This module provides a homework for Linear Regression and Correlation as a part of R. Bloom's Custom version of Collaborative Statistics collection (col10617 and col10619). Two additional homework problems have been added to the original module m17085 from the 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
In 1990 the number of driver deaths per 100,000 for the different age groups was as follows (Source:
The National Highway Traffic Safety Administration's National Center for Statistics and Analysis ):
Age
Number of Driver Deaths per 100,000
15-24
28
25-39
15
40-69
10
70-79
15
80+
25
For each age group, pick the midpoint of the interval for the x value. (For the 80+ group, use 85.)
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:
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:
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.
-0.8533, Yes
No
No.
2.97, Yes
slope = -0.0432. As the year increases by one, the welfare family size decreases by 0.0432 people.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:
OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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