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Oliga [24]
3 years ago
6

Orthogonal explanatory variables. suppose in the modelx2 to xk are all uncorrelated. such variables are called orthogonal variab

les. if this is the case:
a. what will be the structure of the (x’x) matrix?
b. how would you obtain = (x’x)−1x’y?
c. what will be the nature of the var–cov matrix of ?
d. suppose you have run the regression and afterward you want to introduce another orthogonal variable, say, xk 1 into the model. do you have to recompute all the previous coefficients 1 to k? why or why not?
Mathematics
1 answer:
sertanlavr [38]3 years ago
4 0
<span>d. suppose you have run the regression and afterward you want to introduce another orthogonal variable, say, xk 1 into the model. do you have to recompute all the previous coefficients 1 to k? why or why not?</span>
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Mrs.Henderson makes punch by mixing 10.9 liters of apple juice,0.6 liters of orange juice,and 8 liters of ginger ale.she pours e
Nimfa-mama [501]

3.25 liters.

<h3>Further explanation</h3>

<u>Given:</u>

  • Mrs.Henderson makes punch by mixing 10.9 liters of apple juice, 0.6 liters of orange juice, and 8 liters of ginger ale.
  • She poured equally into 6 bowls.

<u>Question:</u>

How much punch is in each bowl?

Express your answer in liters.

<u>The Process:</u>

The two steps for obtaining the amount of punch in each bowl are as follows:

<u>Step-1: </u>the total amount of punch after mixing is the sum of apple juice, orange juice, and ginger ale in liters.

\boxed{ \ 10.9 \ liters + 0.6 \ liters + 8 \ liters = 19.5 \ liters \ }

<u>Step-2: </u>the total amount of punch divided by the number of the bowl is the amount of punch in each bowl.

\boxed{ \ 19.5 \ liters \div 6 \ bowls = \boxed{ \ 3.25 \ liters/bowl \ } \ }

Let's also consider the following quick steps.

<u>Quick steps:</u>

\boxed{ \ \frac{(10.9 + 0.6 + 8) \ liters}{6 \ bowls} = \frac{19.5 \ liters}{6 \ bowls} = \boxed{ \ 3.25 \ liters/bowl \ } \ }

Therefore, the amount of punch in each bowl is 3.25 liters.

<h3>Learn more</h3>
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Keywords: Mrs.Henderson, makes punch by mixin, 10.9 liters of apple juice, 0.6 liters of orange juice, 8 liters of ginger ale, 6 bowls, how much punch is in each bowl? express your answer in liters, the amount, sum, divide

3 0
3 years ago
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Use the table to write and solve an equation to find the number of
exis [7]

Answer:

c = 11

Step-by-step explanation:

Given

Cars\ Sold:-: 8; 9; 12; c

Required

What value of c makes the mean = 10

Mean is calculated as

Mean = \frac{\sum x}{n}

In this case;

Mean = 10 and n = 4;

So, we have:

10 = \frac{8+ 9 + 12 + c}{4}

10 = \frac{29+ c}{4}

Multiply both sides by 4

10 * 4 = 29 + c

40 = 29 + c

Solve for c

c = 40 - 29

c = 11

4 0
3 years ago
How can you prove a triangle is an equilateral triangle? (4 points)
Phoenix [80]

Answer:

A would be correct.

Step-by-step explanation:

Just show that triangles AOB,BOC,COA are all congruent (then all the sides of triangle ABC must be equal). To show this, note that triangles A′BO,A′OC are equilateral since they are all radius of the circles. Line OA′ is perpendicular to line BC. Hence, ∠OBC=∠OCB=30∘.

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3 years ago
(I need the answer right now please) ΔA'B'C' was constructed using ΔABC and line segment EH. 2 triangles are shown. Line E H is
irina1246 [14]

Answer:

The true statements are

1. BD = DB'

3. m∠EFA = 90°

4. The line of reflection, EH, is the perpendicular bisector of BB', AA', and

   CC'

Step-by-step explanation:

* Lets explain how to solve the problem

- Reflection is flipping an object over the line of reflection.

- The object and its image have the same shape and size, but the

  figures are in opposite directions from the line of reflection

- The objects appear as if they are mirror reflections, with right and left

  reversed

- The line of reflection is a perpendicular bisector for all lines joining

  points on the figure with their corresponding images

- Look to the attached figure for more understand

* Lets solve the problem

- ΔA'B'C' was constructed using ΔABC and line segment EH, where

 EH is the reflection line

- D is the mid-point of BB'

- F is the mid-point of AA'

- G is the mid-point of CC'

* Lets find from the answer the true statements

1. BD = DB'

∵ D is the mid point of BB'

- Point D divides BB' into two equal parts

∴ BD = DB' ⇒ <em>True</em>

2. DF = FG

- It depends on the size of the sides and angles of the triangle

∵ We can't prove that

∴ DF = FG ⇒ <em>Not true</em>

3. m∠EFA = 90°

∵ The line of reflection ⊥ the lines joining the points with their

   corresponding images

∴ EH ⊥ AA' and bisect it at F

∴ m∠EFA = 90° ⇒ <em>True</em>

4. The line of reflection, EH, is the perpendicular bisector of BB',

   AA', and CC'

- Yes the line of reflection is perpendicular bisectors of them

∴ The line of reflection, EH, is the perpendicular bisector of BB',

   AA', and CC' ⇒ <em>True</em>

5. ΔABC is not congruent to ΔA'B'C'

∵ In reflection the object and its image have the same shape and size

∴ Δ ABC is congruent to Δ A'B'C'

∴ ΔABC is not congruent to ΔA'B'C' ⇒ <em>Not true</em>

4 0
3 years ago
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11-Across plus 28-Down
Art [367]

Answer:

(11,-28)

Step-by-step explanation:

8 0
3 years ago
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