# 4.3 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 ( $\text{\hspace{0.17em}}x,$ in inches) and the tree’s age ( $\text{\hspace{0.17em}}y,$ in years). The results of the regression are given below. Use this to predict the age of a tree with diameter 10 inches.

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

Interpolation. About $\text{\hspace{0.17em}}60°F.$

## Graphical

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

$r=0.\text{95}$

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

$r=-0.26$

$r=-0.39$

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] . Based on data from 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%?

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 $\text{\hspace{0.17em}}r=0.\text{985}\text{\hspace{0.17em}}$ 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 10 18.54
4 22.22 11 15.76
5 22.74 12 13.68
6 22.26 13 14.1
7 20.78 14 14.02
8 17.6 15 11.94
9 16.52 16 12.76

what is linear equation with one unknown 2x+5=3
-4
Joel
x=-4
Joel
x=-1
Joan
I was wrong. I didn't move all constants to the right of the equation.
Joel
x=-1
Cristian
what is the VA Ha D R X int Y int of f(x) =x²+4x+4/x+2 f(x) =x³-1/x-1
can I get help with this?
Wayne
Are they two separate problems or are the two functions a system?
Wilson
Also, is the first x squared in "x+4x+4"
Wilson
x^2+4x+4?
Wilson
thank you
Wilson
Wilson
f(x)=x square-root 2 +2x+1 how to solve this value
Wilson
what is algebra
The product of two is 32. Find a function that represents the sum of their squares.
Paul
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
hi
John
hi
Grace
what sup friend
John
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
acha se dhek ke bata sin theta ke value
Ajay
sin theta ke ja gha sin square theta hoga
Ajay
I want to know trigonometry but I can't understand it anyone who can help
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
False statement so you cannot prove it
Wilson
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
I want to know partial fraction Decomposition.
classes of function in mathematics
divide y2_8y2+5y2/y2
wish i knew calculus to understand what's going on 🙂
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn