Question

The following are sales revenues for a large utility company for years 1 through 11. Forecast revenue for years 12 through 15. Because we are forecasting four years into the future, you will need to use linear regression as your forecasting method. (Enter your answers in millions.)

YEAR	REVENUE (MILLIONS)
1	$	4,873.2
2		5,070.1
3		5,522.8
4		5,720.8
5		5,507.2
6		5,193.6
7	$	5,087.1
8		5,114.4
9		5,554.4
10		5,737.0
11		5,858.8

Period: Forecast:

12

13

14

15

16

Answer 1

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	4873.2	1	4873.2	4873.2	1
2	5070.1	2	5070.1	10140.2	4
3	5522.8	3	5522.8	16568.4	9
4	5720.8	4	5720.8	22883.2	16
5	5507.2	5	5507.2	27536	25
6	5193.6	6	5193.6	31161.6	36
7	5087.1	7	5087.1	35609.7	49
8	5114.4	8	5114.4	40915.2	64
9	5554.4	9	5554.4	49989.6	81
10	5737	10	5737	57370	100
11	5858.8	11	5858.8	64446.8	121
SIGMA		66	59239.4	361493.9	506

INTERCEPT = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (59239.4 * 506) - (66 * 361493.9) / ((11 * 506) - 66^2) = 5054.99

SLOPE = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((11 * 361493.9) - (66 * 59239.4) / ((11 * 506) - 66^2) = 55.07

LINE EQUATION = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 5054.99 + (55.07 * X)

FOR THE VALUE OF X = 12 FORECAST = 5054.99 + (55.07 * 12) = 5715.83

FOR THE VALUE OF X = 13 FORECAST = 5054.99 + (55.07 * 13) = 5770.9

FOR THE VALUE OF X = 14 FORECAST = 5054.99 + (55.07 * 14) = 5825.97

FOR THE VALUE OF X = 15 FORECAST = 5054.99 + (55.07 * 15) = 5881.04

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