Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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In a statistics course, a linear regression
equation was computed to predict the final exam score from the score on the first test. The
equation was y = 10 + .9x where y is the final exam score and x is the score on the first
test. Carla scored 95 on the first test. On the final exam, Carla scored 98. What
is the value of her residual?
a. | 98 | b. | 2.5 | c. | –2.5 | d. | 0 | e. | None of the
above |
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2.
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In the scatterplot below, if each x-value were
decreased by one unit and the y-values remained the same, then the correlation r
would
a. | Decrease by 1 unit | b. | Decease slightly | c. | Increase
slightly | d. | Stay the same | e. | Can’t tell without knowing the data
values |
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3.
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In regression, the residuals are which of the
following?
a. | Those factors unexplained by the
data | b. | The difference between the observed responses and the
values predicted by the regression line | c. | Those data points
which were recorded after the formal investigation was completed | d. | Possible models unexplored by the investigator | e. | None of the above |
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4.
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Which of the following statements are
true?
I. Correlation and regression require explanatory and response
variables.
II. Scatterplots require
that both variables be quantitative.
III. Every least-square regression line passes through  .
a. | I and II only | b. | I and III only | c. | II and III
only | d. | I, II, and III | e. | None of the above |
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5.
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Suppose the following information was collected,
where X = diameter of tree trunk in inches, and Y = tree height in feet.
If the LSRL equation is y = –3.6
+ 3.1x, what is your estimate of the average height of all trees having a trunk diameter of 7
inches?
a. | 18.1 | b. | 19.1 | c. | 20.1 | d. | 21.1 | e. | 22.1 |
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6.
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Suppose we fit the least squares regression line to
a set of data. What is true if a plot of the residuals shows a curved
pattern?
a. | A straight line is not a good model for the
data. | b. | The correlation must be 0. | c. | The correlation must be positive. | d. | Outliers must be present. | e. | The LSRL might or might not be a good model for the data, depending on the
extent of the curve. |
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7.
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Which of the following are
resistant?
a. | Least squares regression line | b. | Correlation coefficient | c. | Both the least
squares line and the correlation coefficient | d. | Neither the least
squares line nor the correlation coefficient | e. | It
depends |
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8.
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A copy machine dealer has data on the number x of
copy machines at each of 89 customer locations and the number y of service calls in a month at each
location. Summary calculations give  = 8.4, Sx = 2.1,  = 14.2,
Sy = 3.8, and r = 0.86. What is the slope of the least squares regression line of
number of service calls on number of copiers?
a. | 0.86 | b. | 1.56 | c. | 0.48 | d. | None of
these | e. | Can’t tell from the information
given |
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9.
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There is a linear relationship between the number
of chirps made by the striped ground cricket and the air temperature. A least squares fit of
some data collected by a biologist gives the model  = 25.2 +
3.3x, 9 < x < 25, where x is the number of chirps per minute and
 is the estimated
temperature in degrees Fahrenheit. What is the estimated increase in temperature that
corresponds to an increase in 5 chirps per minute?
a. | 3.3°F | b. | 16.5°F | c. | 25.2°F | d. | 28.5°F | e. | 41.7°F |
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10.
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A set of data relates the amount of annual salary
raise and the performance rating. The least squares regression equation is  = 1,400 +
2,000x where y is the estimated raise and x is the performance rating. Which
of the following statements is not correct?
a. | For each increase of one point in performance rating,
the raise will increase on average by $2,000. | b. | This equation
produces predicted raises with an average error of 0. | c. | A rating of 0 will yield a predicted raise of
$1,400. | d. | The correlation for the data is
positive. | e. | All of the above are
true. |
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