http://stat.psu.edu/~mga/401/course.info/lesson8.pdf

http://www.propharmagroup.com/blog/understanding-statistical-intervals-part-2-prediction-intervals

http://www.math.umd.edu/~slud/s430/Handouts/RegrSheet2.pdf

https://www.math.ntnu.no/~omre/TMA4240/H2006/pdf/prediction.pdf

Thank you Jochen Wilhelm for your response. I do understand that those materials are for single new observations. I would like to know if   those curves around the fitted line have a special equation. If that is the case how can it be approximated?

The regression model should tell you the confidence intervals (or standard errors, which you can use to calculate confidence intervals) for the coefficients; you can use these to draw a confidence band around the regression line.

Lesego  -

Prediction intervals require that you estimate the variance of the prediction error for each predicted y-value.  Here is an example for regression through the origin:

 https://www.researchgate.net/publication/263265199_CRE_Prediction_%27Bounds%27_and_Graphs_Example_for_Section_4_of_Properties_of_WLS_article

Whatever your regression, you need the estimated regression line (or curve, and however many regressors), and the estimated variances of the prediction errors.  Even for observed values, the y's, you also have a predicted y in each case, and that is the point on the regression line about which each prediction interval is found.

The residuals are for the y-values, and thus can be seen on a scatterplot to be measured vertically on a two dimensional graph when you have one regressor.  The predicted values fall on the regression line, and the "bands" are set vertically above and below them.

I guess your question has to do with the difference between the use of the estimated standard deviation for a univariate population, to arrive at a confidence interval about a point estimate for a given sample size, versus the use of the estimated  standard deviation of the estimated residuals in linear regression (or actually the estimated standard deviation of the estimated random factors of the estimated residuals in WLS regression), for a given sample size.  For a univariate case, you are looking at a confidence interval, but for your linear regression, you are looking at a series of vertical prediction intervals about predicted y-values.  The ends of the intervals together form those "bands." 

I hope I understood your question correctly.

Note that you may have software that will give you the needed estimates for the variances of the prediction errors. For example, in SAS PROC REG, look for the STDI, which is the square root of the estimated variance of the prediction error, which is the standard error, for an individual prediction error.  But it is important to be certain as to what your particular software is doing.

Cheers - Jim

PS  - The very top of page 5 in the following shows the 'formula' for the variance of the prediction error  (predicted y minus y) for multiple linear regression, no crossterms: 

https://www.researchgate.net/publication/261586154_Using_Prediction-Oriented_Software_for_Survey_Estimation

PSS  -   For the derivation of the prediction bands found in the first link above, see section 4, starting on page 7, in the following link, where you will note that I incorrectly used the word "confidence," when I should have used the word "prediction." 

https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys

Article Using Prediction-Oriented Software for Survey Estimation

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

Article Properties of Weighted Least Squares Regression for Cutoff S...

Lesego - 

Note that in the first link Jochen provides, there is a "1" under a square root sign, shown at the end of that presentation, which is the difference between a confidence interval for a mean and a prediction interval for a point prediction.  That is due to an additional term that is part of the variance of the prediction error which is referred to in "statistical learning," when you have the "correct" (but unknowable) model, as the noise or irreducible error, or similar term, sigma .... the standard deviation of the residuals in that OLS example.  In reality here, it is just an estimate for sigma, and is inflated by the unknown bias from not having the 'exactly correct' model.  The estimated sigma also figures into the other two parts, for the model. (In variance-bias tradeoff literature, there is yet another term required for bias.)

Jim

@James R Knaub, Thank you very much for your thorough answers. You mentioned that " The ends of the intervals together form those "bands"; my question now is can those bands be characterized using equation; those are curves if I am not mistaken

Lesego, it is all in the links I posted. You just have to read and put the pieces together.

Here is another link I found that seems to be particularily simple and easy to follow:

http://www2.stat.duke.edu/~tjl13/s101/slides/unit6lec3H.pdf

and there is even a youtube-video with explanations:

https://www.youtube.com/watch?feature=player_embedded&v=qVCQi0KPR0s

Lesego, if you say what software you are using, people may be able to give more specific advice about how to compute the desired interval.  HTH.

Lesego - I did provide equations for those curves for regression through the origin, and the procedure so you can do it in other cases. -Jim