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I have run simple regression analysis for my work (it is about prediction of body fat using medical images; and I have very low sample size - only 21 samples) and also running the test for regression assumption. The best model (based on lowest RMSE value) show linear appearance in both regression plot and also Q-Q plot of residuals. But the residual and fitted value plot did not show a good scatter pattern throughout the graph -- like an image. The residuals VS fitted value plot

-- Does this plot indicate Heteroscedasity? Could I then test for hetero/homoscedasity using Koenker-Basset test? or Should I do transformation of the data -- I have tried already by taking log but the result is worsen (no model pass the Q-Q plot of residuals)

PS. The data has high biological variation and it is not an outlier.

Please suggest me, I am very new in research field. Thanky you very much in advance

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  • $\begingroup$ Welcome to CV.,// Are these data on humans? If so, it strikes me that a lot of the fitted values for body fat % are very low. $\endgroup$ Commented Apr 15 at 10:34
  • $\begingroup$ It is an animal body - X is %fat by CT scan / Y is %fat in carcass. Almost of data collected in normal and slim body sizem there are only three having a lot of fat. $\endgroup$ Commented Apr 15 at 10:52

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There's nothing wrong with this particular plot. At low fitted values you have far more residuals than at higher fitted values, some are smaller, some are larger, so there is no indication that there is systematically lower or higher variance in any place. Your number of observations is low for diagnosing this though, particularly at high fitted values.

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  • $\begingroup$ Thank you for your comment @Christian Henning. $\endgroup$ Commented Apr 15 at 10:54

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