Deriving and using linear model equation for sales data I have problems with this question. In the first part I get the slope right which is 4.2. Then I try a point and the answer turns out to be wrong. (( the answer is s=4.2t + 84.6)).
I then figured that to get the right answer 1 should be inserted ( for example ) not 2001. Any thought on why is that? I don't get it. 
I will get B right if I inserted 10 not 2010. Still I don't get why should I do that? Is it something wrong with the question? Is it some rule? 
And for C, I always get the answer wrong! The right answer is approximately 27. Thus in 2027

 A: In the question, you are starting to count the sales in 2001, which is the first year in your data set. This is why you need to use 1 in your linear model. The numbers for the year are arbitrary (if we used the Japanese Heisei calendar, the numbers would be different, for instance), so instead we consider 2001 as the first year, that is to say year 1, and calculate accordingly. 
A: I suppose that, in your work, you wrote that
Sales = a + b Years
and that you applied this to the two data points (2001,88.8) and (2004,101.4). This gives you (as you got) b = 4.2 which is the correct slope. From this, you compute the value of "a". If you do it, you will get a = 88.8 - 2001 * 4.2 = -8315.4. This is correct but not very practicable since you will not consider year 1234 or 4567. So, as mentioned by Ben, take any arbitrary reference year. Then your model will be
Sales = a + b (Years - Reference_Year)
For rounding purposes, take as reference year 2000. In this case, your equation is
 (88.4 - 4.2) + 4.2 (Year - 2000) = 84.2 + 4.2 (Year - 2000).
If now, you want to know when the sales will be 200, then 200 = 84.2 + 4.2 (Year - 2000) which leads to (Year - 2000) = 27.57 so Year = 2027.  
Is that clearer now to you ?
