SOLUTION: Fitting a quadratic model to data
Throughout the twentieth century, the eating habits of Americans changed noticeably .Americans started consuming less whole milk and butter and s
Algebra.Com
Question 113530: Fitting a quadratic model to data
Throughout the twentieth century, the eating habits of Americans changed noticeably .Americans started consuming less whole milk and butter and started consuming more skim and low fat milk and margarine. We also started eating more poultry and fish. In this project you will have the opportunity to investigate trends in per capita consumption of poultry during the twentieth century .
We will start by finding a quadratic model y=ax^2+bx+c that has ordered pair solutions that correspond to the data for US. Per capita consumption of poultry given in the table .To do so, substitute each data pair into the equation. Each time, the result is an equation in three unknown: a,b, and c. Because there are three pair of data, we can form a system of three linear equation equations in three unknowns .Solving for the values of a, b, and c gives a quadratic model that represents the given data.
US PER CAPITA CONSUMPTION OF POULTRY (IN POUNDS)
YEAR X POULTRY CONSUMPTION Y (IN POUNDS)
1909 9 11
1969 69 33
2001 101 66
Write the system of equations that must be solved to find the values of a, b, and c needed for a quadratic model of the given data.
Solve the system of equations for a, b c.
Write the quadratic model for the date. Note that the variable x represents the number of years after 1990.
In 1939 the actual U.S per capita consumption of poultry was 12 lbs per person. Based on this information, how accurate do you think this model is for years other than those given in the table?
Use your model to estimate per capita consumption of poultry in 1950.
According to the model, in what year was per capita consumption of poultry 50 pounds per person?
In what year was the per capita consumption of poultry at its lowest level? What was that level?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Fitting a quadratic model to data
Throughout the twentieth century, the eating habits of Americans changed noticeably .Americans started consuming less whole milk and butter and started consuming more skim and low fat milk and margarine. We also started eating more poultry and fish. In this project you will have the opportunity to investigate trends in per capita consumption of poultry during the twentieth century .
We will start by finding a quadratic model y=ax^2+bx+c that has ordered pair solutions that correspond to the data for US. Per capita consumption of poultry given in the table .To do so, substitute each data pair into the equation. Each time, the result is an equation in three unknown: a,b, and c. Because there are three pair of data, we can form a system of three linear equation equations in three unknowns .Solving for the values of a, b, and c gives a quadratic model that represents the given data.
US PER CAPITA CONSUMPTION OF POULTRY (IN POUNDS)
YEAR X POULTRY CONSUMPTION Y (IN POUNDS)
1909 9 11
1969 69 33
2001 101 66
Write the system of equations that must be solved to find the values of a, b, and c needed for a quadratic model of the given data.
----------
y = ax^2+bx+c
-------------
11 = 81a +9b +c
33 = 69^2a + 69b +c
66 = 101^2a + 101b +c
----------------
Solve the system of equations for a, b c.
a=0.0072237319...
b=-0.1967844203...
c=12.1859375...
-------------------
Write the quadratic model for the date. Note that the variable x represents the number of years after 1990.
y = 0.0072237...x^2-0.1967844...x+12.185937....
--------------------------------
In 1939 the actual U.S per capita consumption of poultry was 12 lbs per person. Based on this information, how accurate do you think this model is for years other than those given in the table?
1939-1990=-51
f(-51) = 41.011
The model tends to be more and more inaccurate for years further and
further away from 1990.
--------------------------
Use your model to estimate per capita consumption of poultry in 1950.
1950-1990 = -40
f(-40) = 31.615 obs
-------------------
According to the model, in what year was per capita consumption of poultry 50 pounds per person?
f(-60) is approximately 50 lbs.
x=-60 corresponds to 1990-60 = 1930
--------------------------
In what year was the per capita consumption of poultry at its lowest level?
f(17) = 10.928
x=17 corresponds to 1990+17 = 2007
-----------
What was that level?
f(17) = 10.928 lbs
==========================
Cheers,
Stan H.
RELATED QUESTIONS
When given a data set,
a. How do we determine the type of model to use? (Linear,... (answered by josgarithmetic)
I really need help with part B
When given a data set,
a. How do we determine the... (answered by josgarithmetic)
A monograph written in 1902 states that the mean height of adult American males is 67.0... (answered by Boreal)
story problems are the worst for me could somebody help?
An "N-gauge" train model is... (answered by Earlsdon)
A regression equation gives the best fitting line for a set of data. What does best... (answered by Fombitz)
https://ibb.co/d40WLHJ
Find the best fitting Quadratic model for the data
a)... (answered by math_tutor2020,ikleyn)
In 1950, there were 2247,982 immigrants admitted to a country. In 2001, the (answered by josmiceli)
A nutritionist wants to determine how much time nationally people spend eating and... (answered by Boreal)
This is a question concerning least squares. I was asked to derive the math for fitting a (answered by stanbon)