Question

QUESTION 38 Monthly income, in thousands of dollars (5K), at the Acme Law Firm for the six-month period from October to March is listed in the table below. month income, $K Oct 69.3 Nov 68.6 Dec 69.4 Jan 71.7 Feb 72.3 Mar 74.8 Using the data in the table, what is the naive forecast of monthly income for April (Round to two [2] decimal places.) O $74.80K 572.93K 573.55 $75.11K O 570.28K QUESTION 39 Using the data in the table for part 38, what is the simple 3-month simple moving average forecast for monthly income for April (Round to two [2] decimal places.) O 574.80K 572.93K 573.55K O $75.11K 570.28K Ya

Answer 1

Answer 38:

Naive forecast value for the current month (i.e., April) = Actual Value for the Previous Month (i.e., March)

= $ 74.80 K (Option 1)

Answer 39:

Let,

At = Actual Value for the Month 't'

Then,

Ft = Forecast value using the three months simple moving averages method = (At-1 + At-2 + At-3 ) / 4

= (74.8 + 72.3 + 71.7) / 3

= $ 72.93 K (Option 2)

Answer 40:

Let,

At-1 = Actual income for the previous month

Ft-1 = Forecast income for the previous month

α = Alpha = 0.1 (As given in the question)

Ft = Simple exponential smoothing forecast for the current month = Ft-1 + α (At-1 - Ft-1)

Note: As no specific information is mentioned in the question for the forecast value of the first month (i.e., Oct), we assume it the same as the actual value of that month = 69.3 K

Thus, we get:

At 69.3 68.6 Month Oct Nov Dec Jan Feb Mar Apr 69.4 71.7 F 69.30 69.30 69.23 69.25 69.49 69.77 70.28 72.3 74.8

Calculations:

Forecast for Month Nov = 69.30 + 0.1 ( 69.3 - 69.30 ) = 69.30 Forecast for Month Dec = 69.30 + 0.1 ( 68.6 - 69.30 ) = 69.23 Forecast for Month Jan = 69.23 + 0.1 ( 69.4 - 69.23 ) = 69.25 Forecast for Month Feb = 69.25 + 0.1 ( 71.7 69.25 ) = 69.49 Forecast for Month Mar - 69.49 + 0.1 ( 72.3 - 69.49 ) 69.49 ) = 69.77 Forecast for Month Apr = 69.77 + 0.1 ( 74.8 - 69.77 ) = 70.28

Hence, the correct answer to the given question = Option 5

Answer 41:

Step 1: Find the mean values for both the variables:

Υ 1 69.3 2 68.6 3 69.4 4 71.7 5 72.3 6 74.8 --- Σχ= 21 = 426.1

Where x = Independent Variable = No. of a particular month and y = Dependent Variable = Income ($ K)

x Mean x = n 21 6 = 3.5 Σν Mean y = n 426.1 6 = 71.0167

Step 2: Find the three columns as mentioned below:

y x2 xy 1 69.3 1 4802.49 69.3 2 68.6 4 4705.96 137.2 3 69.4 9 4816.36 208.2 4 71.7 16 5140.89 286.8 5 72.3 25 5227.29 361.5 6 74.8 36 5595.04 448.8 Σχ= 21 Σν ν= 426.1 Σ? = 91 Σv2 = 30288.03 Σ» = 1511.8

Where,

xy = x * y

x2 = x * x

y2 = y * y

Step 3: Find the value of byx:

ηΣχy - (Σx) Σy) byx = ηΣ? - (Σκ)? 6. 1511.8 - 21 - 426.1 6. 91 - (21)? 9070.8 - 8948.1 546 - 441 122.7 105 = 1.1686

Step 4: Find the linear trend equation:

Regression Line y on x y - y = byx (x - 1) y - 71.0167 = 1.1686(x - 3.5) y - 71.0167 = 1.1686x - 4.09 y = 1.1686x - 4.09 + 71.0167 y = 1.1686x + 66.9267

Step 5:

Now, take x = 7 in the linear trend equation as obtained in the previous step:

∴ y = 1.1686 (7) + 66.9267

= $ 75.11 K (Rounded to 2 decimal places) (Option 4)

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