AnswersSC-Statistical Modeling SDPCThe Relationship between Two Quantitative Variables

The Relationship between Two Quantitative Variables Answers

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The scatterplot illustrates the relationship between two quantitative variables: number of seeds planted and the crop yield per square foot.

Question illustration
A
weak and nonlinear.
B
strong and positive.
C
weak and negative.
D
strong and nonlinear.
2
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Football coaches running their summer practices noticed that the players who weighed more typically had slower times for their 40-yard dash.

A
Explanatory variable: season Response variable: player weight
B
Explanatory variable: seasonResponse variable: player 40-yard-dash time
C
Explanatory variable: player weightResponse variable: player 40-yard-dash time
D
Explanatory variable: player 40-yard-dash timeResponse variable: player weight
3

At a dome-style football stadium, sports analysts noticed that as the distance of a field-goal attempt increased, the success rate of a field-goal attempt decreased.

A
Explanatory variable: style of stadiumResponse variable: distance of field-goal attempt
B
Explanatory variable: style of stadiumResponse variable: success rate of field-goal attempt
C
Explanatory variable: success rate of field-goal attemptResponse variable: distance of field-goal attempt
D
Explanatory variable: distance of field-goal attemptResponse variable: success rate of field-goal attempt
4

Among football field-goal kickers, the rate of success for field-goal attempts tends to decrease as the distance for the field-goal attempt increases. The data in the table show various field-goal attempt distances and the success rate at those distances.

Question illustration
A
A graph titled field-goal distance and success rate has distance (yards) on the x-axis, and success rate (percentage) on the y-axis. The points decreases in a line with negative slope. The points match those in the table.
Option A
B
A graph titled field-goal distance and success rate has success rate (percentage) on the x-axis, and distance (yards) on the y-axis. The points decreases in a line with negative slope.
Option B
C
A graph titled field-goal distance and success rate has distance (yards) on the x-axis, and success rate (percentage) on the y-axis. The points decreases in a line with negative slope. The points do not match those in the table.
Option C
D
A graph titled field-goal distance and success rate has success rate (percentage) on the x-axis, and distance (yards) on the y-axis. The points decreases in a line with negative slope.
Option D
5

Which scatterplot demonstrates the strongest relationship between two quantitative variables?

A
A graph has x on the x-axis, and y on the y-axis. Points are scattered throughout the graph.
Option A
B
A graph has x on the x-axis, and y on the y-axis. Points are scattered throughout the graph.
Option B
C
A graph has x on the x-axis, and y on the y-axis. Points increase loosely together.
Option C
D
A graph has x on the x-axis, and y on the y-axis. Points increase tightly together.
Option D
6

Real estate agents in a county with a large, urban residential area noticed that families with larger incomes tend to live in homes that sell for higher prices.

A
Explanatory variable: family incomeResponse variable: price of the home
B
Explanatory variable: price of the homeResponse variable: family income
C
Explanatory variable: type of residential areaResponse variable: price of the home
D
Explanatory variable: price of the homeResponse variable: type of residential area
7

Among players drafted to play professional football, it seems as though those who weigh more tend to have slower 40-yard dash times. The data in the table show various weights (in pounds) and 40-yard dash times (in seconds) for a sample of football players.

Question illustration
A
A graph titled Weight and 40-yard dash times has weight (pounds) on the x-axis, and 40-yard time (seconds). Points are at (4.52, 190), (4.32, 191), (4.48, 180), (4.54, 200), (4.51, 188), (4.39, 180), (4.5, 180), (4.43, 200), (4.53, 191).
Option A
B
A graph titled Weight and 40-yard dash times has 40-yard time (seconds) on the x-axis and weight (pounds) on the y-axis.
Option B
C
A graph titled Weight and 40-yard dash times. The x- and y-axes are not labeled. Points are at (190, 4.52), (191, 4.32), (180, 4.48), (200, 4.54), (188, 4.51), (190, 4.54), (190, 4.5), (180, 4.32), (208, 4.52), (180, 4.39), (180, 4.5), (192, 4.56), (175, 4.32), (191, 4.53), (200, 4.43), (193, 4.61), (208, 4.46), (203, 4.53), (185, 4.36).
Option C
D
A graph titled Weight and 40-yard dash times has weight (pounds) on the x-axis, and 40-yard time (seconds). The x- and y-axes are not labeled.
Option D
8

Exercise science researchers collecting data within their state noticed that teens who spend more time streaming videos spend less time exercising.

A
Explanatory variable: time spent exercisingResponse variable: state of teen’s residence
B
Explanatory variable: time spent streaming videosResponse variable: time spent exercising
C
Explanatory variable: time spent exercisingResponse variable: time spent streaming videos
D
Explanatory variable: state of teen’s residenceResponse variable: time spent streaming videos
9

During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. The data in the table show various numbers of seeds planted per square foot and yields (in pounds per square foot) for a sample of fields.

Question illustration
A
A graph titled number of Seeds and Crop Yield has seeds (per square foot) on the x-axis, and yard (pounds per square foot) on the y-axis. The points curve up to a point, and then curve back down. The points match those in the table.
Option A
B
A graph titled number of Seeds and Crop Yield has yield (pounds per square foot) on the x-axis, and seeds (per square foot) on the y-axis. The points curve to the right, and then to the left.
Option B
C
A graph titled number of Seeds and Crop Yield. The x and y-axes are not labeled.
Option C
D
A graph titled number of Seeds and Crop Yield. The x and y-axes are not labeled.
Option D
10

Which scatterplot demonstrates the strongest relationship between two quantitative variables?

A
A graph has x on the x-axis, and y on the y-axis. Points are scattered throughout the graph.
Option A
B
A graph has x on the x-axis, and y on the y-axis. Points curve up and then down in a line.
Option B
C
A graph has x on the x-axis, and y on the y-axis. Points increase loosely together.
Option C
D
A graph has x on the x-axis, and y on the y-axis. Points decrease loosely together.
Option D

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