As part of the results, your calculator will display a number known as the
correlation coefficient , labeled by the variable
or
(You may have to change the calculator’s settings for these to be shown.) The values are an indication of the “goodness of fit” of the regression equation to the data. We more commonly use the value of
instead of
but the closer either value is to 1, the better the regression equation approximates the data.
Exponential regression
Exponential regression is used to model situations in which growth begins slowly and then accelerates rapidly without bound, or where decay begins rapidly and then slows down to get closer and closer to zero. We use the command “ExpReg” on a graphing utility to fit an exponential function to a set of data points. This returns an equation of the form,
Note that:
must be non-negative.
when
we have an exponential growth model.
when
we have an exponential decay model.
Given a set of data, perform exponential 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 an exponential pattern.
Find the equation that models the data.
Select “ExpReg” from the STAT then CALC menu.
Use the values returned for
a and
b 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 exponential regression to fit a model to data
In 2007, a university study was published investigating the crash risk of alcohol impaired driving. Data from 2,871 crashes were used to measure the association of a person’s blood alcohol level (BAC) with the risk of being in an accident.
[link] shows results from the study
Source:
Indiana University Center for Studies of Law in Action, 2007 . The
relative risk is a measure of how many times more likely a person is to crash. So, for example, a person with a BAC of 0.09 is 3.54 times as likely to crash as a person who has not been drinking alcohol.
BAC
0
0.01
0.03
0.05
0.07
0.09
Relative Risk of Crashing
1
1.03
1.06
1.38
2.09
3.54
BAC
0.11
0.13
0.15
0.17
0.19
0.21
Relative Risk of Crashing
6.41
12.6
22.1
39.05
65.32
99.78
Let
represent the BAC level, and let
represent the corresponding relative risk. Use exponential regression to fit a model to these data.
After 6 drinks, a person weighing 160 pounds will have a BAC of about
How many times more likely is a person with this weight to crash if they drive after having a 6-pack of beer? Round to the nearest hundredth.
Using the STAT then EDIT menu on a graphing utility, list the BAC values in L1 and the relative risk values in L2. Then use the STATPLOT feature to verify that the scatterplot follows the exponential pattern shown in
[link] :
Use the “ExpReg” command from the STAT then CALC menu to obtain the exponential model,
Converting from scientific notation, we have:
Notice that
which indicates the model is a good fit to the data. To see this, graph the model in the same window as the scatterplot to verify it is a good fit as shown in
[link] :
Use the model to estimate the risk associated with a BAC of
Substitute
for
in the model and solve for
If a 160-pound person drives after having 6 drinks, he or she is about 26.35 times more likely to crash than if driving while sober.
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?
