Question

Lab: Trend Projection is a time-series forecasting models that examines historical data. The quantitative goal is to fit the data trend line to a series of historical data points. The qualitative goal is to use the data as a means to project medium to long-term forecast plans. In Industry, this is the method to reduce the SSE, Sum of Squares Errors.

Given the following data, create a Trend Projection with Least Squares Analysis. Compute the slop and intercept of the line. Use the Slope and Intercept data to project demand for 2018. Hint: You need to change the Data to reflect the more recent years:

Boston Data Servers Inc.: Demand Forecast

Forecast Year	Data Server Demand
2011	91
2012	101
2013	85
2014	99
2015	147
2016	180
2017	137

5. To evaluate the model, we compare the historical demand and the trend line. Please comment on your personal findings.

Answer 1

PERIOD	DEMAND	X	Y	XY	X^2
1	91	1	91	91	1
2	101	2	101	202	4
3	85	3	85	255	9
4	99	4	99	396	16
5	147	5	147	735	25
6	180	6	180	1080	36
7	137	7	137	959	49
SIGMA		28	840	3718	140

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

INTERCEPT = (840 * 140) - (28 * 3718) / ((7 * 140) - 28^2) = 68.86

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

SLOPE = ((7 * 3718) - (28 * 840) / ((7 * 140) - 28^2) = 12.79

EQUATION

Y = INTERCEPT + SLOPE(X)

Y = 68.86 + (12.79 * (X))

FOR X = 8 FORECAST 2018 = 68.86 + (12.79 * 8) = 171.18

2. WITH THE SLOPE VALUE, WE CAN SAY THAT THE SERVER DEMAND INCREASES BY 12.79 PER YEAR.