Question-3 The following data represent the GNP of a country in constant 1960 pr
ID: 355058 • Letter: Q
Question
Question-3 The following data represent the GNP of a country in constant 1960 prices for the years 1950 1964 a. Use trend estimation method to forecast the GNP values for the next two years. (10 pts) b. What is the growth rate of this country's GNP over this period? (5 pts) Use the trend equation to calculate forecasts from period 1 to period 15. How accurate would these forecasts have been? Calculate Mean Absolute Deviation. Is there any bias to these forecasts? (10 pts) c. GNP Date Period (t) values 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 50.6 53.6 55.3 56.8 59.3 62.4 66.0 69.3 71.2 73.4 78.6 82.8 88.5 93.6 99.8 6 9 10 12 13 14. 15Explanation / Answer
Answer to question a:
Let the Linear regression equation to be used for trend estimation purpose is :
Y = A + B.T
Y ( dependent variable ) = GNP values
T ( independent variable ) = Period ( t)
A, B = Constants
We place all the values of Y and t in 2 adjacent columns in excel and apply the formula LINEST ( ) to arrive at values of A and B . Accordingly required values are :
A= 43.904 ( rounded to 3 decimal places )
B = 3.355 ( rounded to 3 decimal places )
Y = 43.904 + 3.355.t
To derive GNP values for next 2 years , we have to put t= 16 and t= 17
For t = 16:
Y = 43.904 + 3.355X16 = 43.904 + 53.68 = 97.584 ( 97.58 rounded to 2 decimal places )
For t = 17 :
Y = 43.904 + 3.355 x 17 = 43.904 + 57.035 = 100.939 ( 100.94 rounded to 2 decimal places )
GNP VALUES FOR NEXT TWO YEARS ARE 97.58 AND 100.94
Answer to question b :
Growth of GNP over period 1 to 15 will be = 99.8/50.6 = 1.972
Assuming , compounded growth rate over 15 years, annual growth rate = ( ( 1.972)^(1/15) - 1) x 100 = ( 1.0463 – 1 ) x 100 = 4.63%
GROWTH RATE OF COUNTRY’S GNP OVER THIS PERIOD = 4.63 %
Answer to question c :
Following may be noted :
Absolute deviation ( AD ) for period t = Absolute difference between values GNP =- Actual and GNP – Forecast
Bias for period t = GNP-Actual – GNP-forecast
Please refer below table. The forecasted values of GNP have been calculated as per linear regression equation established in #a . Absolute deviation and Bias for each period have been calculated accordingly as per above formula :
PERIOD
GNP- actual
GNP -Forecast
Absolute deviation ( AD)
Bias
1
50.6
47.26
3.341
3.34
2
53.6
50.61
2.986
2.99
3
55.3
53.97
1.331
1.33
4
56.8
57.32
0.524
-0.52
5
59.3
60.68
1.379
-1.38
6
62.4
64.03
1.634
-1.63
7
66
67.39
1.389
-1.39
8
69.3
70.74
1.444
-1.44
9
71.2
74.10
2.899
-2.90
10
73.4
77.45
4.054
-4.05
11
78.6
80.81
2.209
-2.21
12
82.8
84.16
1.364
-1.36
13
88.5
87.52
0.981
0.98
14
93.6
90.87
2.726
2.73
15
99.8
94.23
5.571
5.57
SUM =
33.832
0.04
Accordingly ,
Mean absolute Deviation = 33.832 / 15 as number of observations = 2.255
Bias = 0.04
GNP VALUES FOR NEXT TWO YEARS ARE 97.58 AND 100.94
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