# 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 (1+cosA)(1-cosA)=sin^2A BINCY Reply good Neha why I'm sending you solved question Mirza Teach me abt the echelon method Khamis exact value of cos(π/3-π/4) Ankit Reply What is differentiation? Intakhab Reply modul questions trigonometry Thamarai Reply (1+cosA)(1-cosA)=sin^2A BINCY differentiate f(t)=1/4t to the power 4 +8 Jessica Reply I need trigonometry,polynomial duru Reply ok Augustine Why is 7 on top Bertha Reply simplify cot x / csc x Catherine Reply 👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay what is the period of cos? SIYAMTHEMBA Reply your question might not seem clear as you asked. ask well to get perfect answers put your question on a table I'm willing to help you Mr Siyamthemba Patrick simplify: cot x/csc x Catherine sorry i didnt realize you were actually asking someone else to put their question on here. i thought this was where i was supposed to. Catherine some to dereve formula for bulky density kurash Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero Rahul Reply questions Thamarai ok AjA sin^4+sin^2=1, prove that tan^2-tan^4+1=0 SAYANTANI Reply what is the formula used for this question? "Jamal wants to save$54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
Kuz Reply
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
Mintah Reply
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
Joju Reply
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx
musah Reply

### Read also:

#### Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

 By By By By By By Nick Swain By