02.03 Exploring Relationships
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School
University of Central Florida *
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Course
32
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by laurennicolenunez
Question 1
(Worth 2 points)
(02.02 MC)
The weight, y, in pounds, of human babies was tracked for the first 12 weeks after birth where
t represents the number of weeks after birth. The linear model representing this relationship
is ŷ = 6.7 + 0.52t. Clarissa wanted to predict the weight of a baby at 16 weeks.
What is this an example of, and is this method a best practice for prediction? Explain your
reasoning.
This is an example of extrapolation. Extrapolation is not a best practice for prediction as the
prediction is not accurate because 16 weeks is outside the given interval of 12 weeks.
This is an example of extrapolation. Extrapolation is a best practice for prediction as the
prediction is accurate even though 16 weeks is outside the given interval of 12 weeks.
This is an example of linear modeling. Linear modeling is a best practice for prediction as
the prediction is accurate even though 16 weeks is outside the given interval of 12 weeks.
This is an example of linear modeling. Linear modeling is not a best practice for prediction
as the prediction is not accurate because 16 weeks is outside the given interval of 12 weeks.
The type of prediction is unable to be determined by the information given.
Points earned on this question: 2
Question 2
(Worth 2 points)
(02.02 MC)
Data were collected on the distance a golf ball will travel when hit by a golf club at a certain
speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards.
The regression line is given by ŷ = 5.32 + 46.73s.
Identify the slope and y-intercept of the regression line. Interpret each value in context.
The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per
hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the speed
is zero miles per hour.
The slope, b = 5.32, indicates that the distance decreases by 5.32 yards for every one mile
per hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the
speed is one mile per hour.
The slope, b = 46.73, indicates that the distance increases by 46.73 yards for every one mile
per hour of speed. The y-intercept, a = 5.32, is the distance estimated by this model if the
speed is zero miles per hour.
The slope, b = 46.73, indicates that the distance decreases by 46.73 yards for every one mile
per hour of speed. The y-intercept, a = 4.17, is the distance estimated by this model if the
speed is one mile per hour.
The slope and y-intercept are unable to be determined from the regression line given.
Points earned on this question: 2
Question 3
(Worth 2 points)
(02.02 LC)
The depth at which sharks dive, y, in feet, as related to the duration of the dive, t, in seconds,
is represented by the linear model ŷ = 5.1 + 10.51t.
If the dive duration is 6 seconds, what is the predicted depth of the dive?
0.09 feet
−0.09 feet
11.1 feet
−68.16 feet
68.16 feet
Points earned on this question: 2
Question 4
(Worth 2 points)
(02.01 LC)
Randolph calculated the correlation coefficient to be 0 when counting bacteria growth over a
period of 14 days. He concluded that there is no relationship between bacteria growth and
time.
Is Randolph correct? Explain your reasoning.
Randolph's conclusion is not correct. If the correlation coefficient is 0, there is not a linear
relationship, but there could be another type of relationship.
Randolph's conclusion is correct. If the correlation coefficient is 0, there is a linear
relationship.
Randolph's conclusion is not correct. If the correlation coefficient is less than 1, there is not
a linear relationship, but there could be another type of relationship.
Randolph's conclusion is correct. If the correlation coefficient is greater than −1, there is not
a linear relationship, but there could be another type of relationship.
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Randolph's conclusion is correct. If the correlation coefficient is less than 1, there is not a
linear relationship, but there could be another type of relationship.
Points earned on this question: 2
Question 5
(Worth 2 points)
(02.02 MC)
The IQ scores and math test scores of third grade students is given by the regression line ŷ =
−23.5 + 0.8534s, where ŷ is the predicted math score and s is the IQ score. An actual math
test score for a student is 73.5 with an IQ of 110.
Find and interpret the residual.
−3.13; The regression line underpredicts the student's math test score.
3.13; The regression line overpredicts the student's math test score.
3.13; The regression line underpredicts the student's math test score.
−3.13; The regression line overpredicts the student's math test score.
82.9; The regression line overpredicts the student's math test score.
Points earned on this question: 2