when
the model increases rapidly at first until it reaches its point of maximum growth rate,
At that point, growth steadily slows and the function becomes asymptotic to the upper bound
is the limiting value, sometimes called the
carrying capacity , of the model.
Logistic regression
Logistic regression is used to model situations where growth accelerates rapidly at first and then steadily slows to an upper limit. We use the command “Logistic” on a graphing utility to fit a logistic function to a set of data points. This returns an equation of the form
Note that
The initial value of the model is
Output values for the model grow closer and closer to
as time increases.
Given a set of data, perform logistic regression using a graphing utility.
Use the STAT then EDIT menu to enter given data.
Clear any existing data from the lists.
List the input values in the L1 column.
List the output values in the L2 column.
Graph and observe a scatter plot of the data using the STATPLOT feature.
Use ZOOM [9] to adjust axes to fit the data.
Verify the data follow a logistic pattern.
Find the equation that models the data.
Select “Logistic” from the STAT then CALC menu.
Use the values returned for
and
to record the model,
Graph the model in the same window as the scatterplot to verify it is a good fit for the data.
Using logistic regression to fit a model to data
Mobile telephone service has increased rapidly in America since the mid 1990s. Today, almost all residents have cellular service.
[link] shows the percentage of Americans with cellular service between the years 1995 and 2012
Source:
The World Bank, 2013 .
Year
Americans with Cellular Service (%)
Year
Americans with Cellular Service (%)
1995
12.69
2004
62.852
1996
16.35
2005
68.63
1997
20.29
2006
76.64
1998
25.08
2007
82.47
1999
30.81
2008
85.68
2000
38.75
2009
89.14
2001
45.00
2010
91.86
2002
49.16
2011
95.28
2003
55.15
2012
98.17
Let
represent time in years starting with
for the year 1995. Let
represent the corresponding percentage of residents with cellular service. Use logistic regression to fit a model to these data.
Use the model to calculate the percentage of Americans with cell service in the year 2013. Round to the nearest tenth of a percent.
Discuss the value returned for the upper limit,
What does this tell you about the model? What would the limiting value be if the model were exact?
Using the STAT then EDIT menu on a graphing utility, list the years using values 0–15 in L1 and the corresponding percentage in L2. Then use the STATPLOT feature to verify that the scatterplot follows a logistic pattern as shown in
[link] :
Use the “Logistic” command from the STAT then CALC menu to obtain the logistic model,
Next, graph the model in the same window as shown in
[link] the scatterplot to verify it is a good fit:
To approximate the percentage of Americans with cellular service in the year 2013, substitute
for the in the model and solve for
According to the model, about 98.8% of Americans had cellular service in 2013.
The model gives a limiting value of about 105. This means that the maximum possible percentage of Americans with cellular service would be 105%, which is impossible. (How could over 100% of a population have cellular service?) If the model were exact, the limiting value would be
and the model’s outputs would get very close to, but never actually reach 100%. After all, there will always be someone out there without cellular service!
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?
