how do you do regression analysis on advertising impact i have data that includes clicks, spend, signups and date. 
for 1 week, i turn off advertising spend to see what clicks and signups are.
the next week, i turn advertising back on to see what the new clicks or signups are.
Given this 2 sets of data, how can i run regression analysis to see how impactful advertising is?
Should i run a regression analysis on y=(signups_week2-signups_week1) and x=(spend_week2-spend_week1) ?
Thanks,
J 
 A: You want to perform an intervention analysis, which is a subset of time series analysis. To perform this analysis you will do 2 separate regressions, one to measure the impact of advertising on clicks and the second to measure the impact of advertising on signups.  
To accomplish this you regress the dependent variable (clicks or signups) for each day on the independent variable which is a dummy variable (or indicator function) which takes the value of 1 if the particular data points was collected with advertising and 0 if the particular dependent data point was collected during the period without advertising.  
The beta coefficient estimated from the regression would reflect the estimate decrease in average clicks or signups from foregoing advertising.  Further the p-value for the beta estimate can be used to determine if there is a statistically significant decline in clicks/signups as a result of excluding advertising, i.e., if the average number of clicks/signups during the non-advertising period is statistically significantly less than during the period with advertising.
A caveat would be that the model described above includes no other exogenous variables besides the existence of advertising.  If any other non-included variables also changed during this period, the beta estimate produced by this regression model would be biased by the marginal impact of the excluded exogenous variables.
A: From the exposition of your problem, I would say that you want to consider a regression on all independent variables while testing the impact of turning "on" and "off" "advertising" (I have to note this is not exactly what you wrote, but it is what I perceived as your intent and will assume the dependent variable is "signups" and all the others are taken as independent ones).
You should do your regression analysis considering as an interaction variable what is called a moderator. The moderator is in this case the simplest one: a dummy variable that is toggled "on" or "off" - i.e. takes value 0 or 1 - for the datapoints associated to having advertisement or not. If you assume that advertisement introduces an offset you will do a regression of the type
\begin{equation}
Y_j = int. + \beta_i X_{i,j} + M_{j}. \alpha.
\end{equation}
In which $X_{i,j}$ and $Y_j$ are your independent and dependent variables; I used the subscript $j$ to denote different observations and $i$ different types of independent variables, respectively. $\beta_i$ the regression coefficients associated to each variable $X_i$ and intercept the intercept term (these are the terms present in a regular regression); $M_j$ represents our dummy variable that takes as value 0 or 1 depending if the observation $j$ in question has its dummy variable turned on or off. I considered the simplest case in which the moderator is associated to a constant $\alpha$ which will be estimated by this method. You can consider instead of $\alpha$ a constant times a term that can depend on the $X_i$, a linear combination of these, etc. However, if you chose to do so, consider to re-center your data before regression to reduce cross-talk between regression terms and allow for an easier interpretation of the results.
I hope I did not present things as unnecessarily complicated for someone who is not acquainted with the subject. As a further reference on the subject I would suggest this book chapter on moderation.
