Question

Problem 4.16 E ques Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). Year Sales 460 510 520 570 575 a) Forecasted sales for year 6 using the trend projection (linear regression) method are sales (round your response to one decimal place). Enter your answer in the answer box and then click Check Answer parts remaining Clear A che certos

Answer 1

1. 614.0

PERIOD	DEMAND	X	Y	XY	X^2
1	460	1	460	460	1
2	510	2	510	1020	4
3	520	3	520	1560	9
4	570	4	570	2280	16
5	575	5	575	2875	25

SIGMA VALUES

X = 15

Y = 2635

XY = 8195

X^2 = 55

In order to find the forecast value, we first need to calculate the intercept and the slope value of the given data:

To calculate it manually, we will use the following formula:

INTERCEPT(B0) = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (2635 * 55) - (15 * 8195) / ((5 * 55) - 15^2) = 440

SLOPE(B1) = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((5 * 8195) - (15 * 2635) / ((5 * 55) - 15^2) = 29

EQUATION

FORECAST = INTERCEPT + SLOPE(PERIOD)

FORECAST= 440 + (29 * PERIOD)

FORECAST

PERIOD	DEMAND	FORECAST
1	460	469
2	510	498
3	520	527
4	570	556
5	575	585
6		614