I would like to know if the coefficient of an independent variable is still relevant if the R-squared is low (assuming the p-value for the independent variable is less than 0.05).
For example, assume I have ice cream sales as my dependent variable and GDP as my independent variable. If I run a regression analysis the R-squared will be very low (say 0.001), because clearly there are other factors that will explain ice cream sales, but the GDP p value is significant (i.e. <0.05) and the coefficient is 0.0001. Can I still conclude from this regression that for every $1 increase in GDP, ice cream sales will increase by 0.0001?
For the avoidance of doubt, I am not interested in predicting future ice cream sales I just want to know if there is a relationship between ice cream sales and gdp and to what extent.
Many thanks in advance.