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BlackZzzverrR [31]
3 years ago
7

The least-squares regression line is_____________. A. the line that passes through the most data points.B. the line that makes t

he sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.C. the line such that half of the data points fall above the line and half fall below the line.D. All of the above
Mathematics
1 answer:
Elanso [62]3 years ago
3 0

Answer:

<h3>The option B) is correct.</h3><h3>That is the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible is correct answer</h3>

Step-by-step explanation:

Given that " The least-squares regression line "

The least-squares regression line is <u>the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.</u>

Therefore option B) is correct

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Question no 6 answer
ExtremeBDS [4]

Answer:

  • a = 1
  • b = -28
  • P(x) = (x +2)(x -3)(x^2 +3x +10)

Step-by-step explanation:

a) Since x+2 is a factor, we know P(-2) = 0.

  P(x) = (((x +2)x +a)x +b)x -60

Then the value of P(-2) is ...

  P(-2) = 0 = (((0)(-2) +a)(-2) +b)(-2) -60 = (-2a +b)(-2) -60 = 4a -2b -60

We know the remainder from division by (x+3) is 60, so

  P(-3) = 60 = (((-3+2)(-3) +a)(-3) +b)(-3) -60 = ((3+a)(-3) +b)(-3) -60

     = (-9 -3a +b)(-3) -60 = 27 +9a -3b -60

  93 = 9a -3b

These two equations can be put into standard form:

  2a -b = 30

  3a -b = 31

Then we have the solution ...

  a = 1 . . . . . (by subtracting the first equation from the second)

  -28 = b . . . by substituting into the first equation

__

b) To show that (x-3) is a factor we need to evaluate P(3).

  P(3) = (((3 +2)(3) +1)(3) -28)(3) -60 = (48 -28)(3) -60 = 0

The function value is 0, so (x -3) is a factor.

__

c) We want to find Q(x) = x^2 +cx +d such that ...

  (x +2)(x -3)Q(x) = P(x)

  (x^2 -x -6)(x^2 +cx +d) = x^4 +2x^3 +x^2 -28x -60

  x^4 +(c-1)x^3 +(-6-c+d)x^2 +(-6c-d)x -6d = x^4 +2x^3 +x^2 -28x -60

This gives rise to the equations ...

  c -1 = 2   ⇒   c = 3

  -6d = -60   ⇒   d = 10

Then P(x) can be factored as ...

  P(x) = (x +2)(x -3)(x^2 +3x +10)

_____

<em>Comment on the attached graph</em>

I like to use a graphing calculator to find real roots of higher-degree polynomials. This graph shows the real zeros to be -2 and +3, so we know that (x +2) and (x -3) are factors. The green curve is P(x) with those factors divided out, so is a graph of Q(x). The vertex of that graph tells us that ...

  Q(x) = (x +1.5)^2 +7.75 = x^2 +3x +10

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3 years ago
Sarah baby-sits her cousins once a week. She gets paid $10 per hour and she includes a travel fee. if she baby-sat for 5 hours a
likoan [24]
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4 years ago
Write the following expression in words x+7
Lady_Fox [76]

Answer:

The sum of 7 and x.

Step-by-step explanation:

PLS GIVE BRAINLIEST

6 0
3 years ago
F(x)=4x^3+3x-2 and g(x)=2x+2 what is the value of f(x)=g(x)?
Arlecino [84]

Answer:

x ≈ 0.916875

Step-by-step explanation:

→ Equate the expressions to each other

4x³ + 3x - 2 = 2x + 2

→ Get all the terms to one side

4x³ + x - 4

→ Solve for x

x ≈  0.916875

8 0
3 years ago
Which number is a solution of the inequality? 3x – 7 &gt; – 1 A. 0 B. 2 C. 5
Softa [21]

Answer:

C. 5

Step-by-step explanation:

3x – 7 > – 1

Add 7 to each side

3x – 7+7 > – 1+7

3x> 6

Divide each side by 3

3x/3 >6/3

x >2

X must be greater than 2


5 0
4 years ago
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