Find the quadratic regression for (-1,1) , (0,0) , (1,1)

Answers

Answer 1

Answer:

3 points define a parabola, so the regression will be unique. You want to find a quadratic polynomial $P_2(x)=\beta_0+\beta_1x+\beta_2x^2$ such that

$\begin{cases}\beta_0-\beta_1+\beta_2=1\n\beta_0=0\n\beta_0+\beta_1+\beta_2=1\end{cases}$

where the system above is generated by setting $P_2(-1)=1$ , $P_2(0)=0$ , and $P_2(1)=1$ .

Since $\beta_0=0$ , we have

$\begin{cases}-\beta_1+\beta_2=1\n\beta_1+\beta_2=1\end{cases}\implies2\beta_2=2\implies\beta_2=1\implies\beta_1=0$

So the regression for the given data points is $P_2(x)=x^2$ .

Related Questions

Which options could be the next step in simplifying this expression?27 + (3 + 41)Choose exactly two answers that are correct.A.27 + 44 (use order of operations) B.30 + 68 (use the distributive property) C.30 + 41 (use the associative property) D.68 + 30 (use the commutative property
Please help and explain
A store bought 9 cases of lightbulbs in May and 8 cases in June. There are 58 lightbulbs in each case. How many lightbulbs did the sore buy altogether??
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A woman wants to send a framed photograph of her family to her parents. The frame is 12 in. long and 7 in. wide. Will the frame lay flat in a box that has a square base, height 4 in., and volume 536 in. cubed?

Which expression is equivalent to a^2/3.

Answers

Hi there, a²/3=1/3a², Therefore, the answer is 1/3a²

A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area (shaded region) of the remaining portion of the circle in square feet? ( where A=rrx2 rr =3.14

Answers

Answer: 56 square feet

Step-by-step explanation:

When a square is inscribed within a circle, the side length of the square is equal to the diameter of the circle, divided by the square root of 2, this is the same as a square being cut out of the circle.

This means that area of the square = $((14)/(√(2) )) ^(2)$

= 98 square feet

Area of the circle is $\pi$ $r^(2)$

= 3.142 X 7 X 7

= 153.958

Area of the remaining portion will be Area of the circle - Area of the square , that is

153 . 958 - 98

= 55. 958

≈ 56 square feet

The area of a rectangle is 123 cm2. If the width is 3 cm, find the length. Let l represent the length of the rectangle.

Answers

Answer:

41 cm

Step-by-step explanation:

123/3

The formula for the area (A) of a rectangle is given by A = l * w, where l is the length and w is the width. We are asked to find the length and we are given the width (3 cm) and the area (123 cm2).

To find the length, we need to manipulate this formula to solve for l. So, divide both sides of the equation by w, this gives us: l = A / w.

We now substitute the given values into this equation:

l = 123 / 3

This simplifies to:

l = 41.0

So, the length of the rectangle is 41.0 cm.

The sum of three decimal numbers is 6. Exactly one of the numbers is less than 1. What could the numbers be?

Answers

you could do 0.9 1.6 3.5 dont know of thats what you ment but they all have decimals :)

I really need him on this please help me asap!Peter needs to determine how many birthday candles his family will need this month. Peter celebrates his birthday on the 5th and his twin sisters celebrate theirs on the 9th. Each person will have their own cake. What is the MOST appropriate word model for this problem?

A. Peter’s Age × One Twin’s Age = Total Candles Needed

B. Peter’s Age + One Twin’s Age = Total Candles Needed

C. Number of Candles in a Typical Box – Peter’s Age = Candles Needed

D. Peter’s Age + Two Times One Twin’s Age = Total Candles Needed

Answers

The answer is D because you are adding how many candles for whatever peters age is and since the twins are both the same age and get their own cake and the same amount of candles you multiply it by two

Answer:

D. Peter’s Age + Two Times One Twin’s Age = Total Candles Needed

What is 28 divide 8232 plz show work

Answers

1. Find the Greatest Common Factor (GCF) of 28,8232
Method 1: By Listing FactorsList out all factors of each number, and find the first common one.28: 1,2,4,7,14,28
8232 : 1,2,3...2744,4116,8232
Therefore, the GCF is 28.Method 2: By Prime FactorsList all prime factors of each denominator, and find the intersection of these primes.28: 2,2,7
8232 : 2,2,2,3,7,7,7
Therefore, the GCF is 2×2×7=28.
2.From above, the GCF is 28
28
3.Divide the numerator (28) by the GCF
28÷28=1
4. Divide the denominator (8232) by the GCF
8232÷28=294
5.Rewrite the fraction in the simplified form
1/1294
therefore your answer is 1294

Hope i help :P

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