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Alexeev081 [22]
3 years ago
9

A regression analysis was performed to determine the relationship between the costs of a product (y), the time to make the produ

ct (x 1), the number of different materials used (x2), and the amount spent on marketing the product (x 3). The estimated regression equation is ý = 83 - 2x1 + 6x 2 + 1.1X 3. What is the estimated cost if the time to make the product is 5 hours, the number of different materials used is 4, and the amount spent on marketing is $100?
a. 83
b. 185.4
c. 213
d. 205.4
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
6 0

Answer:

Correct option: (b) 185.4.

Step-by-step explanation:

The regression analysis is used to predict the value of the response variable (<em>Y</em>) based on one or more than one experimental variable(s) (<em>X</em>).

The general form of the regression equation is:

\hat y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+...+\beta_{n}x_{n}

Here,

<em>α</em> = intercept

\beta _{i} = slope coefficient, (i = 1, 2, 3, ...n)

The regression equation of costs of a product (<em>y</em>) based on the time to make the product (<em>x</em>₁), the number of different materials used (<em>x</em>₂), and the amount spent on marketing the product (<em>x</em>₃) is:

\hat y=83-2x_{1}+0.6x_{2}+1.1x_{3}

The information provided is:

<em>x</em>₁ = 5 hours

<em>x</em>₂ = 4

<em>x</em>₃ = $100

Compute the value of <em>y</em> for the given values as follows:

\hat y=83-2x_{1}+0.6x_{2}+1.1x_{3}

  =83-(2\times 5)+(0.6\times 4)+(1.1\times 100)\\=83-10+2.4+110\\=185.4

Thus, the estimated cost of a product is $185.4.

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Answer:

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Step-by-step explanation:

I suppose that we want to solve the equation:

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To solve this, we first need to isolate one of the variables in one of the equations.

Let's isolate y in the first equation:

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y = (6 + 6*x)/6

y = 6/6 + (6*x)/6

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Now we can replace this in the other equation:

6*x + 3*(1 + x) = 12

6*x + 3 + 3*x = 12

9*x + 3 = 12

9*x = 12 - 3 = 9

x = 9/9 = 1

Now that we know that x = 1, we can replace this in the equation "y = 1 + x" to find the value of y.

y = 1 + (1)  = 2

Then the solution of the system is:

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3 years ago
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8 0
3 years ago
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2 years ago
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country durin
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Year        GDP
  y           (billion $)

1985       577

1986       577+ 3.2% of 577 = 577 * 1.032

1987       577* 1.032 + 3.2% of 577 * 1.032 = 577 * (1.032)^2

1988       577 * (1.032)^3

1989       577 * (1.032)^4

....           .... => model GDP = 577 * (1.032)^ (y - 1985)

Then, for GDP = $3.4 trillion = $3400 billion =>

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Divide both sides by 577:

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Apply logarith to both sides:

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=> y - 1985 = log (5.892548) / log(1.032) = 56.3 years

=> y = 1985 + 56.3 = 2041.3

Answer: 2041


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