression coefficient, a, is the point where the regression line __________ the Yaxis.
Answer: intersects Difficulty: Medium Goal: 4
130. The regression coefficient, a, is the point where the regression line __________ the Yaxis.
Answer: intersects Difficulty: Medium Goal: 4
131. What does the covariance measure? _______
Answer: the degree of association between two variables Difficulty: Hard Goal: Covariance
132. In a regression analysis every value of y is converted to z with the following formula: z = log( y ). What is the conversion called? _______
Answer: a transformation Difficulty: Hard Goal: 4
Multiple Choice
Use the following to answer questions 133138:
Given the following five points: (–2,0), (–1,0), (0,1), (1,1), and (2,3).
133. What is the slope of the line?
A) 0.0
B) 0.5
C) 0.6
D) 0.7
Answer: D Difficulty: Medium Goal: 4
134. What is the Y intercept?
A) 0.0
B) 0.7
C) 1.0
D) 1.5
Answer: C Difficulty: Medium Goal: 4 AACSB: AS
135. What is the standard error of the estimate?
A) 0
B) 0.135
C) 0.367
D) 0.606
Answer: D Difficulty: Medium Goal: 2
136. What is the critical value necessary to determine a confidence interval for a 95% level of confidence?
A) 2.132
B) 2.353
C) 2.776
D) 3.182
Answer: D Difficulty: Medium Goal: 5 AACSB: AS
137. What is the critical value necessary to determine a confidence interval for a 90% level of confidence?
A) 1.533
B) 1.638
C) 2.132
D) 2.353
Answer: D Difficulty: Medium Goal: 5
138. If the regression equation is = 2 – 0.4X, what is the value of when X = –3?
A) 0.8
B) 3.2
C) –10.0
D) 14.0
Answer: B Difficulty: Medium Goal: 4
FillintheBlank
Use the following to answer questions 139145:
A company wants to study the relationship between an employee's length of employment and their number of workdays absent. The company collected the following information on a random sample of seven employees.
139. What is the independent variable (X)? _________________
Answer: number of years employed Difficulty: Medium Goal: 4
140. What is the dependent variable (Y)? _____________________
Answer: number of workdays absent Difficulty: Medium Goal: 4
141. What is the slope of the linear equation? ________________
Answer: 0.6852 Difficulty: Medium Goal: 4
142. What is the Y intercept of the linear equation? ______________
Answer: 7.7407 Difficulty: Medium Goal: 4
143. What is the least squares equation for the data? ___________________
Answer: = 7.7107  0.6852X Difficulty: Medium Goal: 4
144. What is the meaning of a negative slope? _________________________
Answer: as the length of employment increases the number of work days absent decreases Difficulty: Easy Goal: 4
145. What is the standard error of estimate? _____________
Answer: 1.31 Difficulty: Hard Goal: 2
Use the following to answer questions 146150:
The relationship between interest rates as a percent (X) and housing starts (Y) is given by the linear equation = 4094 – 269X.
146. What will be the number of housing starts if the interest rate is 8.25%? ___________
Answer: 1875 (1874.75) Difficulty: Medium Goal: 4
147. What will be the number of housing starts if the interest rate rose to 16%? __________
Answer: zero (0) since you can't have negative housing starts Difficulty: Medium Goal: 4
148. At what interest rate will there be no permits for housing starts? _________
Answer: 15.22 Difficulty: Medium Goal: 4
149. What happens to housing starts as interest rates fall? ________
Answer: housing starts rise Difficulty: Medium Goal: 4
150. For what interest rate will the maximum number of housing starts be achieved? _______
Answer: 0 Difficulty: Medium Goal: 4
Multiple Choice
Use the following to answer questions 151160:
A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected:
