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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

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
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Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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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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