True / False
____T___ 1. The usual objective of regression analysis is to predict estimate the value of one
variable when the value of another variable is known.
____T___ 2. Correlation analysis is concerned with measuring the strength of the relationship
between two variables.
____F___ 3. The term ei in the simple linear regression model indicates the amount of change in
Y for a unit change in X.
____T___ 4. In the sample regression equation y = a + bx, b is the slope of the regression line.
____F___ 5. The coefficient of determination can assume any value between -1 and +1.
____F___ 6. In the least squares model, the explained sum of squares is always smaller than the
regression sum of squares.
____T___7. The sample correlation coefficient and the sample slope will always have the same
sign.
____F___ 8. Given the sample regression equation y = -3 + 5x, we know that in the sample X
and Y are inversely related.
____F___ 9. Given the sample regression equation y = 5 – 6x, we know that when X = 2, Y =
17.
____T___ 10. An important relationship in regression analysis is (Yi  Y) = (Ŷ  Y)  (Yi  Ŷ) .
____T___ 11. Regression analysis is concerned with the form of the relationship among
variables, whereas correlation analysis is concerned with the strength of the
relationship.
____F___ 12. The correlation coefficient indicates the amount of change in Y when X change by
one unit.
____T___ 13. In simple linear regression analysis, when the slope is equal to zero, the
independent variable does not explain any of the variability in the dependent variable.
____T___14. One of the purposes of regression analysis is to estimate a mean of the independent
variable for given values of the dependent variable.
____T___ 15. The variable that can be manipulated by the investigator is called the independent
variable.
____T___ 16. When b = 0, X and Y are not related.
____F___ 17. If zero is contained in the 95% confidence interval for b, we may reject Ho: b = 0
at the 0.05 level of significance.
____F___ 18. If in a regression analysis the explained sum of squares is 75 and the unexplained
sum of square is 25, r2 = 0.33.
____T___ 19. In general, the smaller the dispersion of observed points about a fitted regression
line, the larger the value of the coefficient of determination.
____F___ 20. When small values of Y tend to be paired with small values of X, the relationship
between X and Y is said to be inverse.
____T___ 21. An alternative hypothesis (Ha) is a theory that contradicts the null hypothesis. The
alternative hypothesis will be accepted when there is strong evidence leading us to
reject the null hypothesis.
____T___ 22. The p-value of a test depends on the observed data, but the critical values of a test
do not.
____T___ 23. Other things being equal, decreasing α increases β.
____T___ 24. The larger the p-value associated with a test of hypothesis, the stronger the
support for the null hypothesis.
____F___ 25. The probability that the test statistic will fall in the critical region, given that H0 is
true, represents the probability of making a type II error.
____T___ 26. When the null hypothesis is true, the probability that the test statistic will fall in
the critical region is call the level of significance of the test.
____T___ 27. When we reject a true null hypothesis, we commit a Type I error.
____F___ 28. The alternative hypothesis is the hypothesis that is tested.
____F___ 29. The larger the p-value, the stronger the evidence against the null hypothesis.
____T___ 30. A small p-value provides evidence supporting the alternative hypothesis.
____T___ 31. The p-value of a test is the probability of getting a test statistic as extreme as or
more extreme than the observed one. The probability is calculated based on the
assumption that the null hypothesis is false.
____F___ 32. If the p-value for a test is greater than or equal to the level of significance, we may
reject H0.
____T___ 33. A type I error can occur only when the statistician decides to reject the null
hypothesis.
____F___ 34. The alternative hypothesis always contains a statement of equality.
____T___ 35. If we fail to reject the null hypothesis, we conclude that the null hypothesis may
be true.
____F___ 36. In general, in most practical hypothesis-testing situations, the level of significance
and the p-value will be the same.
____T___ 37. Mathematically, b0 represents the Y-intercept of the line relating X and Y. But
practically speaking, it often times is not interpretable. Only if the value
of 0 is
within the relevant range on the X-values we can interpret b0 as the average value of
Y when X=0. Relevant range refers to the region between the minimum and
maximum X-values observed in the sample.
____T___38. The quantity ̂ 2 is the same as the mean square error (MSE) or Se2 . It is the
variability of the data points around the line.
____F___39. A correlation coefficient of 0.65 indicates a stronger linear relationship between
two variables than does a correlation coefficient of -0.65.
____F__ 40. In general, the larger the dispersion of observed points about a fitted regression
line, the larger the value of the coefficient of determination of 0.42.
____T__ 41. Given the statistically significant sample regression equation ŷ = 4-3x, we know
that in the sample x and y and inversely related.
____F__ 42. The correlation coefficient is the proportion of total variation in Y that is explained
by X.
