I'm working on a paper about a bestseller book's list that shows a TOP20 book every month.
My problem is to prove that the this list is representative of the population of books sold each year.
From 2011-2020 I have: the number of book solds (it is an official estimative) and the amount of books sold on the TOP20 rank.
Using a simple regression total sold x list sold I can get an adjusted Rˆ2 of 0.92 and a p-value of 6.035e-06...
But because my sample is so small, it doesn't make sense to me... Is there a better way to prove the relationship between the total sold and the number from the bestlist?
Whaner -
Are you saying that you let predictor x be the number of books sold for a selected TOP20 book in a given month, and y is the corresponding total number of books sold that year, so that you have 120 (x,y) data points, which have only 10 unique y-values? Or perhaps you combine the 12 x-values corresponding to each y-value, and have 10 data points? You said "small sample" so perhaps that is it.
Hmmm. Well, if you are talking about count data, then the first thing that would come to mind for many would be a poisson regression. I don't know. But this seems different.
If you have a time series, then we could have strong autocorrelation from one period to the next. But this seems different.
If you can consider this as one population, where no omitted variable would have helped discern one year from another ... say GDP for each year may not help because it impacts both x and y ... and x and y-values are plotted regardless of time period, then I guess a simple (x,y) plot of those 10 years may tell you that you can use TOP20 number of books sold to indicate ("predict") total number of books sold in a year, before you see the "official estimate." And it might be very accurate. I expect heteroscedasticity based on the size of predicted y. (See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as determined by Ken Brewer, and https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity.)
Is that what you are doing?
Perhaps you could show a scatterplot of your data so we can better see what you are doing, if that's OK.
From such a scatterplot, and perhaps a "graphical residual analysis" scatterplot with estimated residuals on the y-axis and predicted y on the x-axis, we might see if a quadratic linear regression fits, or a ratio estimator, or what, and how well, and perhaps an indication of heteroscedasticity. Also, new data might be used for a simplified "cross-validation," to avoid overfitting to your particular sample. However, the small sample size is a limitation, unless the relationship is very strong, and it sounds like it might be.
Cheers - Jim
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