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A regression was run to determine whether there is a relationship between the diameter of a tree ( x , in inches) and the tree’s age ( y , in years). The results of the regression are given below. Use this to predict the age of a tree with diameter 10 inches.

y = a x + b a = 6.301 b = −1.044 r = −0.970

61.966 years

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For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?

0 2 4 6 8 10
–22 –19 –15 –11 –6 –2
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1 2 3 4 5 6
46 50 59 75 100 136

No.

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100 250 300 450 600 750
12 12.6 13.1 14 14.5 15.2
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1 3 5 7 9 11
1 9 28 65 125 216

No.

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For the following data, draw a scatter plot. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation? Eyeball the line, and estimate the answer.

Year Population
1990 11,500
1995 12,100
2000 12,700
2005 13,000
2010 13,750
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For the following data, draw a scatter plot. If we wanted to know when the temperature would reach 28 °F, would the answer involve interpolation or extrapolation? Eyeball the line and estimate the answer.

Temperature, °F 16 18 20 25 30
Time, seconds 46 50 54 55 62

Interpolation. About 60 °  F .

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Graphical

For the following exercises, match each scatterplot with one of the four specified correlations in [link] and [link] .

For the following exercises, draw a best-fit line for the plotted data.

Numeric

The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in [link] http://www.census.gov/hhes/socdemo/education/data/cps/historical/index.html. Accessed 5/1/2014. . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?

Year Percent Graduates
1990 21.3
1992 21.4
1994 22.2
1996 23.6
1998 24.4
2000 25.6
2002 26.7
2004 27.7
2006 28
2008 29.4
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The U.S. import of wine (in hectoliters) for several years is given in [link] . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?

Year Imports
1992 2665
1994 2688
1996 3565
1998 4129
2000 4584
2002 5655
2004 6549
2006 7950
2008 8487
2009 9462

Yes, trend appears linear because r = 0. 985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

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[link] shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5?

Year Number Unemployed
1990 750
1992 670
1994 650
1996 605
1998 550
2000 510
2002 460
2004 420
2006 380
2008 320
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Technology

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.

x 8 15 26 31 56
y 23 41 53 72 103

y = 1 . 64 0 x + 13 . 8 00 , r = 0. 987

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x 5 7 10 12 15
y 4 12 17 22 24
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x y x y
3 21.9 11 15.76
4 22.22 12 13.68
5 22.74 13 14.1
6 22.26 14 14.02
7 20.78 15 11.94
8 17.6 16 12.76
9 16.52 17 11.28
10 18.54 18 9.1

y = 0.962 x + 26.86 ,       r = 0.965

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x y
4 44.8
5 43.1
6 38.8
7 39
8 38
9 32.7
10 30.1
11 29.3
12 27
13 25.8
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x y
21 17
25 11
30 2
31 −1
40 −18
50 −40

y = 1 . 981 x + 6 0. 197 ; r = 0. 998

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x y
100 2000
80 1798
60 1589
55 1580
40 1390
20 1202
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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
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Lambiv
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multiple choice question
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appreciation
Eliyee
explain perfect market
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In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
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what is the difference between economic growth and development
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Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
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Jabir
What do you think is more important to focus on when considering inequality ?
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sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
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it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
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suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
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What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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