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Linear Regression and Correlation: Homework is a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

For each situation below, state the independent variable and the dependent variable.

  • A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than all other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers.
  • A study is done to determine if the weekly grocery bill changes based on the number of family members.
  • Insurance companies base life insurance premiums partially on the age of the applicant.
  • Utility bills vary according to power consumption.
  • A study is done to determine if a higher education reduces the crime rate in a population.
  • Independent: Age; Dependent: Fatalities
  • Independent: Power Consumption; Dependent: Utility
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For any prediction questions, the answers are calculated using the least squares (best fit) line equation cited in the solution.

Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows (Source: http:// http://www.census.gov/compendia/statab/cats/transportation/motor_vehicle_accidents_and_fatalities.html ):

Age Number of Driver Deaths per 100,000
16-19 38
20-24 36
25-34 24
35-54 20
55-74 18
75+ 28

  • For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80.)
  • Using “ages” as the independent variable and “Number of driver deaths per 100,000” as the dependent variable, make a scatter plot of the data.
  • Calculate the least squares (best–fit) line. Put the equation in the form of: y ^ = a + bx size 12{y=a+ ital "bx"} {}
  • Find the correlation coefficient. Is it significant?
  • Pick two ages and find the estimated fatality rates.
  • Use the two points in (e) to plot the least squares line on your graph from (b).
  • Based on the above data, is there a linear relationship between age of a driver and driver fatality rate?
  • What is the slope of the least squares (best-fit) line? Interpret the slope.
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The average number of people in a family that received welfare for various years is given below. (Source: House Ways and Means Committee, Health and Human Services Department )

Year Welfare family size
1969 4.0
1973 3.6
1975 3.2
1979 3.0
1983 3.0
1988 3.0
1991 2.9

  • Using “year” as the independent variable and “welfare family size” as the dependent variable, make a scatter plot of the data.
  • Calculate the least squares line. Put the equation in the form of: y ^ = a + bx size 12{y=a+ ital "bx"} {}
  • Find the correlation coefficient. Is it significant?
  • Pick two years between 1969 and 1991 and find the estimated welfare family sizes.
  • Use the two points in (d) to plot the least squares line on your graph from (b).
  • Based on the above data, is there a linear relationship between the year and the average number of people in a welfare family?
  • Using the least squares line, estimate the welfare family sizes for 1960 and 1995. Does the least squares line give an accurate estimate for those years? Explain why or why not.
  • Are there any outliers in the above data?
  • What is the estimated average welfare family size for 1986? Does the least squares line give an accurate estimate for that year? Explain why or why not.
  • What is the slope of the least squares (best-fit) line? Interpret the slope.
  • y ^ = 88 . 7206 0 . 0432 x size 12{y="88" "." "7206" - 0 "." "0432"x} {}
  • -0.8533, Yes
  • No
  • No.
  • 2.93, Yes
  • slope = -0.0432. As the year increases by one, the welfare family size tends to decrease by 0.0432 people.
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Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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