Say I have a years worth of data on donut sales, and I use linear regression with variables such as daily occupancy, daily weather etc. because there is a good correlation between each variable and donut sales. As I am developing this model I find better variables and get a more accurate representation, which is noted by the increased adjusted R-squared value.
Would me improving this model be the best way to improve the forecast for projected sales? I want to very accurately predict my sales over the next year.
I thought the method was a good way to forecast, but I am starting to have doubts because although I am putting much time trying to essentially improve the fit of old data, since forecasting is more random am I just wasting time?
Are there any tips for better forecasting techniques other than linear regression? Thanks
Improving a model's accuracy does not necessarily improve the model's prediction.
Over-fitting a model is one of the biggest mistakes many people make when creating models and it is also one of the hardest things to avoid.
As an example if we wanted to do a linear regression on 10 data points we could take 10 explanatory variables and get an $R^2$ value of 1. However it is also possible that we could explain 99% of the data using only 9 explanatory variables.
There are multiple ways to avoid over-fitting your data. You can and should use some of these techniques in linear regression; cross-validation and regularization.
There are also other techniques such as PCA if you are worried about multicolinearity.
Ridge regression also helps in these cases and is very useful for predictive models but no so much for inference.
In any case you can use Akaike information criterion and Bayesian information criterion to help you determine an appropriate number of explanatory variables.