# Basic statistics help

I found out about these forums from another website they said I may be able to get some quick help here.

Quick background - I own my own business and wanting to do some statistical analysis on the effectiveness of our advertising spend on bringing in new clients to my business. I am in the medical field and did statistics and research methods at university, but this was a long time ago and I am confused reading through my old text books.

I simply want to correlate our advertising spend per month to our new clients per month and see if our increased advertising spends during certain months or quarters correlates to more new clients. I have all the data for several years with new clients for the month and exactly how much was spent on advertising for each month.

Can someone give me some help to figure this out?? Any help would be much appreciated.

• Welcome to math.stackexchange. What sort of statistical analysis are you interesting in? If you just want to determine if the increases advertisement expenditure is worthy, just look at the data, i.e., plot the data and decide. You can then obtain the correlation coefficient, if needed. – user17762 Sep 15 '13 at 0:23
• Thankyou very much for your time. Yes I just want some basic analysis of it in essence to 'prove a point'. I would want to obtain the correlation coefficient to take it one step further, rather then just looking at raw data and drawing conclusions from it. Would the Pearson's R be the right one to use? – loopydean Sep 15 '13 at 3:12
• If you have enough time you can go through some basic regression techniques and time series analysis – Abishanka Saha Sep 15 '13 at 13:07
• I have the correlation coefficient now and understand that. How exactly would I then do some basic regression and time series analysis? – loopydean Sep 15 '13 at 19:13

Since your data is time-series data, I am afraid even the simple correlation coefficient may by misleading, if it is obtained from non-stationary data. Which is not an introductory subject matter in statistics and econometrics.

Data are non-stationary if they exhibit some time trend, or more than one maybe, and not necessarily all to the same direction (upward or downwards). Time series data are non-stationary if the appear more volatile in some time interval compared to some other time interval. The bulk of statistical methods of estimation and inference are designed and are reasonably valid for stationary data. This is a technical requirement, but critical.

The solution would be to "remove" by various techniques available these "non-stationary" features of your data (if they do exist, that is), and thus transform your data to stationary, on which you could run more safely estimations and regressions. This removal could be achieved by running a regression including a time trend in the regressors. Or by first-differencing your data. Or considering a model where errors are assumed heteroskedastic. (I am throwing in terminology so that you have some keywords to search).

A standard reference on time-series analysis, that discusses also matters of non-stationarity is J.D. Hamilton's "Time Series Analysis". You said you have your own business and spending real funds -you wouldn't want, I presume, to let a misapplication of science make you waste these usually scarce funds.