Gasoline consumption in the United States has been steadily increasing. Consumption data from 1994 to 2004 is shown in
[link] .
http://www.bts.gov/publications/national_transportation_statistics/2005/html/table_04_10.html Determine whether the trend is linear, and if so, find a model for the data. Use the model to predict the consumption in 2008.
Year
'94
'95
'96
'97
'98
'99
'00
'01
'02
'03
'04
Consumption (billions of gallons)
113
116
118
119
123
125
126
128
131
133
136
The scatter plot of the data, including the least squares regression line, is shown in
[link] .
We can introduce new input variable,
$\text{\hspace{0.17em}}t,$ representing years since 1994.
The least squares regression equation is:
$C(t)=113.318+2.209t$
Using technology, the correlation coefficient was calculated to be 0.9965, suggesting a very strong increasing linear trend.
Using this to predict consumption in 2008
$\text{\hspace{0.17em}}(t=14),$
Scatter plots show the relationship between two sets of data. See
[link] .
Scatter plots may represent linear or non-linear models.
The line of best fit may be estimated or calculated, using a calculator or statistical software. See
[link] .
Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data. See
[link] .
The correlation coefficient,
$\text{\hspace{0.17em}}r,$ indicates the degree of linear relationship between data. See
[link] .
A regression line best fits the data. See
[link] .
The least squares regression line is found by minimizing the squares of the distances of points from a line passing through the data and may be used to make predictions regarding either of the variables. See
[link] .
Section exercises
Verbal
Describe what it means if there is a model breakdown when using a linear model.
When our model no longer applies, after some value in the domain, the model itself doesn’t hold.
A regression was run to determine whether there is a relationship between hours of TV watched per day
$\text{\hspace{0.17em}}(x)\text{\hspace{0.17em}}$ and number of sit-ups a person can do
$\text{\hspace{0.17em}}(y).\text{\hspace{0.17em}}$ The results of the regression are given below. Use this to predict the number of sit-ups a person who watches 11 hours of TV can do.
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
Y
master
X2-2X+8-4X2+12X-20=0
(X2-4X2)+(-2X+12X)+(-20+8)= 0
-3X2+10X-12=0
3X2-10X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20
x2-4x2-2x+12x+8-20
-3x2+10x-12
now you can find the answer using quadratic
Mukhtar
explain and give four example of hyperbolic function
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.