# How can I remove the effect of one independent variable so I can standardize and compare the values of my dependent variable?

I have a table of television viewership data with each row being one series and the columns being various data about that series, e.g. name, time the series is on TV, length of an episode, how many households watched the show, and the average percent of the show that was watched among people who did watch it.

There is a clear relationship between episode length and average percent views, with longer shows having lower average percent views and shorter shows having higher. I have included a screenshot of these plotted against each other.

My question is, I want to compare average percent viewed between episodes without the effect of episode length to create an index with 1 being average and values above or below indicating better or worse to a standardized degree.

My currents ideas are either...

1) Group series by episode time, find the average "average percent watched" for each group and index on that.

2) Create a linear regression of average percent views and episode length and compare individual episode APV scores to that line, being higher or lower.

How should I go about this? Are either of those ideas statistically sound? Is there something else I should be doing? I am using R to work with this data, if that is relevant.

I apologize if this is too vague, I'm struggling a bit with this and it has been some time since I have worked with this kind of data.

• Stratification, idea 1, is a good place to start. The thing is episode length is correlated with other characteristics of series. The reason we do regression using multiple series characteristics is to isolate the unique effect of episode length. Before going on, the question then is: why are you trying to extract episode length from the data in the first place? – Heteroskedastic Jim Oct 23 '18 at 3:45
• The thought is that the two primary components of "percentage watched" are length of episode and viewer engagement. By moving the effect of episode length, I can compare engagement between shows of different length. Does that make sense? – Donovan192 Oct 23 '18 at 21:18
• *removing. Also, would plotting a line of "averages" and comparing differences of points with that line not be more accurate than binning and comparing to bin average? My worry with the bins is that shows with run times in between say, 30 mins and 60 mins, may get an unfairly low index depending on which bin they're in. – Donovan192 Oct 23 '18 at 21:38
• @Donovan192 do you have any variables that measure viewer engagement? If not, a simple linear regression will allow you to separate the effect of episode length from everything else, but you will not be able to see the components of „everything else“. – Candamir Oct 23 '18 at 23:00
• @candamir That's fine with me, that's what I'm aiming for! Is a linear regression appropriate here or a different type? The chart above looks a bit curved to me. And is it the residuals I'm interested in, then, to see how far a point is from the line that accounts for the effect of run time on percentage viewed? Again it's been a while since I've done regression, so I hope this isn't too vague. – Donovan192 Oct 24 '18 at 0:45

## 1 Answer

Idea nr. 2 does not achieve what you want. Simply speaking, regressing APVs on show length tells you what the impact of the latter is on the former across the entire sample - which, if I understand you correctly, is precisely what you don‘t want.

In case you have other variables in your dataset, then a multiple linear regression might help you. By regressing APVs on show length AND (as an example) the budget of the show AND (as an example) the age of the show, you will be able to isolate the effects from the latter three variables on APVs: the estimated coefficient for the budget of the show will tell you the impact of the budget on APVs while holding the other two explanatory variables constant.

You can even divide the shows into qualitative groups by creating dummy variables (e.g. a variable western that is 1 for all Western shows and 0 otherwise, etc.). Let me know if this is of interest and I can elaborate further. (In particular, don‘t forget to use cross terms when including dummy variables among your regressors.)