Problem 3: Use the sales data given below to determine: Year Sales (units) Year
ID: 364696 • Letter: P
Question
Problem 3:
Use the sales data given below to determine:
Year
Sales (units)
Year
Sales (units)
1995
130
1999
169
1996
140
2000
182
1997
152
2001
194
1998
160
2002
?
(a) the least squares trend line.
(b) the predicted value for 2002 sales.
(c) the MAD.
(d) the unadjusted forecasting MSE.
Problem 4:
For the data below:
Month
Automobile
Battery Sales
Month
Automobile
Battery Sales
January
20
July
17
February
21
August
18
March
15
September
20
April
14
October
20
May
13
November
21
June
16
December
23
(a) Develop a scatter diagram.
(b) Develop a three-month moving average.
(c) Compute MAD.
Year
Sales (units)
Year
Sales (units)
1995
130
1999
169
1996
140
2000
182
1997
152
2001
194
1998
160
2002
?
Explanation / Answer
PLEASE FIND BELOW ANSWER TO PROBLEM 3 :
Let Y = A + B.t is the equation for lest square trend line
Where,
Y ( Dependent variable ) = Sales ( units )
I ( Independent variable ) = Year
A, B are constants
Placing the values of year and sales in two different columns and applying the formula LINEST ( ) , we obtain following values of A and B :
A = - 20746.64
B = 10.464
Therefore, Y = 10.464.t – 20746.64
To predict value for 2002, we put t = 2002 which gives value of Y = 202.288
PREDICTED VALUE FOR 2002 SALES = 202.288
Also to be noted that:
Absolute deviation for period t = Absolute difference in actual sales value and forecasted sales value
Sum of absolute deviation for 7 years ( 1995 to 2001 ) =
Therefore Mean Absolute Deviation ( MAD )
= Sum of Absolute Deviation / 7
= 8.632/7
= 1.233
Squared error ( SE ) for period t = ( Absolute Deviation)^2
Sum of squared Errors for 7 years ( 1995 to 2001 ) =
Therefore Mean Squared Error ( MSE )
= Sum of Squared errors / 7
= 14.22/ 7
= 2.031
MAD = 1,233
UNADJUSTED MSE =2.031
PREDICTED VALUE FOR 2002 SALES = 202.288
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