AnswersEAP-Algebra Functions and Data Analysis BRegression Analysis

Regression Analysis Answers

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The height, in meters, of a machine piston can be modeled by the regression equation y = 4.4sin(0.4x – 1.7) + 2.3, where x represents time, in seconds.To the nearest tenth of a meter, what is the height of the piston after 10 seconds?

A
1.6 m
B
2.5 m
C
3.3 m
D
5.6 m
2
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The height of a plant, y, in centimeters, is measured x weeks after planting a seed. The height can be modeled by the regression equation y = . Which statement best interprets the value 6.88?

Question illustration
A
The plant grows 6.88 cm each week.
B
The initial height of the plant is 6.88 cm.
C
The plant takes 6.88 weeks to reach a height of 2,139.99 cm.
D
The limiting value for the height of the plant is 6.88 cm.
3

Review the table showing the height of a Ferris wheel seat over time.Time (Seconds)Height (Feet)0315102020242327243025382345166057512

A
In the quadratic regression model, the explanatory variable is time and the response variable is the height.
B
In the quadratic regression model, the explanatory variable is the height and the response variable is time.
C
In the trigonometric regression model, the explanatory variable is time and the response variable is the height.
D
In the trigonometric regression model, the explanatory variable is the height and the response variable is time.
4

Alexei writes the power regression equation y = 2.5x1.13 to model the time, in minutes, it takes him to complete level x of a video game. Based on the regression equation, approximately how many minutes will it take him to complete level 4 of the video game?

A
10
B
11
C
12
D
13
5

When running multiple machines in a factory, the total sound power in decibels (dB) can be estimated using the regression equation y = 119.06 + 10logx, where x represents the number of machines.What is the best estimate for the total sound power when 5 machines are running in the factory?

A
121 dB
B
126 dB
C
135 dB
D
169 dB
6

Using historical population data, Jasper determines the logistic regression equation y = for the population, in thousands of people, of his town after x years.To the nearest thousand people, what is the projected population 30 years from now?

Question illustration
A
46,000 people
B
55,000 people
C
143,000 people
D
214,000 people
7

Review the table forecasting a company’s profit based on the number of units sold.Number of UnitsProfit ($)500–10,0001,2003,0002,50027,0003,20040,0003,60045,0004,30047,0005,00045,0006,75020,000

A
The company has an initial loss of about $29,864.
B
The company has an initial profit of about $29,864.
C
The company needs to sell about 29,864 units to break even.
D
The company needs to sell about 29,864 units to maximize its profit.
8

A science class conducts an experiment using a falling object. The class determines that a quadratic regression equation y = –15.9x2 + 99.2 will model the height, in feet, of the object after x seconds. Based on this model, what is the approximate height of the object after 1.5 seconds?

A
51.5 ft
B
63.4 ft
C
83.3 ft
D
85.6 ft
9

The regression equation y = 8.6sin(0.24x – 1.88) + 62.8 models the Fahrenheit temperature in a room x hours after midnight. What is the maximum temperature in the room during the first 24 hours?

A
54.2°F
B
57.0°F
C
62.8°F
D
71.4°F
10

Review the table showing the balance in an investment account over time.Time (Years)Amount ($)130064447486957615990201,483252,200303,614355,833

A
In the power regression model, a represents the initial value and b represents the growth factor.
B
In the power regression model, a represents the growth factor and b represents the initial value.
C
In the exponential regression model, a represents the initial value and b represents the growth factor.
D
In the exponential regression model, a represents the growth factor and b represents the initial value.
11

Yuki collects data on the average number of sunlight hours per month. She determines the regression model y = –2.8sin(0.65x + 120.2) + 12.2 to represent the data, where x = 1 represents January.Based on the regression model, what is the best estimate for the average number of sunlight hours she can expect each day in June?

A
9.4
B
9.9
C
11
D
15
12

Review the table of values.xy–5–9,500–3–750–2–100–1–50015210059,500

A
y = 3.04x5
B
y = –14.15(0.27)x
C
1,434.68x + 444.25
D
y = 1.73x2 + 1,434.71x + 429.33
13

Review the table showing average monthly temperatures in degrees Fahrenheit for several months, where x = 1 represents January.MonthAverage Monthly Temperature (°F)1583604646687708739711255

A
y = 7.57 sin(0.55x + 0.68) + 64.40
B
y = 7.57 sin(0.68x + 0.55) + 64.40
C
y = 7.57 sin(–0.55x – 0.68) + 64.40
D
y = 7.57 sin(–0.68x – 0.55) + 64.40
14

Review the table of values showing the number of days each year from 1990 to 1997 that air quality in San Diego did not meet federal air quality standards.Years since 1989Number of Days139227319414596127281

A
power model; y = 41.21x–0.86
B
exponential model; y = 54.97(0.71)x
C
logarithmic model; y = 39.14 – 17.93 ln x
D
quadratic model; y = 0.60x2 – 10.38x + 46.73

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