Hi Folks, I am really getting confused here, I dont know how to solve these problems 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 16. 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 = 33350
Sum of all values which are product of x.y = 268,200
Sum of all x^2 values = 650
Therefore ,
33350 x 650 – 78 x 268200 21677500 – 20919600 757900
A= ———————————— = —————————— = ————– = 441.66
12 x 650 – 78×78 7800 – 6084 1716
12 X 268200 – 78 X 33350 3218400 – 2601300 617100
B = ———————————– = ————————— = ————- = 359.61
12 X 650 – 78 X 78 7800 – 6084 1716
Therefore Linear regression Equation is :
Y = 441.66 + 359.61.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 = 16
Accordingly,
Y = 441.66 + 359.61 X16 = 441.66 + 5753.76 = 6195.42 ( 6195 rounded to nearest whole number)
Therefore answer as follows:
SLOPE VALUE B FOR ABOVE PROBLEM = 359.61 |
Y INTERCEPT VALUE A FOR THE ABOVE PROBLEM = 441.66 |
FORECAST FOR QUARTER 16 FOR THE ABOVE PROBLEM = 6195 |