151. What is the dependent variable?
A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above
Answer: C Difficulty: Medium Goal: 1
152. What is the independent variable?
A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above
Answer: B Difficulty: Medium Goal: 1
153. What is the Yintercept of the linear equation?
A) –12.201
B) 2.1946
C) –2.1946
D) 12.201
Answer: A Difficulty: Hard Goal: 4
154. What is the slope of the linear equation?
A) –12.201
B) 12.201
C) 2.1946
D) –2.1946
Answer: C Difficulty: Hard Goal: 4
155. What is the value of the standard error of estimate?
A) 9.3104
B) 8.778
C) 8.328
D) 86.68
Answer: A Difficulty: Hard Goal: 2 AACSB: AS
156. What is the value of the coefficient of correlation?
A) 0.6317
B) 0.9754
C) 0.9513
D) 9.3104
Answer: B Difficulty: Hard Goal: 2
157. What is the value of the coefficient of determination?
A) 9.3104
B) 0.9754
C) 0.6319
D) 0.9513
Answer: D Difficulty: Hard Goal: 2
158. The 95% confidence interval for 30 calls is
A) 55.8, 51.5
B) 51.4, 55.9
C) 46.7, 60.6
D) 31.1, 76.2
Answer: C Difficulty: Hard Goal: 5
159. The 95% prediction interval for a particular person making 30 calls is
A) 55.8, 51.5
B) 51.4, 55.9
C) 46.7, 60.6
D) 31.1, 76.2
Answer: D Difficulty: Hard Goal: 5
160. What is the regression equation?
A) = 2.1946 – 12.201X
B) = –12.201X + 2.1946X
C) = 12.201 + 2.1946X
D) = 2.1946 + 12.201X
Answer: B Difficulty: Hard Goal: 4
Use the following to answer questions 161167:
161. What is the standard error of the estimate?
A) 136.8552
B) 12323.56
C) 11.6985
D) Cannot be computed
Answer: C Difficulty: Hard Goal: 2
162. What is the coefficient of determination?
A) 91.8%
B) 8.2%
C) 90.0%
D) Cannot be computed
Answer: A Difficulty: Hard Goal: 2
163. What is the correlation coefficient?
A) 0.81
B) 0.958
C) –0.84
D) 0.006
Answer: B Difficulty: Hard Goal: 2
164. The regression equation is:
A) = 2.179463 – 12.8094 X
B) = 12.80894 + 2.179463
C) 12.8094 X = 2.179463
D) None of the above
Answer: B Difficulty: Medium Goal: 4 AACSB: AS
165. The regression analysis can be summarized as follows:
A) No significant relationship between the variables
B) A significant negative relationship exists between the variables
C) A significant positive relationship exists between the variables
D) For every unit increase in X, Y decreases by 12.8094
Answer: C Difficulty: Medium Goal: 4
166. If testing the hypothesis: H_{0}: = 0, the computed t – statistic is:
A) 9.45
B) 8.84
C) 8.18
D) Cannot be computed
Answer: A Difficulty: Medium Goal: 2
167. Estimate the value of when X = 4.
A) 10.45
B) 3.73
C) 8.20
D) Cannot be computed
Answer: C Difficulty: Medium Goal: 4
Refer To: 13_05
Use the following to answer questions 168169:
A regression analysis yields the following information:
= 2.24 + 1.49 X
S _{y}_{}_{x} = 1.66; x = 32; 31.6; n = 10; x^{2} = 134
168. Compute the 95% confidence interval when X = 4.
A) 0.0, 4.05
B) 4.15, 12.25
C) 2.67, 5.33
D) 6.85, 9.55
Answer: D Difficulty: Hard Goal: 5
169. Compute the 95% prediction interval when X = 4.
A) 0.0, 4.05
B) 2.67, 5.33
C) 4.14, 12.26
D) 6.85, 9.55
Answer: C Difficulty: Hard Goal: 5
Essay
170. What is the purpose of measuring correlation?
Answer: To provide a measure of the linear association between two variables.
Difficulty: Easy Goal: 2 AACSB: CA
171. Select a value for the correlation coefficient and provide a complete interpretation of the correlation coefficient using your selected value.
Answer: Answers will vary depending on the value. A correlation of 0.9 (any number between 1 and +1) indicates a relatively strong (or weak) positive ( or negative) correlation. In this case, as one variable increases, the other variable also increases Difficulty: Medium Goal: 2 AACSB: CA
172. What are the input and the output of linear regression?
Answer: As an input, linear regression requires data for two interval or ratio variables. One is defined as the dependent variable and the other is defined as the independent variable. The output of linear regression is a least squares regression equation of the form = a + b X that can be used to predict the value of the dependent variable for a selected value of the independent variable. Difficulty: Hard Goal: 4
173. What does the coefficient of determination measure?
Answer: For a regression analysis, the coefficient of determination measures the explained variation in the dependent variable as a percent of the total variation. Difficulty: Medium Goal: 2
174. What is the purpose of transformations in regression analysis?
Answer: One assumption of linear regression analysis is that the relationship between the dependent and independent variables is linear. Sometimes this is not true. The purpose of transformations in regression analysis is to transform the variables so they are linearly related.
Difficulty: Medium Goal: 4 AACSB: CA
Statistical Techniques in Business & Economics, Lind/Marchal/Wathen, 13/e
