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
data.subset$Ad.Back 78
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".