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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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Suppose customers in a certain queue are served one at a time sequentially, that the time for each individual customer is Expone
alexandr402 [8]

Answer:

The shape and rate parameters are \frac{1}{12} and 3.

Step-by-step explanation:

Let <em>X</em> = service time for each individual.

The average service time is, <em>β</em> = 12 minutes.

The random variable follows an Exponential distribution with parameter, \lambda=\frac{1}{\beta}=\frac{1}{12}.

The service time for the next 3 customers is,

<em>Z</em> = <em>X</em>₁ + <em>X</em>₂ + <em>X</em>₃

All the <em>X</em>_{i}'s are independent Exponential random variable.

The sum of independent Exponential random variables is known as a Gamma or Erlang random variable.

The random variable <em>Z</em> follows a Gamma distribution with parameters (<em>α</em>, <em>n</em>).

The parameters are:

\alpha =\lambda=\frac{1}{12}\\n=3

Thus, the shape and rate parameters are \frac{1}{12} and 3.

5 0
3 years ago
What IS 23443x/3.14159
mamaluj [8]

Answer:

7462.14496x

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Which graph represents the solution to this inequality? 16x-80x&lt;37+27
marin [14]

Answer:

A

Step-by-step explanation:

Hope this helps

8 0
2 years ago
A baby elephant weighs 1,400 pounds, which is 7,437 pounds less than her mother. Write an equation to express the weight of the
erica [24]
Let's say that y is the weight of the mother and x is the weight of the baby.
We know that the baby is 7437 pounds less than the mother, which means you need to add 7437 pounds to the baby's weight to get the mother's.
We can show it like this:
x+7437=y.
We know what the baby's weight is (1400 lbs), so just sub it in:
1400+7437=y
y=8837 lbs
The mom weighs 8837 pounds.
4 0
3 years ago
Martin says that f(x)=2(4)^x starts at 4 and has a constant ratio of 2. What error did Martin make? Explain.
grigory [225]

Answer:

A general exponential equation is written as:

f(x) = A*(r)^x

Where:

A is the initial value, this is the value that the function takes when x = 0.

r is the rate of growth

x is the variable.

In this case, the function is:

f(x) = 2*(4)^x

The initial value is:

f(0) = 2*(4)^0 = 2*1 = 2

The initial value is 2.

And the rate of growth is 4.

So Martin seems to mixed these two values (he said initial value = 4, and rate  = 2, which is the opposite of what we found)

8 0
2 years ago
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