____T__ 43. Given Ho: β1 = 0 and Ha: β1 ≠ 0, intuitively, we would be unable to reject the null
hypothesis if the sample slope ̂1 was close to “0”. The farther it was from “0” the
more plausible the alternative hypothesis would be.
____T__ 44. Rejection of H0 in regression analysis implies that there is not a statistically
significant relationship between X and Y.
____T__ 45. Type II error is the probability or risk assumed by accepting the null hypothesis
when it is actually false.
____T__ 46. A z or t statistic tells us the number of standard deviation our sample slope is from
Zero under the null. The larger the z, the more plausible Ha:
____F__ 47. Given the statistically significant sample regression equation y = -3 + 5x, we know
that in the sample X and Y are inversely related.
____T__ 48. A type I error is the rejection of a true null hypothesis.
____T__ 49. In general, the smaller the dispersion of observed points about fitted regression line,
the larger the value of the coefficient of determination.
____T___ 50. At the 5% level, b̂1 is said to deviate form β1 by more than 1.96 standard
deviations, at most 5% of the time (hence, favors Ha)
____T___ 51. Given Ho: µ = 8.8, Ha: µ ≠ 8.8 and Z =
7.2  8.8 = -4 indicates that the value 7.2
0.4
is 4 standard error below 8.8.
Select the correct answer for the following questions
52. The variable about which the investigator wishes to make predictions or estimates is called
the
a. dependent variable
b. unit of association
c. independent variable
d. discrete variable
53. In regression analysis, the quantity that gives the amount by which Y changes for a unit
change in X is called the
a. coefficient of determination
b. slope of the regression line
c. Y intercept of the regression line
d. correlation coefficient
54. In the equation y = b0 +b1 (x), b0 is the
a. coefficient of determination
c. y intercept of the regression line
b. slope of the regression line
d. correlation coefficient
55. In the equation y = b0 + b1 (x), b1 is the
a. coefficient of determination
b. slope of the regression line
c. y intercept of the regression line
d. correlation coefficient
56. In regression and correlation analysis, the measure whose values are restricted to the range 0
to 1, inclusive, is the
a. coefficient of determination
b. slope of the regression line
c. y intercept of the regression line
d. correlation coefficient
57. In regression and correlation analysis, the measure whose values are restricted to the range -1
to +1, inclusive, is the
a. coefficient of determination
b. slope of the regression line
c. y intercept of the regression line
d. correlation coefficient
58. The quantity (Yi  Yˆ ) 2 is called the _______________ sum of square.
a. least
b. explained
c. total
d. unexplained
59. If, in the regression model, b = 0, we say there is _____________ linear relationship between
X and Y.
a. an inverse
b. a significant
c. a direct
d. no
60. If, in the regression model, b is negative, we say there is _____________ linear relationship
between X and Y.
a. an inverse
b. a significant
c. a direct
d. no
61. The _______________ sum of square is a measure of the total variability in the observed
values of Y that is accounted for by the linear relationship between the observed values of X
and Y.
a. unexplained
b. total
c. error
d. explained
62. If two variables are not related, we know that ________________.
a. their correlation coefficient is equal to zero.
b. the variability in one of them cannot be explained by the other.
c. the slope of the regression line for the two variables is equal to zero.
d. all of the above statements are true.
63. In simple linear regression analysis, if the correlation coefficient is equal to 1.0,
______________.
a. the slope is equal to 1.0
b. all the variability in the dependent variable is explained by the independent variable.
c. the y intercept is equal to 1.0
d. the relationship between the two variables can be described as a bivariable normal
distribution.
64. The following results were obtained from a simple linear regression analysis. Total sum of
square = 5.7640. Explained sum of squares = 5.5415. Unexplained sum of squares = 0.2225.
The coefficient of determination is ____
a. 0.0402
b. 0.0386
c. 0.9805
d. 0.9614
65. The following results were obtained as part of a simple linear correlation analysis: Y = 97.98
– 4.33x regression sum of squares = 2680. 27. Error sum of squares = 125.40. Total sum of
squares = 2805.67. The sample correlation coefficient is ____
a. -0.9774
b. 0.9553
c. 0.2114
d. 0.0447
66. The following equation describes the relationship between output and labor input at a sample
of work stations in a manufacturing plant: ŷ = 2.35 + 2.20x. Suppose, for a selected work
station, the labor input is 5. The predicted output is _____________.
a. 4.55
b. 2.35
c. 2.20
d. 13.35
67. In regression and correlation analysis, the entity on which sets of measurements are taken is
called the ______________.
a. dependent variable
b. independent variable
c. unit of association
d. discrete variable
68. The quantity
a. least
c. explained
 Yˆ  Y 
2
is called the _____________ sum of squares.
