Answered! Hi Folks, I am really getting confused here, I dont know how to solve these problems by using simple linear…

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. The following table shows a firms sales for a product line during the 12 quarters of the past three years. x represents the quarter number and y represents the sales. The related data for the computation of linear regression model is also given (1) (2) (3) (4) 600 600 1,550 3.100 1.500 4,500 6,000 1,500 16 2,400 12,000 25 18,600 3,100 36 2,600 18,200 49 23,200 2900 64 34,200 3,800 81 4,500 100 10 45,000 121 4,000 44,000 144 12 4900 58,800 78 268,200 6500 33.350 By using the simple linear regression formula to derive the sales forecast: Y a bX

Expert Answer

 In a Linear Regression Equation , where:

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
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