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Please confirm if we can make use of Normal Q-Q Plot to determine for normality of continuous variables, when the independent var is plotted against the dependent var, prior to conducting a regression analysis. If a straight line is obtained as attached, does this confirm that the sample data is normally distributed.

To double check the above, I conducted a normality test using Shapiro-Wilk Test. I obtained p<0.05, implying they were not normal.

How should I proceed? enter image description here

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    $\begingroup$ The only thing ever assumed normal in regression is the reiduals of the model. Not the independent variables, and not the dependent variable. $\endgroup$ – Matthew Drury Sep 4 '17 at 14:46
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    $\begingroup$ Your observed values are clearly discrete at 2(1)8 and so not continuous at all; hence why you expect it to be normally distributed is unclear. That said, the approximation looks about as good as is likely -- yet it is also irrelevant, as regression makes no assumptions about marginal distributions. $\endgroup$ – Nick Cox Sep 4 '17 at 14:47
  • $\begingroup$ There is also an implication that linear regression may not be a good choice for you. Could the response ever be zero or negative? $\endgroup$ – Nick Cox Sep 4 '17 at 14:49
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    $\begingroup$ On the contrary, @Matthew Drury's comment implies that is a fair thing to do. $\endgroup$ – Nick Cox Sep 4 '17 at 15:56
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    $\begingroup$ Voting to close as unclear. OP is asking what to do next, but this plot alone cannot tell us. $\endgroup$ – Nick Cox Sep 5 '17 at 6:22