# Regression Relationship Between Fraction and Whole Number

I am trying to determine the best regression model to use to determine if there is a relationship between clicks (independent variable) (represented as a whole number) and sql % (sql/sal)(represented as fraction)(dependent variable).

Can any explanation of this data be valid if I were to run a linear regression on these two metrics (clicks and sql %)?

As I pointed out, sql % is the output of dividing sql/sal. Both sql and sal are represented in my table. Would using either metric in the regression act as a substitute for the dependent variable in the original regression I'm trying to run (clicks,sql %)?

I currently ran a linear regression on clicks and sql % and there is a R-Square of 0.018 which makes sense when looking at the plotted data points and clearly seeing that there is no linear fit.

Data:

date    sals    sql %   sqls    clicks
9/1/17  31      0.32    10      18
9/2/17  9       0.11    1       17
9/3/17  10      0       0       11
9/4/17  15      0       0       11
9/5/17  41      0.41    17      7


Since your variables $$sqls$$ and $$sals$$ both seem to be counts you could choose Poisson regression. The disadvantage of linear modelling of the $$sql %$$ is that it is bounded at zero and unity whereas linear regression gives predictions potentially outside that range. If you use Poisson regression you model $$\log(sqls)$$ as a function of $$clicks$$ using $$\log(sals)$$ as an offset. This gives the multiplicative effect of $$clicks$$ on $$sqls$$ by exponentiating the coefficient. There are many posts on this site going into more detail about Poisson regression. It is widely available in statistical software like Stata or R.