# 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.

## Linear Functions

Determine whether the algebraic equation is linear. $\text{\hspace{0.17em}}2x+3y=7$

Yes

Cos45/sec30+cosec30=
Cos 45 = 1/ √ 2 sec 30 = 2/√3 cosec 30 = 2. =1/√2 / 2/√3+2 =1/√2/2+2√3/√3 =1/√2*√3/2+2√3 =√3/√2(2+2√3) =√3/2√2+2√6 --------- (1) =√3 (2√6-2√2)/((2√6)+2√2))(2√6-2√2) =2√3(√6-√2)/(2√6)²-(2√2)² =2√3(√6-√2)/24-8 =2√3(√6-√2)/16 =√18-√16/8 =3√2-√6/8 ----------(2)
exercise 1.2 solution b....isnt it lacking
I dnt get dis work well
what is one-to-one function
what is the procedure in solving quadratic equetion at least 6?
Almighty formula or by factorization...or by graphical analysis
Damian
I need to learn this trigonometry from A level.. can anyone help here?
yes am hia
Miiro
tanh2x =2tanhx/1+tanh^2x
cos(a+b)+cos(a-b)/sin(a+b)-sin(a-b)=cotb ... pls some one should help me with this..thanks in anticipation
f(x)=x/x+2 given g(x)=1+2x/1-x show that gf(x)=1+2x/3
proof
AUSTINE
sebd me some questions about anything ill solve for yall
cos(a+b)+cos(a-b)/sin(a+b)-sin(a-b)= cotb
favour
how to solve x²=2x+8 factorization?
x=2x+8 x-2x=2x+8-2x x-2x=8 -x=8 -x/-1=8/-1 x=-8 prove: if x=-8 -8=2(-8)+8 -8=-16+8 -8=-8 (PROVEN)
Manifoldee
x=2x+8
Manifoldee
×=2x-8 minus both sides by 2x
Manifoldee
so, x-2x=2x+8-2x
Manifoldee
then cancel out 2x and -2x, cuz 2x-2x is obviously zero
Manifoldee
so it would be like this: x-2x=8
Manifoldee
then we all know that beside the variable is a number (1): (1)x-2x=8
Manifoldee
so we will going to minus that 1-2=-1
Manifoldee
so it would be -x=8
Manifoldee
so next step is to cancel out negative number beside x so we get positive x
Manifoldee
so by doing it you need to divide both side by -1 so it would be like this: (-1x/-1)=(8/-1)
Manifoldee
so -1/-1=1
Manifoldee
so x=-8
Manifoldee
Manifoldee
so we should prove it
Manifoldee
x=2x+8 x-2x=8 -x=8 x=-8 by mantu from India
mantu
lol i just saw its x²
Manifoldee
x²=2x-8 x²-2x=8 -x²=8 x²=-8 square root(x²)=square root(-8) x=sq. root(-8)
Manifoldee
I mean x²=2x+8 by factorization method
Kristof
I think x=-2 or x=4
Kristof
x= 2x+8 ×=8-2x - 2x + x = 8 - x = 8 both sides divided - 1 -×/-1 = 8/-1 × = - 8 //// from somalia
Mohamed
i am in
Cliff
hii
Amit
how are you
Dorbor
well
Biswajit
can u tell me concepts
Gaurav
Find the possible value of 8.5 using moivre's theorem
which of these functions is not uniformly cintinuous on (0, 1)? sinx
helo
Akash
hlo
Akash
Hello
Hudheifa
which of these functions is not uniformly continuous on 0,1