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3 years ago

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The forecast for week 13 is 747. (Enter your response rounded to the nearest whole number.) Specify the mean absolute deviatio

n (MAD) and mean absolute percent error (MAPE). (Enter your responses rounded to two decimal places.)

1 answer:

son4ous [18]3 years ago

7 0

Answer:

a) MAD without the forecast = 43.71

MAD with the forecast = 45.59

b) MAPE = 0.097 = 9.7%

Step-by-step explanation:

642 602 656 747 663 618 731 726 679 737 664 740

Mean Absolute deviation is given as

MAD = [Σ|x - μ|]/N

We first calculate the mean

Mean = Σx/N

Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12

Mean = (8205/12) = 683.75

absolute deviations from the mean

|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|

Absolute deviations from the mean

41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25

= 524.5

MAD = [Σ|x - μ|]/N

MAD = (524.5/12)

MAD = 43.71

If we include the forecast on the 13th week

642 602 656 747 663 618 731 726 679 737 664 740 747

Mean = (8205+747)/13

Mean = 688.62

absolute deviations from the mean

|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|

Absolute deviations from the mean

= 46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38

= 592.62

MAD = (592.62/13)

MAD = 45.59.

b) MAPE is used to check forecast errors

MAPE = (1/N) Σ [|x-f|/x]

where N = Sample size = 12

x = each variable

f = the forecasted value = 747

x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740

Σ [|x-f|/x]

= 0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009

Σ [|x-f|/x] = 1.164

MAPE = (1.164/12)

MAPE = 0.097 = 9.7%

Hope this Helps!!!

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Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

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The range is the interval ----> [0,20]

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V is the volume in gallons

we know that

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so

For V=0

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The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$10x^{2} -17x+3=0$

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so

$10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})$

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we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

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$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(10)=-(10)^{2}+20(10)+100=200$

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$b=20$

Substitute

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For f(x)=0

$4x^{2} -1=0$

Solve for x

$4x^{2}=1$

$x^{2}=\frac{1}{4}$

take square root both sides

$x=(+/-)\frac{1}{2}$

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In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

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therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

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The equation of a vertical parabola in vertex form is equal to

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take the point (2,3) and substitute in the quadratic equation to solve for a

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$3=a(2-4)^2-1$

$3=4a-1$

$4a=4$

$a=1$

The quadratic equation is

$y=(x-4)^2-1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

so

For y=0

$(x-4)^2-1=0$

Solve for x

$(x-4)^2=1$

take square root both sides

$(x-4)=(+/-)1$

$x=4(+/-)1$

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The x-intercepts are the points (3,0) and (5,0)

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