Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the equation $y=\beta_{0}+\beta_{1} x$ of the least-squares line that best fits the given data points.$(0,1),(1,1),(2,2),(3,2)$

$y=0.9+0.4 x$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 6

Applications to Linear Models

Vectors

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

02:21

Find the equation $y=\beta…

02:05

03:15

Find the equation of the l…

03:31

03:39

03:37

02:45

02:43

03:50

02:03

Determine whether the give…

Okay, So question is we need to find best fit line using the square method. And the model is why is equals, Toby Bitter not plus bitter one time sex and the points are given to us. So let's assume a solution is metrics. Form is ex Bitta equals two. Why? Yeah, your exes metrics representing coefficient off beat or not, and coefficient of b town. So since bitter not coefficient is one so it will be one. And here proficiently sex. So that is zero right. So 10 next will be 11 12 and 13 So this is our ex. And why is the output that is represented by this value? So that is 112 to Okay, so now we have all the datas. And here Vita is nothing but beat or not And Vita one. Okay, so now we can substitute that in our metrics equation. So we have 10111213 times beater. So we'll write it as beat only. Here we have 1122 Okay, So now to solve this, we need to have a square metric so we'll multiply by x transpose a pre multiplying. So x transpose will be 10111213 right times 11110123 Vita is equals to 10111213 times 1122 Okay, so now we can solve this. Okay, so this row will be multiple, er with this column so we'll have one times one plus one times one plus one times one plus one times one writes thing. Okay, so that gives for second on This will be multiplied with this and adding it will give one plus two plus three. So that this six then multiplying this with this one. So that will give us again. Six and 0123 multiplied With this one will give us zero plus one square plus two squared plus three squares on nine plus 4, 13, 13 plus one. For them times bitta is equals toe. Now we can multiply this and this value. So one times one all this one little gives him and I think it really one plus 1 to 2 plus 244 plus 26 And this into this gives us zero plus one plus four. That is five plus six. So it is 11. Okay, so now we have our metric situation and it is square metrics. So now we can sort beetle will be 466 14 in wars times 6 11. Right now in worse. Off these metrics will be 14 times four minus six times six. And we know we just have to interchange this 14 and four diagonally and we have to interchange this with minus sign. Right, So this will be minus six and minus six. And this is six and 11 on multiplying. This time we get 20 and multiplying this we get 18 and this is it. Okay. So arbiter not and beat a one is equals toe 18 by 20 which is 200.9 and eight by 20 inches. 200.4 therefore a model list. Why? It calls 2.9 plus 0.4 x on that is answer. Thank you

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Find the equation $y=\beta_{0}+\beta_{1} x$ of the least-squares line that b…

Find the equation of the least squares line associated with the given set of…

Determine whether the given points are on the graph of the equation.$$y=…

06:44

All vectors are in $\mathbb{R}^{n}$ . Mark each statement True or False. Jus…

05:29

Classify the quadratic forms in Exercises $9-18 .$ Then make a change of var…

03:58

Show that $\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}$ or $\left\{\mathbf…

03:01

[M] Find formulas for the voltages $v_{1}$ and $v_{2}$ for the circuit in Ex…

14:14

Let $A$ be a $2 \times 2$ matrix with eigenvalues 3 and 1$/ 3$ and correspon…

05:03

In Exercises $3-6,$ solve the initial value problem $\mathbf{x}^{\prime}(t)=…

01:10

Compute the orthogonal projection of $\left[\begin{array}{l}{1} \\ {7}\end{a…

01:36

Determine which of the matrices in Exercises $7-12$ are orthogonal. If ortho…

02:50

Verify the statements in Exercises $19-24 .$ The matrices are square.If …

01:41

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.