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Hi Folks, I am really getting confused here, I dont know how to solve these problems based on the deseasonalized demands (yd) (i.e., without seasonal effect) by using simple linear regression formula to derive the sales forecast: Y = a + b X . Please help me to find the slope value (b) and Y- intercept value (a) and the forcast for quater 15, i.e., the III quater of year 4, and the forcast for quater 20 of the above problem . I would really apprecite it. Please please show me the work and how you came to the answers? I dont need directly answers without showing me the calcualtions and the method how you got to those answers please. I want to learn and understand the materials.
Expert Answer
Y = a + b.x
( Sum of all y values)x (Sum of all x^2 values) – (sum of all x values)x(sum of all xy values)
A = ——————————————————————————————————————-
n x ( Sum of all x^2 values) – ( sum of x values)^2
n x (sum of all values which are product of x.y) – ( sum of x values)x(sum of y values)
B = ———————————————————————————————————————-
n x ( Sum of all x^2 values) – ( sum of x values)^2
Here,
A = Y intercept value
B = Slope Value
N = number of data = 12
Sum of x values = 78
Sum of y values ( deseasonalized demand) = 33350.1
Sum of all values which are product of x.y = 265706.9
Sum of all x^2 values = 650
Therefore ,
33350.1 x 650 – 78 x 265706.9 21677565 – 20725138.2 952426.8
A= ————————————— = —————————— = ————– = 555.02
12 x 650 – 78×78 7800 – 6084 1716
12 X 265706.9 – 78 X 33350.1 3188482.8 – 2601307.8 587175
B = ———————————– = ————————— = ————- = 342.17
12 X 650 – 78 X 78 7800 – 6084 1716
( OR 342.2 ROUNDED TO ONE DECIMAL POINT)
Therefore Linear regression Equation is :
Y = 555.02 + 342.17.X
Y = Forecast value for sales
X = Quarter number
Thus in order to find out sales value for quarter 16, we need to find out value of Y for X = 15
Accordingly,
Y = 555.02 + 342.17 x 15 = 555.02 + 5132.55 = 5687.57 ( 5688 rounded to nearest whole number)
Note : Value of Y 555.02 is nearest to value 554.9 ( which is one of the options in answer to question 7). Therefore answer to question 7 will be “554.9”
Similarly Forecast for quarter 20 will be:
Y = 555.02 + 342.17 X 20 = 555.02 + 6843.4 = 7398.42
Therefore answer as follows:
| NEW SLOPE VALUE B FOR ABOVE PROBLEM = 342.2 |
| Y INTERCEPT VALUE A FOR THE ABOVE PROBLEM = 554.9 |
| FORECAST FOR QUARTER 15 FOR THE ABOVE PROBLEM = 5688 |
| FORECAST FOR QUARTER 20 FOR THE ABOVE PROBLEM = 7398.42 |
