I suppose you mean index number as in a way to express changes through time, as in the case here.
That is a way to make comparisons and to summarize data more efficiently. Regression analyses are done to predict or estimate outcomes of a dependent variable with respect to changes in independent variables. For example, in biology laboratories regression analysis is done to predict or estimate bacterial population based on optical density.
While making indices you make a base value then calculate future values with respect to that value. In the case of regression, basically, you collect data from your independent variable (e.g. optical density) and your dependent variable (e.g. bacterial population). Then, based on these values (and depending on the method, e.g. least squares) you come up with a line (curve, or plane depending on the type of regression) that describes the relationship in the best terms. To accomplish this, you make use of parameters and predictors (e.g. optical density in the example above). Then you use that line for further estimations.
For example, after I measure optical densities of 30 bacterial samples that I know the population size of, I perform regression analysis and have a line that estimates the change in bacterial population with respect to optical density. In case I get a sample with unknown population but known optical density, I can "plug in" that optical density value to estimate how much bacterial cells I have in that new sample.
As you can see, although there may be cases where you can use index values for estimation the way they work are fundamentally different.