You write
My data was not normally distributed so i have to transform data
This is not correct. OLS regression makes no assumptions about the distribution of the data, other than the DV having to be continuous. It makes assumptions about the errors, which we examine by looking at residuals.
I did log transformation and inverse transformation.
Do either of these make sense in your context? The inverse of particulate matter per parts of air is parts of air per particulate matter. Does that make sense to use? The log of a ratio is the log of the numerator minus the log of the denominator. That doesn't seem sensible to me, but I am no expert in this field.
Instead of changing your data to fit the model, change your model to fit the data. You could use robust regression, quantile regression, maybe a regression tree, or something else.
The Adjusted R-squared for log transformation is :0.07918 and Adjusted
R-squared for inverse transform is :0.1002.Now according to rule i
must select model with high value of Adjusted R-square
No, you don't. Data analysis is rarely a matter of rules. You need to think about your problem. As David Cox put it:
There are no routine statistical questions, only questionable
statistical routines
As for your graphs, they are very nice and they show that neither of your models is really great. You do have some extreme values of rain. I'd first check if those were errors. It might make sense to take the log of rain. This essentially changes additivity (what happens when there is 1 more cm of rain?) to multiplicativity (what happens when there is twice as much rain?) and that might be good. It would emphasize small changes at low levels of rain, which might make sense, substantively.
Or, maybe a spline or rainfall would be good.