b. total
d. unexplained
69. If, in the regression model, b is positive, we say there is ____________ linear relationship
between X and Y.
a. an inverse
b. a direct
c. a significant
d. no
70. If, as X increase, Y tends to increase, we say there is ____________ linear relationship
between X and Y.
a. an inverse
b. a direct
c. a significant
d. no
71. The explained sum of squares divided by the total sum of squares yield the _______.
a. F statistic
b. total mean square
c. p value
d. coefficient of multiple determination
72.A ___________ provides clues regarding the likely form and strength of the relationship
between two variables.
a. regression model
b. scatter diagram
c. correlation model
d. histogram
73. The variability about the sample regression line is measure by the _____________ sum of
squares.
a. unexplained
b. total
c. explained
d. histogram
74. The failure to reject a false null hypothesis is called the ____________ error.
a. Standard
b. Critical
c. Type I
d. Type II
75. The probability of rejecting a true null hypothesis is also referred to as the
_____________ for the test.
a. p-value
b. Critical
c. rejection region
d. level of significance
76. We commit a Type I error if we ____________ a true null hypothesis.
a. fail to reject
b. reject
c.
accept
d. compute
77. The two kinds of statistical hypotheses are the null hypothesis and the _____________
hypothesis.
a. accepted
b. rejected
c. alternative
d. null
78. The _______________ hypothesis is the hypothesis that tested.
a. accepted
b. rejected
c. alternative
d. null
79. The statistic that is used as a decision maker in a hypothesis-testing procedure is called
the __________________
a. test statistic
b. sample statistic
c. unbiased statistic
d. relevant statistic
80. When we test a hypothesis about the difference between two population means, it is
desirable that sample variances be _______________ if the population variances are
unknown and the sample sizes are small.
a. small
b. large
c. pooled
d. unequal
81. When one tests a hypothesis using the t distribution, the p value is usually
______________
a. expressed as a interval
b. not computed
c. smaller than α
d. greater than α
82. Values of the test statistic that separate the acceptance region from the rejection region
are called ______________ values.
a. critical
b. p
c. sample
d. expected
83. The null and alternative hypothesis are _______________
a. independent
b. statements about a sample
c. complementary
d. statements about a sampling distribution
.
84. Which of the following is not part of the hypothesis-testing procedure about a population
mean?
a.
b.
c.
d.
Choosing the probability of committing a Type I error.
Stating the decision rule
Computing the mean of the population
Making the statistical decision
85. When we test a hypothesis about the difference between two population means,
It is necessary that the samples be _________________
a. independent
b. selected before the level of significance is selected.
c. Selected before the hypothesis are formulated
d. Equal in size when unpaired data are used.
86. The following results were obtained as part of a simple linear regression analysis.
2
Yˆ  9.779  18 .8571 x , r  0.84 , S e  7.508 , s b  2.0724
We wish to test Ho: β = 0. The computed value of the test statistics is ________
a. 2.5116
c. 3.623
b. 0.9165
d. 9.099
87. The following results were obtained as part of a simple linear regression analysis.
2
Ŷ  37 .2895  1.2024 x , sb  0.2934 , r  0.6774
For each unit change in x, the change in y is equal to_____________.
a. 1.2024
c. 37.0895
b. 0.6774
d. 0.2934
88. The following results were obtained as part of a simple linear regression analysis.
2
Yˆ  8.2064  1.2771 x , r  0.61 , sb  0.3610 , MSE = 25.485
When the independent variable is equal to 5, the estimate of Ŷ is ____________
a. 0.7810
c. 5.0483
b. 14.5919
d. 0.2934
89. If there is a direct relationship between X and Y, the slope of the regression line showing
the relationship between the two variables is _______________.
a. negative
c. between 0 and +1
b. between -1 and +1
d. positive
90. From a sample of 16 observations the following sums of squares were computed:
 y
i
 y 2  100
 y
i
 yˆ 2  84
For testing Ho: β = 0, one may compute from these data a value of the test statistic of
_____________.
a. 2.67
c. 0.16
b. 0.84
d. 1.19
91. In simple linear regression analysis, the slope of the line, b, will always have the same
sign as the:
a. standard error of the estimate, Se
b. coefficient of determination, r2
c. correlation coefficient, r
d. y intercept, a
e. none of the above
92. In simple linear regression analysis, if the correlation coefficient is equal to 1.0, then
a. the slope is equal to 1.0
b. all the variability in the dependent variable is explained by the independent variable.
c. The Y intercept is equal to 1.0.
d. The relationship between the two variables can be described as a normal distribution.
e. None of the above.