prediction/confident interval

Hi all

I have a set of observed data with three columns, year, x and y. x is avaliable from 1980 to 2010. y is avaliable from 1980 to 1990. My aim is to predict y for 2010.

I have used two methods. The first method is to build simple linear regression using 1980 to 1990 x and y data, and then estimate y for 2010 using the 2010 x value. As x and y is highly correlated and residual plot looks ok, I think this method is ok.

The problem is on the 2nd method. Firstly, I find the changes of x and y from one year to next. Say d_{x,81} is the x value at year 1981 minus the x value at year 1980. Secondly, I use these differences/changes to fit a simple linear regression. I found that the relationship between d_x and d_y is still very strong for 1980 to 1990. The intercept is not statistically significant but the slope is strongly significant. Thirdly, to estimate y for 2010, I added the observed y value in 1990 and the estimated d_{y91}. Then I used the estimated y in 1991 and the estimated d_{y92} to create the estimated y for 1992. I continue this until 2010.

Results from method one and two are similar.

I would like to know

(1) is the second method correct to estimate y for 2010?

(2) how do I calculate the confident interval for the estimated y for 2010 for the second method? The estimated y at 2010 is a sum of observed y at 1990 and all estimated d_{y} from 1991 to 2010

Any advice?

Re: prediction/confident interval

Hey aviccs.

It sounds like you are looking at a population prediction model versus a point prediction model. Both of these have very specific formulae in the simple linear regression.

Do you have a table of formulae for population and prediction model calculations for the mean and variances? (In graduate school for statistics, you have dozens and dozens of formulae per subject making it quite difficult to not only memorize, but also derive)

Re: prediction/confident interval

Hi, I don't know about population predictiom model and point prediction model and I don't have a table of formula to remember at uni.

Here, I would like to find out the prediction interval for mean for method 2. I know how to get prediction interval for mean for method 1.