# STATS 30 Questions Exam 2015

| October 3, 2018

Question 1(2
points)
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In choosing the “best-fitting” line through a set of
points in linear regression, we choose the one with the:
Question 1 options:

smallest
sum of squared residuals

largest
sum of squared residuals

smallest
number of outliers

largest
number of points on the line

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Question 2(2
points)
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In linear regression, a dummy variable is used:
Question 2 options:

to
represent residual variables

to
represent missing data in each sample

to
include hypothetical data in the regression equation

to
include categorical variables in the regression equation

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Question 3(4
points)
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A multiple regression analysis included 4 independent variables
results in sum of squares for regression of 1400 and sum of squares for error
of 600. The multiple coefficient of determination will be:
Question 3 options:

.300

.700

.429

.084

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Question 4(2
points)
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A “fan” shape in a scatterplot indicates:
Question 4 options:

a
nonlinear relationship

the
absence of outliers

sampling
error

unequal
variance

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Question 5(2
points)
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In regression analysis, the variables used to help explain or
predict the response variable are called the
Question 5 options:

independent
variables

dependent
variables

regression
variables

statistical
variables

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Question 6(2
points)
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A scatterplot that appears as a shapeless mass of data points
indicates:
Question 6 options:

a
curved relationship among the variables

a
linear relationship among the variables

a
nonlinear relationship among the variables

no
relationship among the variables

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Question 7(2
points)
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The coefficient of determination (.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_821add.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>) can be interpreted as
the fraction (or percent) of variation of the
Question 7 options:

explanatory
variable explained by the independent variable

explanatory
variable explained by the regression line

response
variable explained by the regression line

error
explained by the regression line

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Question 8(2
points)
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The correlation value ranges from
Question 8 options:

0
to +1

-1
to +1

-2
to +2

-.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_821b4f.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”> to+ .gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_821b64.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>

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Question 9(2
points)
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To help explain or predict the response variable in every
regression study, we use one or more explanatory variables. These variables are
also called predictor variables or independent variables.
Question 9 options:

True

False

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Question 10(2
points)
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When the scatterplot appears as a shapeless swarm of points,
this can indicate that there is no relationship between the response variable Y
and the explanatory variable X, at least none worth pursuing.
Question 10 options:

True

False

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Question 11(2
points)
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A useful graph in almost any regression analysis is a
scatterplot of residuals (on the vertical axis) versus fitted values (on the
horizontal axis), where a “good” fit not only has small residuals,
but it has residuals scattered randomly around zero with no apparent pattern.
Question 11 options:

True

False

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Question 12(2
points)
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A negative relationship between an explanatory variable X and a
response variable Y means that as X increases, Y decreases, and vice versa.
Question 12 options:

True

False

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Question 13(4
points)
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A regression analysis between weight (Y in pounds) and height (X
in inches) resulted in the following least squares line:.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_821d03.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>= 140 +
5X. This implies that if the height is increased by 1 inch, the weight is
expected to increase on average by 5 pounds.
Question 13 options:

True

False

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Question 14(4
points)
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In regression analysis, if the coefficient of determination is
1.0, then the coefficient of correlation must be 1.0.
Question 14 options:

True

False

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Question 15(4
points)
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The residual is defined as the difference between the actual and
fitted values of the response variable.
Question 15 options:

True

False

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Question 16(4
points)
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If the coefficient of correlation is -0.88, then the percentage
of the variation in Y that is explained by the regression is 77.44%.
Question 16 options:

True

False

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Question 17(4
points)
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The coefficient of determination R2is the square of the coefficient of correlation.
Question 17 options:

True

False

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Question 18(4
points)
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A regression analysis between sales (in \$1000) and advertising
(in \$) resulted in the following least squares line:.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_8220e1.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>= 32 + 8X. This implies
that an increase of \$1 in advertising is expected to result in an increase of
\$40 in sales.BE
CAREFUL!
Question 18 options:

True

False

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Question 19(2
points)
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A multiple regression model has the form.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/eq_822106.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>.The coefficient b1is
interpreted as the change in Y per unit change in X1.
Question 19 options:

True

False

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Question 20(4
points)
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This question and the
next two are based on the following information:

The maker of theSuper Bsoftball bat is interested in determining how certain factors
affect the sales of its new model bat. The data below compares the number of
bats (Y) that were sold, the average selling price (), and the
disposable income per household () in the surrounding area at 10 large sporting
goods stores that carry theSuper Bbat.
Simple regression was used to compare each independent variable to the number
of bats sold. The regression output from Excel is shown below:
.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/quiz_2_material_part2-img-3.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>

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Is there evidence of a linear relationship between the number of bats sold and
the average selling price of the bats? Support your response. If you believe
there is a linear relationship, characterize the relationship (i.e., positive,
negative, strong, weak, etc.).
Question 20 options:

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Question 21(4
points)
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Is there evidence of a linear relationship between the number of
bats sold anddisposable
income in the area? Support your response If you believe there is a linear
relationship, characterize the relationship (i.e., positive, negative, strong,
weak, etc.).

Question 21 options:

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Question 22(2
points)
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Which of the two variables, the average selling price or the
disposable income would you select for a simple linear regression model to
predict the number of bats sold?
Question 22 options:

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Question 23(3
points)
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This question and the
next seven are based on the following information:

The marketing manager of a large supermarket chain would like to determine the
effect of shelf space (in feet) on the weekly sales of international food (in
hundreds of dollars). A random sample of 12 equal â€“sized stores is selected,
with the following results:

.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/quiz_2_material_part2-img-5.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>

Below is a scatterplot for this data. Comment on the relationship between shelf
space and weekly sales.

.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/quiz_2_material_part2-img-6.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>
Question 23 options:

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Question 24(5
points)
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Use StatTools to obtain the indicated simple
linear regression results for the data given in Question 23. The output (with
blank cells A-E) is given below.

Provide the correct values for cells A, B, C, D, and E.

.gif” alt=”https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-GAG%20Quiz%202%20Summer%202010/quiz_2_material_part2-img-7.gif?_&d2lSessionVal=SXvKbBrVzbsvNU7dsbgpIWCEA”>
Question 24 options:

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Question 25(2 points)
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What is the least squares estimate of theY-intercept?
Question 25 options:

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Question 26(2
points)
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What is the least squares estimate of theslope?
Question 26 options:

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Question 27(2
points)
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Interpret the meaning of the slopeb.
Question 27 options:

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Question 28(4
points)
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Predict the average weekly sales (in hundreds of dollars) of
international food for stores with 13 feet of shelf space for international
food.
Question 28 options:

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Question 29(4 points)
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Would it be appropriate to predict the average weekly sales (in
hundreds of dollars) of international food for stores with 35 feet of shelf
space for international food? Why or why not?
Question 29 options:

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Question 30(4
points)
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State the value of the coefficient of determination, R2,
and interpret its meaning.
Question 30 options:

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