# Is this linear model a good fit?

Is this simple linear regression a good fit? Are there any transformations that would improve it?

The data is discrete interval count vs discrete interval count (the count of steps walked per time)

• Variables: time spend walking ~ steps walked
• Dependent: time spend walking
• Explanatory: steps walked

without log transform

with log transform on explanatory

with log transform on dependent

with log transform on dependent and explanatory

• What are your data? What are your variables? How many explanatory variables are there? What are you hoping to accomplish with this model? Etc. Sep 14 at 0:55
• QQ plot shows normality assumption may be violated (a bit heavy in the tails), and Residual vs Fitted plot gives some evidence that linearity assumption may be violated. A log transformation on the explanatory may improve your linearity, and a log transformation on the dependent may improve normality. My advice is to start with the linearity as that may solve the normality.
– jros
Sep 14 at 15:00
• @jros added those log transforms. It appears linearity was fixed by a log transform on both. Log transform on both does seem to fatten the tails, I am not sure of the implications of this. Sep 15 at 6:27
• You've missed out the most basic graph of all: a scatter plot of time versus steps with fitted line superimposed In this example, I'd be concerned with whether a fitted function should respect the origin 0 steps, 0 time. Sep 15 at 9:10
• This should be about the substance as well as the statistics. On the face of it time and steps should be proportional as a good first approximation. But people get tired etc. and so I would expect some curvature. And there is nothing here about whether your data are heterogeneous because of mixing different people and/or different conditions. Sep 15 at 9:34