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
For any prediction questions, the answers are calculated using the least squares (best fit) line equation cited in the solution.
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:
$\widehat{y}=a+\text{bx}$
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.
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:
$\widehat{y}=a+\text{bx}$
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.
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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?
Source:
OpenStax, Collaborative statistics (custom online version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11476/1.5
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