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Choosing the Best Model — Unit test Answers

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1
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A marathon runner is interested in split times, which is the time to complete the first half of the race and the second half of the race. She collects split times for 10 runners and summarizes the data in the table.

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Option
Option A
B
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Option B
C
Option
Option C
D
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Option D
2
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Bacteria growth was measured over a one-month period. Scatterplot A displays the number of cells measured over the recorded number of days. Two transformations of the data are shown in the next two graphs. Scatterplot B displays the relationship between the number of days and the natural log of the number of cells of bacteria. Scatterplot C displays the relationship between the natural log of the number of days and the natural log of the number of cells of bacteria. Which model best represents the relationship between the number of days and the number of cells of bacteria?

Question illustration
A
A linear model would best represent the relationship because scatterplot A is fairly linear.
B
An exponential model would best represent the relationship because scatterplot B is fairly linear.
C
A linear model would best represent the relationship because scatterplot B is fairly linear.
D
A power model would best represent the relationship because scatterplot C is fairly linear.
3

A homeowner notices that the electric bill for the house is often much higher in the summer months. Collecting data from the last 18 monthly electric bills, the amount of each bill is plotted against the mean temperature for each month. The logs of both the mean monthly temperature and the electric bill are taken in order to develop a linear model.

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A
A linear model is appropriate because the residual plot shows a random scatter.
B
A logarithmic model is appropriate because logarithms were used to transform the data sets.
C
A power model is appropriate because the scatterplot of log temperature and log bill is roughly linear, and the residual plot shows no distinct pattern.
D
An exponential model is appropriate because the scatterplot of log temperature and log bill is roughly linear.
4

The fare charged for a rideshare service is a function of the distance traveled. However, the fare differs according to the time of day, availability, and other variables. The distance and fares for 10 rides are shown in the table. The equation of the least-squares regression line is ŷ = 5.20 + 2.33x, where ŷ is the predicted fare and x is the distance.

Question illustration
A
2.33
B
5.21
C
11.36
D
42.49
5

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay).

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A
Hospitals with more beds cause longer lengths of stay.
B
The size of the hospital does not appear the have an influence on length of stay.
C
More complex medical cases are often taken by larger hospitals, which increases the lengths of stay for larger hospitals.
D
More complex medical cases are often taken by larger hospitals, which decreases the lengths of stay for larger hospitals.
6

Given the least-squares regression line, , what is the predicted amount of an unstable element that is left after 6 years?

Question illustration
A
0.53 gram
B
1.699 grams
C
5.468 grams
D
8.365 grams
7

A sports analyst is interested in the relationship between the number of three-point shots players attempt in a game and the number of points scored. To investigate the relationship, he collects a simple random sample of 15 games and records the number of three-point shots attempted and the total number of points scored. He finds the equation of the least-squares regression line to be ŷ = 65.7 + 0.729x, where ŷ is points scored and x is the number of three-point shots attempted. The residual plot is shown.

Question illustration
A
No, the residuals are relatively large.
B
No, there is a clear pattern in the residual plot.
C
Yes, there is no clear pattern in the residual plot.
D
Yes, about half of the residuals are positive and half are negative.
8

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a market research survey and was used to obtain the regression equation ŷ = –0.227x + 50.455, where x represents the price of a bobblehead (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $29.99?

A
–6.80773 units
B
43.64727 units
C
50.455 units
D
90.154 units

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Choosing the Best Model — Unit test Answers…