# 4.3 Fitting linear models to data  (Page 6/14)

 Page 6 / 14
$x$ $y$
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
 $x$ 21 25 30 31 40 50 $y$ 17 11 2 –1 –18 –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
 $x$ 900 988 1000 1010 1200 1205 $y$ 70 80 82 84 105 108

$y=0.\text{121}x-38.841,r=0.998$

## Extensions

Graph $\text{\hspace{0.17em}}f\left(x\right)=0.5x+10.\text{\hspace{0.17em}}$ Pick a set of five ordered pairs using inputs $\text{\hspace{0.17em}}x=-2,\text{1},\text{5},\text{6},\text{9}\text{\hspace{0.17em}}$ and use linear regression to verify that the function is a good fit for the data.

Graph $\text{\hspace{0.17em}}f\left(x\right)=-2x-10.\text{\hspace{0.17em}}$ Pick a set of five ordered pairs using inputs $\text{\hspace{0.17em}}x=-2,\text{1},\text{5},\text{6},\text{9}\text{\hspace{0.17em}}$ and use linear regression to verify the function.

$\left(-2,-6\right),\left(1,\text{−12}\right),\left(5,-20\right),\left(6,\text{−22}\right),\left(9,\text{−28}\right);\text{\hspace{0.17em}}$ Yes, the function is a good fit.

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:

$\left(\text{46},\text{1},600\right),\left(\text{48},\text{1},\text{55}0\right),\left(50,\text{1},505\right),\left(\text{52},\text{1},\text{54}0\right),\left(\text{54},\text{1},\text{495}\right).$

Use linear regression to determine a function $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ where the profit in thousands of dollars depends on the number of units sold in hundreds.

Find to the nearest tenth and interpret the x -intercept.

$\left(\text{189}.8,0\right)\text{\hspace{0.17em}}$ If 18,980 units are sold, the company will have a profit of zero dollars.

Find to the nearest tenth and interpret the y -intercept.

## Real-world applications

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

$\left(\text{25}00,2000\right),\left(\text{265}0,2001\right),\left(3000,2003\right),\left(\text{35}00,2006\right),\left(\text{42}00,2010\right)$

Use linear regression to determine a function $\text{\hspace{0.17em}}y,$ where the year depends on the population. Round to three decimal places of accuracy.

$y=0.00587x+\text{1985}.4\text{1}$

Predict when the population will hit 8,000.

For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

$\left(\text{46},\text{25}0\right),\left(\text{48},\text{3}05\right),\left(50,\text{35}0\right),\left(\text{52},\text{39}0\right),\left(\text{54},\text{41}0\right).$

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds.

$y=\text{2}0.\text{25}x-\text{671}.\text{5}$

Predict when the profit will exceed one million dollars.

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

$\left(\text{46},\text{25}0\right),\left(\text{48},\text{225}\right),\left(50,\text{2}05\right),\left(\text{52},\text{18}0\right),\left(\text{54},\text{165}\right).$

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds.

$y=-\text{1}0.\text{75}x+\text{742}.\text{5}0$

Predict when the profit will dip below the $25,000 threshold. ## Chapter review exercises ## Linear Functions Determine whether the algebraic equation is linear. $\text{\hspace{0.17em}}2x+3y=7$ Yes #### Questions & Answers find the value of 2x=32 Felix Reply divide by 2 on each side of the equal sign to solve for x corri X=16 Michael Want to review on complex number 1.What are complex number 2.How to solve complex number problems. Beyan use the y -intercept and slope to sketch the graph of the equation y=6x Only Reply how do we prove the quadratic formular Seidu Reply hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher Shirley Reply thank you help me with how to prove the quadratic equation Seidu may God blessed u for that. Please I want u to help me in sets. Opoku what is math number Tric Reply 4 Trista x-2y+3z=-3 2x-y+z=7 -x+3y-z=6 Sidiki Reply Need help solving this problem (2/7)^-2 Simone Reply x+2y-z=7 Sidiki what is the coefficient of -4× Mehri Reply -1 Shedrak the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1 Alfred Reply An investment account was opened with an initial deposit of$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma