Question

1. Following table shows the monthly sales of cars at a dealership:

Month	Number of cars Sold
1	79
2	79
3	86
4	93
5	101
6	107
7	102
8

Answer the following questions based on the data given above. Show your calculations.

1. What is the Trend equation for the above data? (25 Points)

ANS:

2. What is the expected sales for the 8^th month based on the Trend method? (10 Points)

ANS:

3. How much error is there in this forecasting method using MAD?                 (15 Points)

ANS:

Answer 1

The linear regression equation is also called trend line

1	79
2	79
3	86
4	93
5	101
6	107
7	102
28	647

Sum of X = 28
Sum of Y = 647
Mean X = 4
Mean Y = 92.4286
Sum of squares (A) = 28 ( Sum of squares calculated in worksheet at the down)
Sum of products (B = 140 ( Sum of producs calculated in worksheet at the down)

Regression Equation = y=mx+c

b = B/A = 140/28 = 5

a = M_Y - bM_X = 92.43 - (5*4) = 72.42857

y= 5x + 72.42857

y= 5x + 72.42857

Annexure : Calculations

X-X1	(x-x1)* (x-x1)	Y-Y1	(x-x1) *( y-y1)
-3	9	-13.4286	40.2857
-2	4	-13.4286	26.8571
-1	1	-6.4286	6.4286
0	0	0.5714	0
1	1	8.5714	8.5714
2	4	14.5714	29.1429
3	9	9.5714	28.7143
		-0.0002
	28		140

Answer 2

X=8

y= 5x + 72.42857

112.428

Answer 3

Population size:7
Mean= 92.428571428571

Mean Absolute Deviation (MAD): 9.5102040816327