Trend Line Help

#1
I'm struggling with the problem below and really need a starting place. Can someone please explain how they knew which formula to use? How do I forecast in this scenario?

3. The following data give the sales in millions of dollars for a company for the given years:

Years Sales

2001 3.1

2002 3.6

2003 4.3

2004 4.9

2005 5.2

2006 6.1

2007 6.9

2008 7.2

a) Give the equation of the trend line for this time series. Round to 3 decimal places.

b) Interpret the intercept in the context of this problem. Move decimal appropriately in your answer.

c) Interpret the slope of sales in the context of this problem. Move decimal appropriately in your answer.

d) Forecast sales for the year 2012. Move decimal appropriately in your answer.

e) What % of the increase in sales is explained by the lineaer trend over the time series?
 
#2
Hi,

it is difficult to give you a starting point without knowing what you exactly had in school/university. Are you allowed to use statistical software? The simplest approach for (a) would be to estimate a linear regression model (e.g. based on R) with the year as predictor and the Sales as the outcome. schematically, the formula would look like this: Sales = A + B*Year + error. However, much more elaborated regression methods would be so called "AR(I)MA" models which are frequently used to model time series data.
(b) the intercept "A" tells you the sales of the company in the year "0". Since this does not make sense, you should consider the variable "Year-2000" instead, if this variable equals to zero, this represents the sales at the year 2000
 

Miner

TS Contributor
#3
Always start by plotting the data. Next, examine the plot for any trends, then for any signs of seasonality, and finally for cyclicity. Question a) implies that there is a trend, so is the trend linear (y = b0 + b1X), polynomial (y = b0 + b1X + b2X^2), exponential or S-curve? If linear (most likely in an introductory course), this is a straightforward OLS regression.
 
#4
Hello,

Thanks for responding! I am allowed to use stat software, yes. But I am still confused. I am going to work through the problem tonight and post what I have completed.