For shape of association, I used a generalized additive model for a smooth time series plot. Let's say for cardiovascular disease and temperature. I got a W like shape of graph which is non-linear of course.
For the regression model
Again, we made another plot in the regression model using the smooth term for one of the covariates for example temperature. This smooth plot showed a linear graph with a line not any U V or W shape.
My question is what plot we can assume to be representing a true relationship?
My regression model graph for temperature is showing a linear relationship. so does that mean it satisfies the condition of the regression model?
the "true" relationship is shown in a graph of DV against against the IVs, not by a plot of a model. This is called a response surface analysis. Then the regression prediction equation (called a response surface) is plotted.Notice by the way the plots are made using all IVs at the same time NOT one at a time. How well the model works is measured by the distances between the 2 surfaces, the residuals. BTW the linear assumption in OLS regression means linear in the regression coefficients, not the x's. For full details, See Chapter 11 of https://www.google.com/search?q=Montgomery+Design+of+Experiments&rlz=1C1CHBF_enUS874US874&oq=Montgomery+Design+of+Experiments&aqs=chrome..69i57.18614j0j1&sourceid=chrome&ie=UTF-8for some examples. Best, David Booth To get the plots in R, see:
https://www.google.com/search?q=plotting+response+surfaces+in+R&rlz=1C1CHBF_enUS874US874&oq=plotting+response+surfaces+in+R&aqs=chrome..69i57.15791j0j1&sourceid=chrome&ie=UTF-8
Best, D. Booth
Dear Hasan Bin Sohail
The shape of association doesn't depend on your model. Actually, the shape of association depends on the nature of your data. Every model with bigger coefficient of determination has better fit to your data which is a suitable tool for making decision. Meanwhile satisfying regression assumptions are very important to make a correct comparison.
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