# Measuring impact of advertising on retail sales

I have a dataset of retail products which contains weekly sales for 12 different items in a single category. For each item, I have three dummy variables representing different types of advertising (FrontCover,BackCover,Inside) that could be run for that item that week. The data is weekly, and seasonal for a year so I have the frequency set to 52.

I have a two part question:

1. How can I convert the advertising coefficients to % lifts when the data is seasonal?

What I can do now is subset the data for a single item, and run multiple regression using tslm() from the R forecast package and read the coefficients to determine the lift for that item. However with tslm() I also have 51 other seasonal coefficients. How can I state this as a %?

    x
(Intercept) 601.7857143
data.subset$Ad.Front 249.4285714 data.subset$Ad.Inside    243.4285714
season2 92.5
season3 113.2142857
season4 -31.71428571
season5 189.7142857
season6 -25.21428571
season7 124.5
season8 77.21428571
season9 71.71428571
season10    -25.5
season11    -161.2142857
season12    47.21428571
season13    -13
season14    -47.5
season15    9.214285714
season16    -33.5
season17    -76.5
season18    54.71428571
season19    52.71428571
season20    -90.78571429
season21    -27.28571429
season22    -124.2857143
season23    -101.2857143
season24    -23.71428571
season25    38.71428571
season26    -225.2142857
season27    -47.78571429
season28    -46
season29    27
season30    43.28571429
season31    1498.5
season32    791.7142857
season33    666.7857143
season34    1913.5
season35    1657
season36    119
season37    -205.7857143
season38    -420.2142857
season39    -152.7857143
season40    -360.2142857
season41    -123.7857143
season42    77.21428571
season43    -40.78571429
season44    -10.78571429
season45    -48.78571429
season46    73.21428571
season47    81.21428571
season48    26.21428571
season49    -1.785714286
season50    25.21428571
season51    -105.2142857
season52    -161.2142857


2. My second question is how do I extrapolate this for the entire category? If I have the above information for 12 items, how can I look at the coefficients collectively? That is, I want to say "Front page advertising has x% lift for Category A".