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

 Page 6 / 14
 $x$ $y$ 900 70 988 80 1000 82 1010 84 1200 105 1205 108

$y=0.\text{121}x-38.841,\text{\hspace{0.17em}}r=0.998$

## Extensions

Graph $f\left(x\right)=0.5x+10$ . Pick a set of 5 ordered pairs using inputs and use linear regression to verify that the function is a good fit for the data.

Graph $f\left(x\right)=-2x-10$ . Pick a set of 5 ordered pairs using inputs and use linear regression to verify the function.

$\left(\text{−2},-6\right),\left(\text{1},\text{−12}\right),\left(\text{5},\text{−2}0\right),\left(\text{6},\text{−22}\right),\left(\text{9},\text{−28}\right)$ ; $y=-2x-10$

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:

.

Use linear regression to determine a function $P$ 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.

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:

Use linear regression to determine a function $y,$ 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:

.

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:

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. $2x+3y=7$ Yes Determine whether the algebraic equation is linear. $6{x}^{2}-y=5$ Determine whether the function is increasing or decreasing. $f\left(x\right)=7x-2$ Increasing. #### Questions & Answers How can you tell what type of parent function a graph is ? Mary Reply generally by how the graph looks and understanding what the base parent functions look like and perform on a graph William if you have a graphed line, you can have an idea by how the directions of the line turns, i.e. negative, positive, zero William y=x will obviously be a straight line with a zero slope William y=x^2 will have a parabolic line opening to positive infinity on both sides of the y axis vice versa with y=-x^2 you'll have both ends of the parabolic line pointing downward heading to negative infinity on both sides of the y axis William y=x will be a straight line, but it will have a slope of one. Remember, if y=1 then x=1, so for every unit you rise you move over positively one unit. To get a straight line with a slope of 0, set y=1 or any integer. Aaron yes, correction on my end, I meant slope of 1 instead of slope of 0 William what is f(x)= Karim Reply I don't understand Joe Typically a function 'f' will take 'x' as input, and produce 'y' as output. As 'f(x)=y'. According to Google, "The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain." Thomas Sorry, I don't know where the "Â"s came from. They shouldn't be there. Just ignore them. :-) Thomas GREAT ANSWER THOUGH!!! Darius Thanks. Thomas Â Thomas It is the Â that should not be there. It doesn't seem to show if encloses in quotation marks. "Â" or 'Â' ... Â Thomas Now it shows, go figure? Thomas what is this? unknown Reply i do not understand anything unknown lol...it gets better Darius I've been struggling so much through all of this. my final is in four weeks 😭 Tiffany this book is an excellent resource! have you guys ever looked at the online tutoring? there's one that is called "That Tutor Guy" and he goes over a lot of the concepts Darius thank you I have heard of him. I should check him out. Tiffany is there any question in particular? Joe I have always struggled with math. I get lost really easy, if you have any advice for that, it would help tremendously. Tiffany Sure, are you in high school or college? Darius Hi, apologies for the delayed response. I'm in college. Tiffany how to solve polynomial using a calculator Ef Reply So a horizontal compression by factor of 1/2 is the same as a horizontal stretch by a factor of 2, right? KARMEL Reply The center is at (3,4) a focus is at (3,-1), and the lenght of the major axis is 26 Rima Reply The center is at (3,4) a focus is at (3,-1) and the lenght of the major axis is 26 what will be the answer? Rima I done know Joe What kind of answer is that😑? Rima I had just woken up when i got this message Joe Can you please help me. Tomorrow is the deadline of my assignment then I don't know how to solve that Rima i have a question. Abdul how do you find the real and complex roots of a polynomial? Abdul @abdul with delta maybe which is b(square)-4ac=result then the 1st root -b-radical delta over 2a and the 2nd root -b+radical delta over 2a. I am not sure if this was your question but check it up Nare This is the actual question: Find all roots(real and complex) of the polynomial f(x)=6x^3 + x^2 - 4x + 1 Abdul @Nare please let me know if you can solve it. Abdul I have a question juweeriya hello guys I'm new here? will you happy with me mustapha The average annual population increase of a pack of wolves is 25. Brittany Reply how do you find the period of a sine graph Imani Reply 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 Jhon Reply 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 Baptiste Reply the sum of any two linear polynomial is what Esther Reply divide simplify each answer 3/2÷5/4 Momo Reply divide simplify each answer 25/3÷5/12 Momo how can are find the domain and range of a relations austin Reply 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? Diddy Reply 6000 Robert more than 6000 Robert For Plan A to reach$27/month to surpass Plan B's $26.50 monthly payment, you'll need 3,000 texts which will cost an additional$10.00. So, for the amount of texts you need to send would need to range between 1-100 texts for the 100th increment, times that by 3 for the additional amount of texts...
Gilbert
...for one text payment for 300 for Plan A. So, that means Plan A; in my opinion is for people with text messaging abilities that their fingers burn the monitor for the cell phone. While Plan B would be for loners that doesn't need their fingers to due the talking; but those texts mean more then...
Gilbert
can I see the picture