# 2.4 Fitting linear models to data  (Page 5/14)

 Page 5 / 14

A regression was run to determine whether there is a relationship between the diameter of a tree ( $x,$ in inches) and the tree’s age ( $y,$ in years). The results of the regression are given below. Use this to predict the age of a tree with diameter 10 inches.

$\begin{array}{l}y=ax+b\\ a=6.301\\ b=-1.044\\ r=-0.970\end{array}$

61.966 years

For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?

 0 2 4 6 8 10 –22 –19 –15 –11 –6 –2
 1 2 3 4 5 6 46 50 59 75 100 136

No.

 100 250 300 450 600 750 12 12.6 13.1 14 14.5 15.2
 1 3 5 7 9 11 1 9 28 65 125 216

No.

For the following data, draw a scatter plot. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation? Eyeball the line, and estimate the answer.

 Year Population 1990 11,500 1995 12,100 2000 12,700 2005 13,000 2010 13,750

For the following data, draw a scatter plot. If we wanted to know when the temperature would reach 28 °F, would the answer involve interpolation or extrapolation? Eyeball the line and estimate the answer.

 Temperature, °F 16 18 20 25 30 Time, seconds 46 50 54 55 62

## Graphical

For the following exercises, match each scatterplot with one of the four specified correlations in [link] and [link] .

$r=0.\text{95}$

$r=-0.\text{89}$

C

$r=0.26$

$r=-0.39$

B

For the following exercises, draw a best-fit line for the plotted data.

## Numeric

The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in [link] http://www.census.gov/hhes/socdemo/education/data/cps/historical/index.html. Accessed 5/1/2014. . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?

 Year Percent Graduates 1990 21.3 1992 21.4 1994 22.2 1996 23.6 1998 24.4 2000 25.6 2002 26.7 2004 27.7 2006 28 2008 29.4

The U.S. import of wine (in hectoliters) for several years is given in [link] . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?

 Year Imports 1992 2665 1994 2688 1996 3565 1998 4129 2000 4584 2002 5655 2004 6549 2006 7950 2008 8487 2009 9462

Yes, trend appears linear because $r=0.\text{985}$ and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

[link] shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5?

 Year Number Unemployed 1990 750 1992 670 1994 650 1996 605 1998 550 2000 510 2002 460 2004 420 2006 380 2008 320

## Technology

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.

 $x$ 8 15 26 31 56 $y$ 23 41 53 72 103

$y=\text{1}.\text{64}0x+\text{13}.\text{8}00$ , $r=0.\text{987}$

 $x$ 5 7 10 12 15 $y$ 4 12 17 22 24
 $x$ $y$ $x$ $y$ 3 21.9 11 15.76 4 22.22 12 13.68 5 22.74 13 14.1 6 22.26 14 14.02 7 20.78 15 11.94 8 17.6 16 12.76 9 16.52 17 11.28 10 18.54 18 9.1

 $x$ $y$ 4 44.8 5 43.1 6 38.8 7 39 8 38 9 32.7 10 30.1 11 29.3 12 27 13 25.8
 $x$ $y$ 21 17 25 11 30 2 31 −1 40 −18 50 −40

$y=-\text{1}.\text{981}x+\text{6}0.\text{197}$ ; $r=-0.\text{998}$

 $x$ $y$ 100 2000 80 1798 60 1589 55 1580 40 1390 20 1202

The average annual population increase of a pack of wolves is 25.
how do you find the period of a sine graph
Period =2π if there is a coefficient (b), just divide the coefficient by 2π to get the new period
Am
if not then how would I find it from a graph
Imani
by looking at the graph, find the distance between two consecutive maximum points (the highest points of the wave). so if the top of one wave is at point A (1,2) and the next top of the wave is at point B (6,2), then the period is 5, the difference of the x-coordinates.
Am
you could also do it with two consecutive minimum points or x-intercepts
Am
I will try that thank u
Imani
Case of Equilateral Hyperbola
ok
Zander
ok
Shella
f(x)=4x+2, find f(3)
Benetta
f(3)=4(3)+2 f(3)=14
lamoussa
14
Vedant
pre calc teacher: "Plug in Plug in...smell's good" f(x)=14
Devante
8x=40
Chris
Explain why log a x is not defined for a < 0
the sum of any two linear polynomial is what
Momo
how can are find the domain and range of a relations
the range is twice of the natural number which is the domain
Morolake
A cell phone company offers two plans for minutes. Plan A: $15 per month and$2 for every 300 texts. Plan B: $25 per month and$0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
6000
Robert
more than 6000
Robert
can I see the picture
How would you find if a radical function is one to one?
how to understand calculus?
with doing calculus
SLIMANE
Thanks po.
Jenica
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic. Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15) it's standard equation is x^2 + y^2/16 =1 tell my why is it only x^2? why is there no a^2?
what is foci?
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
how to determine the vertex,focus,directrix and axis of symmetry of the parabola by equations