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Nimfa-mama [501]
3 years ago
8

What is the quadratic regression equation for the data set? ​ ​ ​ PLEASEE HELP ME

Mathematics
1 answer:
Soloha48 [4]3 years ago
8 0
You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b

Computing this, you'd find that

\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}

which means the first choice is correct.
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Find the value of the 60th term of the following sequence: 33, 28, 23, 18
Otrada [13]

Step-by-step explanation:

The first term of the AP i.e a = 33

and common difference i.e d = 28-33 = -5

So, 60th term = a +(n-1)d = a+ 59d

= 33 + 59( -5)

= 33- 295

= - 262

4 0
2 years ago
5 pounds of rice at a store cost $6.50 use the ray tool to graph the cost C, vs pounds of rice
Kobotan [32]

Given that 5 pounds of rice at a store cost $6.50.

Then 1 pounds of rice at a store cost = $6.50/5= $1.3

So the equation for the cost can be written as:

C=1.3P just like we write equation y=mx

Now we have to graph the cost C, vs pounds of rice.

Variable for Pounds of rice is not given so let it be "P"

So let's make a table for number of pounds (P) and cost (C) the we can graph the points from that table to get the final graph.

Attached graph is the final graph.

4 0
2 years ago
determine the time necessary for P to double when it is invested at interest rate r compounded annually, monthly, daily, and con
ziro4ka [17]

Answer:

Step-by-step explanation:

sasasa

7 0
3 years ago
196 divided by 3.5=_____
kykrilka [37]
196 divided by 3.5 = 56!

Hope this helps!
5 0
3 years ago
Read 2 more answers
A radio disc jockey has 7 songs on this up coming hour's playlist: 2 are rock songs, 2 are reggae songs and 3 are country songs.
SVETLANKA909090 [29]

Answer:

Probability that song selected after first selection is rock = 2/7

Probability that song selected from the remaining after second selection is country rock = 1/2

Step-by-step explanation:

Total number of songs = 7

After first selection, probability that the song selected is rock = 2/7

After second selection, probability that the song selected from the remaining is a country song = 3/6 = 1/2

8 0
3 years ago
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