AnswersDRHS GA-Statistical ReasoningTransforming to Achieve Linearity

Transforming to Achieve Linearity — Unit test Answers

12 verified answers
1
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The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed, and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7%

Question illustration
A
ŷ = –7.611 + 0.186x
B
ŷ = 0.186 – 7.611x
C
ŷ = 2.567 + 0.035x
D
ŷ = 0.035 + 2.567x
2
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The scatterplot illustrates the relationship between two quantitative variables.

Question illustration
A
This relationship is weak.
B
This relationship contains two unusual points.
C
This relationship contains more than two unusual points.
D
This relationship has no unusual points.
3

The scatterplot illustrates the relationship between two quantitative variables.

Question illustration
A
weak, positive, and linear.
B
strong, negative, and linear.
C
weak because it contains unusual points.
D
positive and linear with no unusual points.
4

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).

Question illustration
A
There is little association between number of beds and lengths of stay.
B
A short stay (under two days) is equally likely for smaller and larger hospitals.
C
There is a positive relationship between number of beds and lengths of stay.
D
There is a negative relationship between number of beds and lengths of stay.
5

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in price by $1, the predicted number of pieces increases by 0.08.
B
For each increase in price by $1, the predicted number of pieces increases by 1.20.
C
For each increase in the number of pieces by 1, the predicted price increases by $0.08.
D
For each increase in the number of pieces by 1, the predicted price increases by $1.20.
6

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.
7

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters.

Question illustration
A
passes through each data point.
B
is least able to make accurate predictions for the data.
C
minimizes the sum of the squared vertical distances from the points to the line
D
maximizes the sum of the squared vertical distances from the points to the line.
8

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, what is the value of r2?

Question illustration
A
0.83
B
0.91
C
0.99
D
1.22
9

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
10

Machine engineers are designing a new ice machine for use in restaurants. They notice that designs that use cubes containing higher volumes of water take longer to freeze.

A
Explanatory variable: shape of iceResponse variable: time to freeze
B
Explanatory variable: time to freezeResponse variable: volume of water
C
Explanatory variable: volume of waterResponse variable: time to freeze
D
Explanatory variable: type of restaurantResponse variable: time to freeze
11

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a 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). Which statement best describes the meaning of the y-intercept of the regression line?

A
When the demand for bobbleheads is 0 units, the predicted price is $0.
B
When the demand for bobbleheads is 0 units, the predicted price is $50.455.
C
When the price of a bobblehead is $0, the predicted demand is 50.455 units. This interpretation is not meaningful because a bobblehead cannot have a price of $0.
D
When the price of a bobblehead is $0, the predicted demand is 0.227 units. This interpretation is not meaningful because a bobblehead cannot have a price of $0.
12

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).

Question illustration
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.
13

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the results are given in the computer output.Which of the following represents the average distance between the actual weight and the predicted weight of the bass?

Question illustration
A
1.80
B
3.771
C
13.610
D
24.87
14

Bacteria growth was measured over a one-month period. The number of cells were counted for a certain number of days. A regression analysis was completed and is displayed in the computer output.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. A regression equation for this relationship is .

Question illustration
A
A linear model is appropriate because the residual plot is curved.
B
A linear model is appropriate because many of the residuals are close to zero.
C
A linear model is not appropriate because the residual plot shows a clear pattern.
D
A linear model is not appropriate because the y-intercept of the regression equation is negative.

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